A DULT B AS IC S KILLS
I NSTRUCTOR T RAINING M ANUAL
T EACHING
M ATH
IN
C ONTEXT
A Tool Kit for Adult Basic
Skills Educators
Dianne B. Barber
Appalachian State University
NC Community College System
Editors: Jackie McInturff, David Thompson, and Ryan Trent
Graphic Design and Layout: Dianne Barber
Copyright
Appalachian State University exclusively grants to the North Carolina State
Board of Community Colleges, its officers and employees, and volunteers
affiliated with North Carolina community based literacy organizations acting
within the scope of their duties a royalty-free, irrevocable license to reproduce
and use the work(s) in connection with education, research, and public service
functions.
This manual may not, in whole or in part, be copied, photocopied, reproduced,
translated, or converted to any electronic or machine readable form by any
individual or organization other than the above mentioned parties without prior
written consent of the Adult Basic Skills Professional Development Project acting
in partnership with Appalachian State University.
© 2007 Adult Basic Skills Professional Development Project and
Appalachian State University.
Adult Basic Skills Professional Development Project
Appalachian State University
ASU Box 32047
Boone, NC 28608-2047
(828) 262-2269
www.abspd.appstate.edu
Table of Contents
Acknowledgments
v
Preface
vi
1
Teaching Math
Introduction
Workplace Math
Everyday Math
Collaborative Learning
Class Projects
2
Culinary Math
Introduction
Seeing is Believing Equivalencies
Common Abbreviations for Weights
and Measures
Equivalent Measures and Weights
Card Game
Standard English Equivalent Measures
and Weights
Recipes – More or Less
Finding Recipe Yields
Metric Measurements in Recipes
Scooping up the Food
The Mill
Markup for Menu Pricing
Percent Loss, Portions, and Cost
Cooking with Ratios
Finding Percents of Meat Cuts
Check, Please
Ordering Food for Large Groups
1-1
1-3
1-5
1-6
1-8
1-8
2-1
2-5
2-7
2-11
2-21
2-33
2-37
2-43
2-49
2-57
2-61
2-65
2-69
2-73
2-77
2-83
2-85
iii
3
4
5
iv
Healthcare Math
Introduction
Counting Tablets
All About Measurement
Measurement: Terms and Abbreviations
Measurements and Approximate
Equivalents
Conversion Practice & Dosage
Calculations
Projecting the Need for Nurses
Estimated Shortages for Registered
Nurses
Healthcare Occupation Growth
How Satisfied are Registered Nurses?
Heart Rate, Age, and Gender
Lung Capacity
Understanding Medicine Labels
Horticulture Math
Introduction
Landscape Geometry: Perimeter and Area
Volume of Planting Containers
Landscaping with Bricks, Blocks, and
Pavers
Soil, Mulch, and Stone
Seeding a Lawn
Hands-on Seed Mixtures
Grass Seed Mixtures
Cost of Seed Mixtures
Sod for an Instant Lawn
Insecticides and Herbicides
All About Fertilizer
Resources and Bibliography
Internet Resources
Books and Articles
Bibliography
3-1
3-5
3-7
3-13
3-17
3-23
3-31
3-39
3-43
3-47
3-51
3-55
3-59
3-63
4-1
4-5
4-7
4-17
4-25
4-29
4-37
4-43
4-47
4-53
4-59
4-63
4-69
5-1
5-3
5-10
5-15
Acknowledgments
The Adult Basic Skills Professional Development Manual Teaching Math in
Context: A Tool Kit for Adult Basic Skills Educators was made possible
through the collaboration of many individuals who generously shared
their expertise from years of teaching math in adult education. To them
we extend our heartfelt gratitude. In addition, we extend our appreciation
to the countless educators serving in instruction and training roles across
the state.
We thank the North Carolina Community College System for its financial
and professional support. We extend thanks to President Martin
Lancaster, Dr. Randy Whitfield, Ms. Katie Waters, Ms. Sillar Smith, Mr.
Robert Allen, and Ms. Lou Ann Parker for continued contributions to the
Adult Basic Skills Professional Development Project.
Without the contributions of the Adult Basic Skills directors, instructors,
and trainers this manual would be incomplete. We extend to each a hardy
“Thank You!”
A special thanks goes to Laverne Franklin who helped with ideas for
lesson plans; William Barber, who reviewed, proofread, and provided
answer keys for handouts; and David, Jackie, and Ryan who worked as a
team to edit this manual. Without the dedication and skill of these
individuals, this manual would not be possible. Thanks Team!
Dianne B. Barber, Director
Adult Basic Skills Professional Development Project
v
Preface
The purpose of this manual is to provide research-based information,
lesson plans, and activities for high-quality interactive training and math
programs in Adult Basic Skills. Much research and experience in math
and numeracy training precedes its writing. The manual’s efficacy as a
reference encourages customization to meet your needs.
Research concerning teaching math to adult learners is minimal.
However, we have integrated research in math and numeracy, actual
classroom experience with adult learners, and feedback from Adult Basic
Skills instructors in the field to write this manual.
Teaching plans are provided to enhance training, teaching, and learning.
These plans are only samples of the types of activities that can be used
for effective math instruction and training. Using this manual in
conjunction with the Adult Basic Skills Professional Development Training
Manual: Effective Training to plan training activities will give participants
firsthand experiences in how to teach math based on students’ interests
and needs. During training, discuss adapting the activities to reach a
variety of math skill levels within the multi-level classroom.
Instructors and trainers are encouraged to remain abreast of current
research in the field and to conceptualize adaptations of the information
and activities found in this manual. To assist in this endeavor we have
included a bibliography of all works cited, works consulted, and Internet
links. At the time of writing, all Website links were active. Due to the
ever-changing world of technology, Internet sites may change or be
deleted. You may wish to supplement these resources with your own.
This manual is the 13th volume in the Adult Basic Skills Professional
Development Instructor Training Manual Series. Each manual is designed
to enrich the user’s knowledge base and provide opportunities for
professional development. For a complete listing of training manuals,
videos, and CD-ROMs visit our Website at www.abspd.appstate.edu.
vi
Teaching Math
1-2
Teaching Math
Introduction
Reluctant, apprehensive, frustrated math students can become willing,
involved, and competent math students. The goal of this training manual
is to help you facilitate that change in your basic skills math students.
Adult Basic Skills students who have spent years fearing math or hating
math, and probably failing in math, can learn to succeed in math. They
can even learn to like math (Glass, 2001).
How can those things possibly happen? They can happen when students
learn that math can be fun, math can be practical, and math can work for
them. Many students are mentally challenging you, the instructor, to
show them that math has any practical value – so show them! Then the
only remaining obstacle for them will be their “knowledge” that they are
not good in math. But if you guide them to successful experiences in
math, and they continue to work for success because the math they are
doing interests them, one day they will realize they were wrong – that
they can do math (Barber, Kitchens, & Barber, 1997). Many people get
larger monetary rewards from their work than Adult Basic Skills
instructors, but very few will ever know the elation that you can
experience when you help bring about that important change in your
students.
People do math because math makes their lives better (Gal, 1993;
Withnall, 1995). Math can protect us from being cheated or shortchanged. Math skills enhance our job opportunities. Math skills make our
lives more fun. Math skills help us maintain our homes, cook, budget our
money, understand the news, and plan trips and vacations. Math helps us
understand our own health and can protect us from medication errors,
including errors that have potentially devastating consequences. Math
skills help us protect and nurture our children and care for aging family
members. Math is an important, and integral, part of life.
Many students try to treat math as an alien and incomprehensible subject
to be avoided (Curtain-Phillips, 2004). To teach math to those students,
you need to patiently, but persistently, work at discrediting that attitude.
The process should begin with demonstrating how students are already
using math in their own lives. By showing students there are math
concepts that they have already mastered, you begin the process of
verifying they can do math well.
Teaching Math
1-3
Math is important because it is so useful in our both our daily lives and
in the workplace (Glass, 2001). This training manual provides several
lesson plans that will build on everyday applications of math for many
Adult Basic Skills students. Of course, not every student will have used,
or will plan to use, every application illustrated in this manual. By
knowing your students and their backgrounds and experiences, you will
be able to choose and emphasize those exercises that will elicit interest
from the greatest number of students.
A report on how Adult Basic Skills programs should tailor instruction to
the workplace entitled Breaking Through: Helping Low-Skilled Adults
Enter and Succeed in College and Careers advises Adult Basic Skills
instructors to directly link education to economic payoffs (Liebowitz &
Taylor, 2004). Their rationale is that most students are there to enhance
their future job opportunities, with a goal of increased financial rewards.
The report argues that the most effective educational approaches tie
what students are learning to high demand occupations. Students need to
be made aware there are numerous job opportunities in a particular field,
and then shown applications of their education to that field. This training
manual includes lesson plans that address job opportunities in culinary,
healthcare, and horticulture fields as well as lesson plans that illustrate
math skills that would be required for working in those jobs and for
advancement.
Liebowitz and Taylor (2004) recommend bringing together math and
other basic skills with the ways that occupations or career paths use
those skills. To enhance this effort, it is recommended that instructors
focus on high demand occupations. Instructors can inspire student
learning by taking time to emphasize opportunities for higher wages and
increased chances for future career advancements.
Another of their recommendations that you may want to implement is to
engage employers in the teaching/learning process. If there is a large
industry in your area, representatives of that industry may be recruited
to speak to the class about their job needs and the math skills they would
like their employees to have. Tying math instruction to that type of
introduction from a large employer alleviates the need for the instructor
to convince students that the math skills being addressed have a practical
application. The same goal could be accomplished with a panel of smaller
employers.
1-4
Teaching Math
This manual has two objectives. One is to provide you with lesson plans
that can make math interesting, fun, and obviously applicable to your
training needs and/or students’ lives. The second objective is to inspire
you to seek out additional math applications in the workplaces and
everyday lives of your students, and to develop additional lesson plans
that will further encourage your students to excel at math. Please
remember to share those lesson plans with other trainers and instructors,
so we can all do a better job of teaching math as a fun, essential, and
obtainable skill.
One of the chapters in this training manual focuses on math in the
healthcare industry. One of the lesson plans in that chapter encourages
students to learn to evaluate the quantity of medication they are giving a
family member or themselves. Another lesson plan addresses career
opportunities in health professions. Some of the classroom discussions
that are suggested in these and other lesson plans focus on life and
career issues, thus demonstrating to all students how math is used as a
tool for enhancing a person’s opportunities and a person’s welfare. The
contexts for these exercises were deliberately chosen to encourage
students to use math without making math seem to be the major focus.
Students cannot doubt the value of math when it is being used in
applications that might help them make life-enhancing, or even lifesaving, decisions.
Workplace Math
Numeracy has to do not only with quantity and number but also with
dimension and shape, patterns and relationships, data and chance, and
the mathematics of change. Adult Basic Education and General Education
Diploma (GED) mathematics instruction should be less concerned with
school mathematics and more concerned with the mathematical demands
of the lived-in world: the demands that adults meet in their roles as
workers, family members, and community members. Therefore we need
to view the new term, numeracy, not as a synonym for mathematics but
as a new discipline defined as the bridge that links mathematics and the
real world (Schmitt, 2000, p. 4).
Most jobs require skills in basic arithmetic as well as the ability to apply
those skills (Dingwall, 2000, p. 4). Cashiers need to be able to make
change when the register quits working, and find discounted prices when
the discounts were not properly entered in the computer. Construction
Teaching Math
1-5
workers need measurement skills and often need to calculate quantities
or prices. Employees need to be able to predict paycheck amounts and
evaluate withholdings for taxes and social security as well as elective
withholdings.
Some people like for their bosses, personnel office workers, etc. to do all
that math for them. However, most people aspire to job advancement and
higher wages or salaries with better benefits. Math is one of the basic
skills that enhance one’s chances for promotion or finding a better job
elsewhere.
Workplace math is a good place to begin when teaching math to Adult
Basic Skills students because so many students have some mastery of
workplace math, plus the need to be competent in workplace math is
obvious to them (Zemke & Zemke, 1981). Workplace math is an area
where they have experienced success in math, and success in math builds
the confidence that is so vital to overcoming math fears and phobias.
Enhancing math skills will help students become better employees,
experience greater job satisfaction, and advance in their chosen careers
(Numeracy in Focus, 1995).
Everyday Math
Do you have enough money to buy lunch? Do you have enough money to
pay your credit card bill this month? How much interest will you save if
you pay off a loan or credit card instead of paying the minimum balance?
Will you be able to take the vacation you want this year without
borrowing money, and if you have to borrow money how much will you
need to borrow? These are just a few of the questions that relate to the
math of our personal finances. When students can relate to the questions
being asked, and can see the relevance of these questions to their lives,
they see the value of learning math skills (Yasukawa, Johnston, & Yates,
1995).
How much fertilizer should you buy in order to fertilize your lawn? How
much paint will you need to paint your house? How many posts will it
take to build a fence around your property or swimming pool? How much
money can you save by making these calculations and home
improvements yourself rather than hiring someone else to do them?
These are just a few of the many questions that illustrate how math is
used to maintain personal property. Since most students aspire to
becoming homeowners and living the American dream, these types of
1-6
Teaching Math
questions can help them see how math skills can make their lives more
enjoyable (Sal, van Groenestign, Manly, Schmitt, & Tout, 1999).
How much money will you save per month if you buy the car that is
expected to get better gas mileage? How much money will you save on
interest if you choose a 36-month auto loan rather than a 48-month loan?
How many more weeks can you drive your car before it is time for the
next scheduled maintenance? How many more miles can you drive before
you will need to stop for gasoline? These and many other questions
illustrate how automobile owners and drivers use math. For the vast
majority of adult students, their car is an absolutely essential part of
their lives.
How much flour will you need to make half of the recipe? How much
money will you be able to save by stocking up on a food item when it is
one of the advertised specials? How much sugar will you need to borrow
from a neighbor to complete a recipe (unless you really don’t care about
the recipe and are just borrowing because he or she is really cute)? How
much of each ingredient will you need to purchase to triple a recipe for a
dinner party? What time will you need to start baking if more than one
item needs to go in the oven, and the items require cooking at different
temperatures? These are just a few possible questions that relate to
cooking and entertaining.
How long will a prescription last if someone needs to take it three times a
day? How much medication should you take per dose, and how much
should you take if you are instructed to double the regular dose? How
much will you save by purchasing a generic drug? How far apart are the
contractions? What is the heart rate of an accident victim? These and
many other questions can be the difference between feeling good or
feeling rotten, between good health and poor health, and possibly
between life and death. They offer pretty convincing reasons for learning
math skills.
These examples were chosen not only to illustrate the importance of
math in everyday life, but also because these areas offer numerous
opportunities to draw on students’ previous experiences. “The particular
life situations and perspectives that adults bring to the classroom can
provide a rich reservoir for learning” (Imel, 1998, p. 2).
Teaching Math
1-7
Collaborative Learning
You will see that the lesson plans in this training manual call for students
to work in pairs or groups. Many lesson plans also suggest that students
report their findings to the entire class, and that the class members have
numerous opportunities to learn from each other. In this manual, much
emphasis has been placed on collaborative learning because collaborative
learning works, especially with Adult Basic Skills students (Leonelli &
Schwendeman, 1994). Students who have experienced failures in more
traditional math classrooms need a different approach; repeating the
instructional methods that failed in the past is likely to result in more
failure and more frustration.
Students are often more willing to learn from each other than from a
power figure. This helps the student who is being “taught” by a peer, but
often helps the peer much more. Learning something well enough to
explain it, and therefore “teach” it, requires a level of understanding that
students seldom achieve otherwise. Furthermore, explaining a math
concept or procedure to a peer helps the student put that concept or
procedure into their own “long term memory” bank. Then the student
“teacher” will be more likely to be able to use those concepts and
procedures well into the future (Gardner, 1999).
Look for additional ways and opportunities to incorporate collaborative
learning into math instruction. Share your successes with other Adult
Basic Skills instructors. Both you and the other instructors will benefit
from that interaction, which is, in itself, a form of collaborative learning.
Class Projects
Although this manual does not make suggestions for class projects, some
of the lesson plans could easily be expanded to projects that would help
a family in need or make a major difference in the community. If your
students suggest that a particular lesson plan topic could be used in this
manner, encourage them to explore the costs and benefits of such a
project. Whether or not they actually initiate the work phase of the
project, the planning phase would require a lot of practice in math
applications. At the very least, they would all get to see math in real-life
applications.
1-8
Teaching Math
Culinary Math
2-2
Culinary Math
Culinary Math
Table of Contents
Introduction
2-5
Seeing is Believing Equivalencies
2-7
Common Abbreviations for Weights and Measures
2-11
Equivalent Measures and Weights Card Game
2-21
Standard English Equivalent Measures and Weights
2-33
Recipes – More or Less
2-37
Finding Recipe Yields
2-43
Metric Measurements in Recipes
2-49
Scooping up the Food
2-57
The Mill
2-61
Markup for Menu Pricing
2-65
Percent Loss, Portions, and Cost
2-69
Cooking with Ratios
2-73
Finding Percents of Meat Cuts
2-77
Check, Please
2-83
Ordering Food for Large Groups
2-85
Culinary Math
2-3
2-4
Culinary Math
Introduction
The food service industry has shown phenomenal
growth over the last 50 years. As Americans become
more and more dependent on that industry, job
opportunities in the culinary arts continue to
increase at a rapid pace that shows no sign of
slowing down. While many see working at a fastfood
franchise as a dead-end job, those who obtain the
math skills required for management aspects of the
food service industry will have many opportunities
for advancement.
Measurement skills are required in many occupations, but especially in
the culinary arts. Chefs, short-order cooks, etc. must be able to determine
quantities of ingredients when recipes are being modified and when
fractions or multiples of recipes are required. Food preparation often
requires conversion of one unit of measurement to another. Units of
measurement in recipes do not always correspond to those on ingredient
labels. This chapter includes lesson plans designed to help students learn
math by practicing measurement skills in this context.
Many students who will not work as a professional chef will become
“amateur chefs” because they enjoy entertaining or simply enjoy cooking.
Whether as a hobby or a profession, food preparation can be a fun
activity for those who have the math and measuring skills to become
good at it. Advancement opportunities are plentiful for good cooks and
chefs. They can advance in careers such as restaurant management or
ownership. Of course, the business aspect of the food service industry
requires additional math skills.
Restaurants and other businesses that specialize in food preparation are
very focused on the profit margin. Ingredients must be ordered or
purchased in the most cost-effective manner. Determining and comparing
costs is an important application of math skills.
Profit becomes dependent on menu or product
pricing, which also requires math skills. The
applications of math to the ability to compete and
earn a profit in the food service industry are
obvious.
Culinary Math
2-5
Price and quantity calculations must be made to order supplies and
maintain adequate inventory of ingredients. Cost and income analysis can
make the difference between success and failure in this competitive
industry. Those who desire advancement in this aspect of culinary arts
need to improve their math skills. If they do so, rewarding and lucrative
careers may be in their future.
2-6
Culinary Math
Seeing is Believing Equivalencies
Goal:
Students will be able to see, work with, and recognize
differences between units of measurement and their
equivalents.
Materials:
•
A variety of different size containers (pints, quarts, and gallons),
measuring cups and spoons, and food scales to measure ounces,
pounds, grams, and kilograms
•
Colored liquid such as tea (1-2 gallons)
•
Dry beans, rice, or other dry “ingredient” to measure
•
Paper and markers (for preparation only)
•
Handout: Standard English and Metric Equivalent Measures and
Weights
Preparation:
1. Collect measuring instruments needed to make the measurements
listed on the handout. Note: If you do not have the instruments to
actually allow students to do all of the measurements, make
samples of each measurement so students can see exactly how
much each measurement is, then adjust the remainder of the
activity.
2. Make 1-2 gallons of tea or other colored liquid.
3. Using the handout as a guide, set up several “measuring” stations
around the classroom such as stations to measure ingredients
using cups, pints, quarts, milliliters, liters, etc.; a second station to
measure ingredients using measuring spoons and grams; a third
station that includes measuring spoons and cups; and a fourth
station with scales for pounds, ounces, grams, and kilograms. Be
sure to include ingredients, liquid and/or dry, for students to
measure.
Culinary Math
2-7
4. Make a list of the measurements students are to make at each
station and tape it to the table or post it on the wall above the
table. Be sure it is large enough to be easily read.
5. Make copies of the “Standard English and Metric Equivalent
Measures and Weights” handout for each student.
Procedure:
1. Ask students how measurement plays a role in their daily lives.
Allow time for students to share their knowledge and experience.
2. Advise students that today’s activity is about measurement. Ask
students questions such as, “How much is a cup? a teaspoon? a
quart? a bushel?” Then ask about common metric measurements
such as a gram, liter, and kilogram. Note: A gram is about the
weight of a regular size paper clip and a kilogram is about the
weight of a big book or dictionary.
3. Advise students that everyone will have a better understanding of
these measurements as well as “mental images” to take with them.
4. Distribute the “Standard English and Metric Equivalent Measures
and Weights” handout.
5. Allow students to choose a partner.
6. Advise students they are to work with their partner to “prove” each
of the equivalent measures listed at each station using the
ingredients, containers, and measuring instruments provided. As
they complete each measurement, they should mark it on their
handout. You may need to demonstrate how to use some of the
instruments, especially the scales.
7. Allow time for students to complete the indicated measurements.
Assessment:
2-8
•
Observe students as they make the assigned measurements.
•
Allow time for students to reflect on what they learned from this
activity.
Culinary Math
Standard English and Metric
Equivalent Measures and Weights
1 pinch
1 teaspoon
3 teaspoons
1 tablespoon
2 tablespoons
1 ounce
4 tablespoons
8 tablespoons
12 tablespoons
16 tablespoons
1 cup
2 cups
1 pint
4 cups
1 quart
16 cups
2 pints
4 quarts
5 fifths
2 quarts
8 quarts
4 pecks
8 ounces
16 ounces
1 pound
1 pound
2 pounds
8 pounds
12 dozen
32 ounces
64 ounces
128 ounces
1 gram
1 kilogram
Culinary Math
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
1/8 teaspoon
5 milliliters
1 tablespoon
15 milliliters
1 ounce
28 grams
¼ cup
½ cup
¾ cup
1 cup
240 milliliters or 0.24 liters
1 pint
.047 liters
1 quart
0.95 liters
1 gallon
1 quart
1 gallon
1 gallon
1 magnum
1 peck
1 bushel
1 fluid cup
1 pound
454 grams or 0.45 kilograms
1 fluid pint
1 fluid quart
1 fluid gallon
1 gross
1 quart
½ gallon
1 gallon
0.035 ounces
2.2 pounds
2-9
2-10
Culinary Math
Common Abbreviations for Weights
and Measures
Goal:
Students will be able to play games that require
the matching of common measurement terms
with their abbreviations. Through playing the
games, students learn and/or review
abbreviations used for measurement.
Materials:
•
Sets of “Measurement Terms and Abbreviations” cards
Preparation:
1. Review the measurement terms and abbreviations provided on the
cards at the end of this activity. You may wish to delete or add
cards to the set given. Blank cards are provided.
2. Make a copy of the “Measurement Terms and Abbreviations” cards
on cardstock. Cut the cards apart to make one set. Make enough
sets of cards so each group of 2-4 students can have a set.
3. Be sure each card set is thoroughly shuffled.
4. Review the rules given on the following page and decide which
game (Matching or Concentration) the students will play.
Procedure:
1. Briefly review the measurement terms and abbreviations students
will be using to play the game.
2. Explain the rules for the game that the students are to play.
3. Allow students to form groups of 2-4 players. Give each group one
set of the “Measurement Terms and Abbreviations” cards.
4. Allow students to play until all groups finish at least one game.
5. Be sure to collect the cards for future use.
Culinary Math
2-11
Assessment:
•
As students play the game, observe their participation and
involvement.
Extension:
•
Allow students to make different rules for the games.
•
Allow students to make rules for a new game.
Rules for Matching Card Game:
1. Tell students that when you say, “GO,” they are to spread the cards
on the table, face up, so that all students can look for matches.
2. Students within each group work together to pair up each term
with its correct abbreviation as quickly as possible. When they
have finished, they should announce they are done.
3. When a team announces they have finished, all groups stop
working while their matches are checked for correctness. If there
are errors, all groups continue to play.
4. Repeat until one group has correctly matched all their cards. This
team is the winner.
Rules for Concentration Card Game:
1. Have one student place the cards face down on the table so the
rows and columns of cards make a rectangle. Space should be left
between rows and columns so that cards can easily be turned over.
2. Students take turns choosing two cards. For each turn, the student
turns two cards face up to see if they match. If the cards match, the
student keeps the two cards. If not, the student replaces the cards
face down in the same position.
3. Students continue to take turns until all the cards have been
matched.
4. The winner is the student with the most pairs.
2-12
Culinary Math
Measurement Terms and Abbreviations
tsp (t)
teaspoon
tbsp (T)
tablespoon
c
cup
pt
pint
Culinary Math
2-13
Measurement Terms and Abbreviations
2-14
qt
quart
gal
gallon
oz
ounce
lb
pound
Culinary Math
Measurement Terms and Abbreviations
Culinary Math
bch
bunch
doz
dozen
ea
each
crt
crate
2-15
Measurement Terms and Abbreviations
meter
m
decimeter
dm
centimeter
cm
millimeter
mm
2-16
Culinary Math
Measurement Terms and Abbreviations
kilometer
km
hectometer
hm
decameter
dam
cubic
centimeter
cm3
Culinary Math
2-17
Measurement Terms and Abbreviations
2-18
cubic
meter
m
milliliter
ml
liter
l
gram
g
3
Culinary Math
Measurement Terms and Abbreviations
kilogram
kg
degrees
Celsius
ºC
degrees
Fahrenheit
ºF
Culinary Math
2-19
2-20
Culinary Math
Equivalent Measures and Weights Card
Game
Goal:
Students will be able to play games that require
matching equivalencies used in the food service
industry. Through playing the games, students learn
and/or review the equivalencies.
Materials:
•
Sets of “Equivalent Measurements” cards
Preparation:
1. Review the equivalent measures and weights provided on the cards
at the end of this activity. You may wish to delete or add cards to
the set given. Blank cards are provided.
2. Make a copy of the “Equivalent Measurements” cards on cardstock.
Cut the cards apart to make one set. Make enough sets of cards so
that each group of 2-4 students can have a set.
3. Be sure each card set is thoroughly shuffled or have students
shuffle the cards prior to using them.
4. Review the rules given on the following page and decide which
game (Matching or Concentration) the students will play.
Procedure:
1. Briefly review the equivalent measures and weights students use to
play the game.
2. Explain the rules for the game.
3. Allow students to form groups of 2-4 players. Give each group one
set of the “Equivalent Measurements” cards.
4. Allow students to play until all groups finish at least one game.
5. Be sure to collect the cards for future use.
Culinary Math
2-21
Assessment:
•
As students play the game, observe their involvement.
Extension:
•
Allow students to make different rules for the games.
•
Allow students to make rules for a new game.
Rules for Matching Card Game:
1. Tell students that when you say “GO,” they are to spread the cards
on the table, face up, so that all students can look for matches.
2. Students within each group work together to pair up each
equivalent but different measurement as quickly as possible. When
they have finished, they should announce they are done. Note: Do
not pair cards with same measurements.
3. When a team announces they have finished, all groups stop
working while their matches are checked for correctness. If there
are errors, all groups continue to play.
4. Repeat until one group has correctly matched all their cards. This
group is the winner.
Rules for Concentration Card Game:
1. Have one student place the cards face down on the table so that the
rows and columns of cards make a rectangle. Space should be left
between rows and columns so that cards can easily be turned over.
2. Students take turns choosing two cards. The student turns two
cards face up to see if they match. If the cards match (different
measurement but equivalent), the student keeps the two cards. If
not, the student replaces the cards face down in the same position.
3. Students continue to take turns until all the cards have been
matched.
4. The winner is the student with the most equivalent pairs.
2-22
Culinary Math
Equivalent Measurements
1 pinch
1/8 teaspoon
3 teaspoons
1 tablespoon
2 tablespoons
1 ounce
4 tablespoons
¼ cup
Culinary Math
(approximately)
2-23
Equivalent Measurements
8 tablespoons
½ cup
12 tablespoons
¾ cup
16 tablespoons
1 cup
2 cups
1 pint
2-24
Culinary Math
Equivalent Measurements
4 cups
1 quart
16 cups
1 gallon
2 pints
1 quart
4 quarts
1 gallon
Culinary Math
2-25
Equivalent Measurements
2-26
5 fifths
1 gallon
2 quarts
1 magnum
8 quarts
1 peck
4 pecks
1 bushel
Culinary Math
Equivalent Measurements
8 ounces
1 fluid cup
16 ounces
1 pound
1 pound
1 fluid pint
2 pounds
1 fluid quart
Culinary Math
2-27
Equivalent Measurements
2-28
8 pounds
1 fluid gallon
12 dozen
1 gross
32 ounces
1 quart
64 ounces
½ gallon
Culinary Math
Equivalent Measurements
128 ounces
1 gallon
1 gram
0.035 ounces
1 kilogram
2.2 pounds
28 grams
1 ounce
Culinary Math
2-29
Equivalent Measurements
454 grams or
0.45 kg
1 pound
5 milliliters
1 teaspoon
15 milliliters
1 tablespoon
240 milliliters
or 0.24 liters
1 cup
2-30
Culinary Math
Equivalent Measurements
.047 liters
1 pint
0.95 liters
1 quart
1 liter
1.06 quarts
Culinary Math
2-31
2-32
Culinary Math
Standard English Equivalent
Measures and Weights
Goal:
Students will be able to read and interpret tables
of equivalent measures to solve food service
industry related situations involving conversions.
Materials:
•
Handouts: (1) Standard English Equivalent Measures and Weights
(2) Make it Equal
•
Calculators
Preparation:
1. Make copies of the handouts for each student.
2. If students have not completed the Seeing is Believing Equivalencies
activity earlier in this chapter, obtain measuring containers and
samples of the different measurements so that students can see
the similarities and differences.
Procedure:
1. Give each student a copy of the “Standard English Equivalent
Measures and Weights” handout.
2. Explain the different measurements used on the handout.
Demonstrate several equivalent measures if students have not
completed the Seeing is Believing Equivalencies activity earlier in
this chapter.
3. Discuss the importance of accurate conversions and calculations in
the food service industry. Be sure the discussion includes why (1)
accurate measurements allow for consistency in food preparation
and (2) weight is the most accurate measure for dry ingredients. A
cup can hold different amounts based on how packed or loose the
item in the cup is, whereas one pound will always be one pound.
Culinary Math
2-33
4. Give each student a copy of the “Make it Equal” handout. Review
the concepts of ratio and proportion. Demonstrate several
examples and then allow students to work together or
independently to solve the remainder of the problems.
5. Allow students to share solutions and discuss areas of difficulty in
solving the problems.
Assessment:
•
Ask students to write and solve a realistic word problem similar to
one of the problems on the handout. Collect, review, and give
students feedback.
Extension:
•
Use the student-written word problems for practice and review.
•
Invite a guest speaker from a culinary arts program and/or another
food service industry employee to visit and share how
equivalencies and other math concepts are used in their jobs. Allow
time for questions and discussion.
Answers for Handout:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
2-34
1 quart
2 quarts
4 pounds
4 quarts
2 cups
1 cup
1 pint
1 quart
64 ounces
1 ½ quarts
1 gallon
9 pints
1 tablespoon
3 tablespoons
1 cup
½ cup
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
1 pint
1 quart
½ gallon
2 fluid quarts
1 gallon
80 quarts
8 quarts
¼ teaspoon
30 gallons
2 quarts
2 quarts
4 pecks
3 ½ cups or 1 ¾ pints
5 cups or 2 ½ pints
6 cups or 3 pints or 1 ½ quarts
8 cups or 4 pints or 2 quarts
Culinary Math
Standard English Equivalent Measures and Weights
Culinary Math
1 pinch
=
1/8 teaspoon
3 teaspoons
=
1 tablespoon
2 tablespoons
=
1 ounce
4 tablespoons
=
¼ cup
8 tablespoons
=
½ cup
12 tablespoons
=
¾ cup
16 tablespoons
=
1 cup
2 cups
=
1 pint
4 cups
=
1 quart
16 cups
=
1 gallon
2 pints
=
1 quart
4 quarts
=
1 gallon
5 fifths
=
1 gallon
2 quarts
=
1 magnum
8 quarts
=
1 peck
4 pecks
=
1 bushel
8 ounces
=
1 fluid cup
16 ounces
=
1 pound
1 pound
=
1 fluid pint
2 pounds
=
1 fluid quart
8 pounds
=
1 fluid gallon
12 dozen
=
1 gross
32 ounces
=
1 quart
64 ounces
128 ounces
=
=
½ gallon
1 gallon
2-35
Make it Equal
1. 32 ounces = ____ quart(s)
15. 16 tablespoons = ____ cup(s)
2. 64 ounces = ____ quart(s)
16. 8 tablespoons = ____ cup(s)
3. 64 ounces = ____ pound(s)
17. 1 pound = ____ pint(s)
4. 128 ounces = ____ quart(s)
18. 2 pounds = ____ quart(s)
5. 16 ounces = ____ cup(s)
19. 4 pounds = ____ gallon(s)
6. 8 ounces = ____ cup(s)
20. 4 pounds = ____ fluid quart(s)
7. 2 cups = ____ pint(s)
21. 8 pounds = ____ gallon(s)
8. 4 cups = ____ quart(s)
22. 20 gallons = ____ quart(s)
9. 8 cups = ____ ounce(s)
23. 1 peck = ____ quart(s)
10. 6 cups = ____ quart(s)
24. 2 pinches = ____ teaspoon(s)
11. 16 cups = ____ gallon(s)
25. 120 quarts = ____ gallon(s)
12. 18 cups = ____ pint(s)
26. 4 pints = ____ quart(s)
13. 3 teaspoons = ____ tablespoon(s)
27. 1 magnum = ____ quart(s)
14.
9 teaspoons = ____ tablespoon(s)
28. 1 bushel = ____ peck(s)
In the food service industry, liquids and solids are often measured by
weight. If a scale is not available and a recipe calls for the following, how
much liquid measure would you use?
29. 1 ¾ pounds of water
31. 3 pounds of apple juice
30. 2 ½ pounds of 2% milk
32. 4 pounds of skimmed milk
2-36
Culinary Math
Recipes – More or Less
Goal:
Students will be able to multiply and divide whole
numbers and fractions to convert recipes to obtain a
specified number of servings.
Materials:
•
Handouts: (1) Changing Recipes
(2) Recipes
(3) Standard English Equivalent Measures and Weights
from the Standard English Equivalent Measures and
Weights lesson (optional)
•
Additional recipes (ask students to bring in recipes or use recipes
from books or magazines)
Preparation:
1. Review the handouts and decide if you need to provide students
with a copy of the “Standard English Equivalent Measures and
Weights.”
2. Make copies of the handout(s), one for each student.
3. Ask each student to bring in a recipe or provide recipes from books
or magazines.
Procedure:
1. Begin with a discussion about how most of us have learned to
follow a recipe at some point and the fact that ingredients have
relationships to each other is an important concept in cooking.
Most recipes are written to serve a certain number of people. What
if you have a recipe that makes 3 dozen cookies and you only want
1 dozen, or maybe you need 6 dozen for the bake sale? Ask
students if they have ever doubled or halved a recipe. Allow time
for students to share their knowledge and experience.
2. Explain that, in the food service industry, it is often necessary to
convert a recipe to make very large batches. For instance, a bakery
Culinary Math
2-37
may sell over a hundred pumpkin pies at Thanksgiving. Someone
has to determine the amount of ingredients needed to make all
those pies while making sure the relationships between all the
ingredients stay the same.
3. Tell students that today it is going to be their turn to convert
recipes for more or less servings.
4. Distribute the “Changing Recipes” handout (and the “Standard
English Equivalent Measures and Weights” handout if you decide to
use it), one per student.
5. Demonstrate how to find the “working factor” and convert several
ingredients.
6. Allow time for students to complete the handout and ask
questions.
7. Examine the answers for the handout. Discuss how hard it would
be to get exact measures for some of the ingredients in the
Oatmeal Raisin Cookie recipe, i.e. 2/3 egg, 5/12 cup, etc. However,
when recipes are given in pounds and ounces, it is much easier to
obtain exact measures, which is important for recipe consistency.
8. Distribute the “Recipes” handout.
9. Let students choose a partner. Explain that they are to work
together to:
a. Copy their recipes onto the blank “Recipes” handout, being
sure to include step-by-step directions.
b. Half the recipe.
c. Double the recipe.
d. Carefully check their work, i.e. copying and math.
Assessment:
•
Allow time for discussion of the math used to complete the task.
Ask questions such as, “What happens to the denominator of a
fraction when you half it?”
•
Allow students to self-assess their work through sharing of
answers.
2-38
Culinary Math
Extension:
•
Let students publish a recipe book from the recipes they brought in
by adding additional recipes.
Answers for Handout:
Oatmeal Raisin Cookies
3 dozen
1 dozen
10 dozen*
granulated sugar
1 cup
1/3 cup
3 1/3 cups
shortening
½ cup
1/6 cup or 3 tbsp
1 2/3 cups
eggs
2
2/3 egg or 1
6 2/3 eggs or 7
milk
¼ cup
4 teaspoons
5/6 cups
flour
1 ½ cups
½ cup
5 cups
raisins
1 ¼ cups
5/12 cup
4 1/6 cups
oatmeal
1 2/3 cups
5/9 cup
5 5/9 cups
salt
½ tsp
1/6 tsp
1 2/3 tsp
cinnamon
1 tsp
1/3 tsp
3 1/3 tsp
baking soda
1 tsp
1/3 tsp
3 1/3 tsp
Soft Dinner Rolls
4 dozen
1 ½ dozen
6 dozen
granulated sugar
5 oz
1 7/8 oz
7 ½ oz
shortening
5 oz
1 7/8 oz
7 ½ oz
salt
½ oz
3/16 oz
¾ oz
dry milk
1 ½ oz
9/16 oz
2 ¼ oz
eggs
2 oz
¾ oz
3 oz
flour
2 lbs
¾ lb or 9 oz
3 lbs
water
1 lb
3/8 lb or 6 oz
1 ½ lbs
yeast
2 ½ oz
15/16 oz
3 ¾ oz
9” Lemon Pies
4 Pies
1 Pie
15 Pies
granulated sugar
1 lb 12 oz
7 oz
6 lbs 9 oz
butter
2 oz
½ oz
7 ½ oz
salt
¼ oz
1/16 oz
15/16 oz
lemon juice
9 oz
2 ¼ oz
33 ¾ oz or 2 lbs 1 ¾ oz
egg yolks
6 oz
1 ½ oz
22.5 oz or 1 lb 6 ½ oz
corn starch
4 oz
1 oz
15 oz
water
2 lbs
½ lb or 8 oz
7 ½ lbs
grated lemon peel
1 ½ oz
3/8 oz
5 5/8 oz
Culinary Math
2-39
Changing Recipes
In the food service industry, recipes often need to be
converted to feed a specific number of people. One
way to do this is to find a “working factor” which is
used to find the new amount of each ingredient.
Steps to changing the portion size of recipes:
1. Find a working factor: working factor = new yield ÷ old yield.
2. Multiply each ingredient by the working factor to find the amount of
each ingredient needed for the indicated portions.
Determine the amount of each ingredient needed to prepare the indicated
portions.
Oatmeal Raisin Cookies
Ingredient
3 dozen
granulated sugar
1 cup
shortening
½ cup
eggs
2
milk
¼ cup
flour
1 ½ cups
raisins
1 ¼ cups
oatmeal
1 2/3 cups
salt
½ tsp
cinnamon
1 tsp
baking soda
1 tsp
1 dozen
10 dozen*
*Even though you probably would not mix 10 dozen at one time, you may
want to know how much of each ingredient to purchase to make 10
dozen for a bake sale or to sell at a bakery.
2-40
Culinary Math
Changing Recipes, continued
Ingredients for recipes used in the food service
industry are often given by weight.
Soft Dinner Rolls
Ingredient
4 dozen
granulated sugar
5 oz
shortening
5 oz
salt
½ oz
dry milk
1 ½ oz
eggs
2 oz
flour
2 lbs
water
1 lb
yeast
2 ½ oz
1 ½ dozen
6 dozen
9” Lemon Pies
Ingredient
4 Pies
granulated sugar
1 lb 12 oz
butter
2 oz
salt
¼ oz
lemon juice
9 oz
egg yolks
6 oz
cornstarch
4 oz
water
2 lbs
grated lemon peel
1 ½ oz
Culinary Math
1 Pie
15 Pies
2-41
Recipes
Title:
Ingredient
Serves ______
Serves ______
Serves ______
Preparation and cooking directions:
Use back if additional space is needed.
2-42
Culinary Math
Finding Recipe Yields
Goal:
Students will be able to add, multiply, and divide
to find the number of servings for a given recipe
by finding the total weight or measurement of the
ingredients, converting the total to the desired
units, and dividing by a portion size to find the
recipe yield.
Materials:
•
Handout: What is the Yield?
•
Calculators
Preparation:
1. Review the handout to determine if you want to add additional
practice problems or recipes.
2. Make copies of the handout, one for each student.
Procedure:
1. Explain the definition of yield. Yield is the amount of portions,
servings, or units a particular recipe will produce. Explain that most
recipes give an approximate yield. However, in the food service
industry, the serving may be larger or smaller, thus requiring the
chef or business owner to determine a “new” yield.
2. Ask students if they have ever developed a new recipe. If so, how
did they determine the yield? Explain that finding the yield for
recipes is important in the food service industry. The business
owner uses the yield to determine how much must be charged for
each individual serving.
3. Advise students they will be finding the yield for several recipes.
Explain that recipes may be written in two different ways, i.e., using
either measurements or weights for ingredients. To find the yield,
the total weight or measurement of all the ingredients must be
Culinary Math
2-43
determined and converted to the same units as the portion size,
and then divided by the desired portion size.
4. To find the yield, students must be able to easily convert from
pounds to ounces and from quarts, pints, teaspoons, and
tablespoons to cups. Review these equivalencies and conversions.
Remind students that only “like” ingredients can be added.
5. Distribute the “What is the Yield?” handout and calculators.
6. Demonstrate how to find the yield of the first recipe on the
handout. The serving size and ingredients are given in weight. To
find the yield:
a. Find the total weight for all the ingredients.
b. Convert total weight to ounces.
c. Divide the total weight (ounces) by the serving portion
weight.
d. The result is the yield or number of portions.
7. Demonstrate how to find the yield of the second recipe on the
handout. The serving size and ingredients are given in
measurement. To find the yield:
a. Find the total measurement for all the ingredients.
b. Convert total measurement to cups.
c. Divide the total measurement by the serving portion
measurement.
d. The result is the yield or number of portions.
8. Allow students to find the yield of the other recipes given on the
handout.
Assessment:
•
2-44
As students complete the handout, check their work to see if they
found the correct yields. If not, allow time for students to work
with peers to find errors.
Culinary Math
Extension:
•
Allow students to find additional recipes on the Internet where
ingredients are given in weight so they can find the yield.
•
Allow students to make a recipe that a bakery might use by
converting a traditional recipe into weights and then doubling or
tripling the ingredients. Students could exchange recipes to
determine yields.
Answers for Handouts:
1. 165 dinner rolls
2. 42 servings of fruit salad
3. 14 coffee cakes
4. 20 servings of cheese vegetable spread/dip
Culinary Math
2-45
What is the Yield?
1. How many 1½ oz dinner rolls can be made from
the recipe below?
1 lb 4 oz
1 lb 4 oz
Dinner Rolls
granulated sugar
shortening
2 oz
salt
6 oz
dry milk
6 oz
whole eggs
7 lbs 8 oz
flour
4 lbs
water
10 oz
yeast
2. How many ½ cup servings can be made from
the recipe below?
2 quarts
1 pint
apples, chopped
1 pint
oranges, chopped
1 cup
pineapple, chopped
3 cups
1 cup
1 quart
2-46
Fruit Salad
cranberries, chopped
sugar
lemon flavored gelatin
hot water
Culinary Math
What is the Yield?, continued
3. How many 12 oz coffee cakes can be made from the recipe below?
Coffee Cakes
1 lb
granulated sugar
1 lb
shortening
1 oz
salt
3 lbs
bread flour
1½ lb
pastry flour
12 oz
whole milk
4 oz
dry milk
2 lbs
water
8 oz
yeast
1 lb
chopped pecans
¼ oz
mace
1 oz
vanilla
4. How many ¼ cup servings can be made from the recipe below?
Cheese Vegetable Spread/Dip
2 cups
cream cheese
1 cup
4T
green pepper, minced
8T
onion, minced
8T
celery, minced
4T
pimiento, chopped
2t
hot sauce
2t
worcestershire sauce
½ cup
Culinary Math
blue cheese
mayonnaise
2-47
2-48
Culinary Math
Metric Measurements in Recipes
Goal:
Students will be able to convert recipes from the metric
system to the U.S. customary system and from the U.S.
customary system to the metric system when given a
table of equivalents.
Materials:
•
Handouts: (1) Weights and Measures: U.S. Customary and Metric
System Equivalents
(2) Metric and U.S. Customary Recipes
(3) Our Favorite Recipes
•
Recipes
•
Calculators
Preparation:
1. Ask students to bring in a copy of their favorite recipes. You may
want to collect these before you actually plan to use them to be
sure you have an ample supply. If not, add some of your favorites.
2. Decide if students will need a review of common abbreviations
used for measurements. If so, consider having them play the games
from the Common Abbreviations for Weights and Measures lesson,
or at least review the abbreviations prior to completing this lesson.
3. Make copies of the handouts, one for each student.
Procedure:
1. Discuss how the United States uses one system of measurement
while most of the rest of the world uses the metric system.
2. Distribute and explain the “Weights and Measures: U.S. Customary
and Metric System Equivalents” handout. Distribute calculators.
Demonstrate how to complete several of the conversion problems
using ratios and proportions, and then allow students to complete
the handout.
Culinary Math
2-49
3. Connect converting from metric to U.S. customary units and vice
versa to sharing recipes or using a recipe from another country. For
example, if you wanted to send a recipe to a friend in France, would
you send it with measurements in cups and pounds and hope it
turned out right, or would you convert it to metric values,
guaranteeing that the recipe would be just as delicious in France as
in the United States? Or if a friend sent you a recipe in metric units,
would you be able to prepare it?
4. Explain that now they will have the job of converting recipes from
one unit of measure to another.
5. Distribute the “Metric and U.S. Customary Recipes” handout.
6. Demonstrate how to convert several measurements. For example, if
the recipe calls for 2 cups of flour, you would need to convert to
liters, therefore since 1 cup = .24 liters then 2 cups = .48 liters. If
the recipe calls for 2/3 cup sugar, multiply 2/3 by .24 = .16 liters.
7. Allow time for students to complete the conversions then share
and discuss answers.
8. Distribute the “Our Favorite Recipes” handout. Advise students
they are to copy their favorite recipe onto this handout, and then
convert it to the other unit of measure. Remind them to convert the
cooking temperature, if necessary.
Assessment:
•
Students will self-assess their work when they share and discuss
their conversions.
Extension:
•
Have students prepare a lunch using only metric measurement
recipes.
•
Have students visit the “Cooking by Number” website at
http://www.learner.org/exhibits/dailymath/meters_liters.html (or
similar sites) to learn more about the metric measurement system.
•
Collect the “Our Favorite Recipes” handouts. Allow students to add
artwork and publish a class cookbook. Consider adding recipes
2-50
Culinary Math
developed in other lessons from this chapter as part of the
publication.
•
Discuss other careers where metric conversions would be an
important job skill.
Answers for Handouts:
1.
2.
3.
4.
5.
6.
7.
8.
9.
.48 liters
2.08 cups
0.6 liters
0.71 liters
428 ºF
177 ºC
4.24 pints
0.75 cups
0.179 ounces
U.S. Customary
1c
½ lb
1 tsp
½ tsp
3 tbsp
1½c
2
2/3 c
1 tsp
½c
¾c
1¼ c
350ºF
13 x 9 inches
Culinary Math
10.
11.
12.
13.
14.
15.
16.
17.
18.
1.4 teaspoons
.44 cups
45 milliliters
6.67 ounces
22.86 centimeters
0.1 teaspoons
2.5 milliliters
2.42 pounds
1.36 kilograms
Continental Cake
Ingredients
chopped dates
butter
baking soda
salt
cocoa
flour
eggs
sugar
vanilla
chopped nuts
chocolate chips
brown sugar
cooking temperature
pan size
Metric
240 ml
227 g
5 ml
2.5 ml
45 ml
360 ml
2
160 ml
5 ml
120 ml
180 ml
300 ml
177ºC
33 cm x 23 cm
2-51
Answers for Handouts:, continued
U.S. Customary
.26 lb ≈ ½ cup
.37 lb ≈ ¾ cup
.11 lb ≈ 3.3 tbsp
2 tsp
0.6 tsp
2
1.04 cups ≈ 1 cup
1/5 cup or 3.3 tbsp
428ºF
7.9 ≈ 8 in square
U.S. Customary
1.65 lbs
.11 lb ≈ 3.3 tbsp
.55 lbs ≈ 1 cup
4 tbsp
0.4 tsp
.26 lbs ≈ ½ cup
1
2/3 cup
.55 lb ≈ 1 cup
446ºF
9.8 ≈ 10 in round
Cornbread
Ingredients
flour
cornmeal
sugar
baking powder
salt
eggs
milk
vegetable oil
cooking temperature
pan size
Strawberry Shortcake
Ingredients
strawberries, sliced
sugar
flour
baking power
salt
butter
egg
milk
whipping cream
oven temperature
pan size
Metric
120 g
170 g
50 g
10 ml
3 ml
2
250 ml
50 ml
220ºC
20 cm square
Metric
750 g
50 g
250 g
60 ml
2 ml
120 g
1
160 ml
250 ml
230ºC
25 cm round pan
Reference:
“Cooking by Numbers.” (2007). Retrieved February 11, 2007, from Math in
Daily Life Website:
http://www.learner.org/exhibits/dailymath/meters_liters.html
2-52
Culinary Math
Weights and Measures: U.S. Customary and Metric
System Equivalents
1 gram
=
0.035 ounces
1 kilogram
=
2.2 pounds
28 grams
=
1 ounce
454 grams or 0.45 kg
=
1 pound
5 milliliters
=
1 teaspoon
15 milliliters
=
1 tablespoon or ½ fluid ounce
240 milliliters or 0.24 liters
=
1 cup
0.47 liters
=
1 pint
0.95 liters
=
1 quart
1 liter
=
1.06 quarts
0 degrees Celsius
5
C = ( F " 32)
9
2.54 centimeters
=
32 degrees Fahrenheit
9
F = C + 32
5
1 inch
=
! of the following: !
Convert each
1. 2 cups = _______ liters
10. 7 milliliters = _______ teaspoons
2. ½ liter = _______ cups
11. 100 grams = _______ cups
3. 2 ½ cups = ________ liters
12. 3 tablespoons = _______ milliliters
4. 1 ½ pints = ________ liters
13. 200 milliliters = _______ ounces
5. 220ºC = _______ ºF
14. 9 inches = _______ centimeters
6. 350ºF = _______ ºC
15. 0.5 ml = _______ teaspoons
7. 2 liters = _______ pints
16. ½ teaspoon = _______ milliliters
8. 170 grams = _______ cups
17. 1.1 kilogram = _______ pounds
9. 5 grams = _______ ounces
18. 3 pounds = ______ kilograms
Culinary Math
2-53
Metric and U.S. Customary Recipes
Complete the recipes below so that ingredients
are given in metric and U.S. customary units of
measurement.
Continental Cake
U.S. Customary
2-54
Ingredients
1c
chopped dates
½ lb
butter
1 tsp
baking soda
½ tsp
salt
3 tbsp
cocoa
1½c
flour
2
eggs
2/3 c
sugar
1 tsp
vanilla
½c
chopped nuts
¾c
chocolate chips
1¼ c
brown sugar
350ºF
cooking temperature
13 x 9 inches
pan size
Metric
Culinary Math
Metric and U.S. Customary Recipes, continued
Cornbread
U.S. Customary
Ingredients
Metric
flour
120 g
cornmeal
170 g
sugar
50 g
baking powder
10 ml
salt
3 ml
eggs
2
milk
250 ml
vegetable oil
50 ml
cooking temperature
220ºC
pan size
20 cm square
Strawberry Shortcake
U.S. Customary
Culinary Math
Ingredients
Metric
strawberries, sliced
750 g
sugar
50 g
flour
250 g
baking power
60 ml
salt
2 ml
butter
120 g
egg
1
milk
160 ml
whipping cream
250 ml
oven temperature
230ºC
pan size
25 cm round pan
2-55
Our Favorite Recipes
Ingredients
U.S. Customary
Metric
Preparation and cooking directions:
2-56
Culinary Math
Scooping up the Food
Goal:
Students will be able to use information from a
table and divide fractions to determine the
servings available from different foods.
Materials:
•
Handout: Scooping up Portion Control
•
Calculators
Preparation:
1. Review the lesson and handout to determine if it is appropriate for
your students or if you will need to make adjustments.
2. Make copies of the handout, one for each student.
Procedure:
1. Ask if any of the students have ever worked in a restaurant or
cafeteria. If so, ask the students to share how portion control was
managed.
2. Explain that one way the food service industry controls portions is
through the use of different size scoops.
3. Distribute the “Scooping up Portion Control” handout and
calculators.
4. Allow students to examine the chart and compare the different
scoop sizes. Discuss the different scoop sizes and the foods each
size scoop may be used for to control portion size.
5. Demonstrate how to determine the number of portions when a
scoop size is specified.
a. Determine whether the bulk food is given in volume or
weight, and then find the volume or weight of the scoop
size indicated.
Culinary Math
2-57
b. Convert the volume or weight of the bulk food into the
same units as the scoop.
c. Divide the total volume or weight by the volume or weight
of the scoop.
d. The result is the number of portions that can be made
from the bulk amount indicated.
6. Allow time for students to work in small groups to complete the
questions on the handout then discuss and share their results.
Assessment:
•
In addition to observing students’ efforts and participation, you
can choose several problems to grade for correctness.
Extension:
•
Have students identify any other areas where scoops may be used
for measurement.
Answers for Handouts:
1. 52, 42
2. 48, 59
3. 73, 58
4. 96, 72
5. 30, 40
6. 40, 48
7. 192, 232
Reference:
Strianese, A. J. and Strianese, P. P. (2001). Math principles for food service
occupations, 4th ed. Albany, NY: Delmar Publishing.
2-58
Culinary Math
Scooping up Portion Control
In the food service industry, portion size is often controlled through the
use of different size scoops. The chart below gives some of the common
scoop sizes, volumes, and weights.
Scoop #
Volume
Weight
(approximate)
5 1/3 oz
6
2/3 cup
8
½ cup
4 oz
10
2/5 cup
3 ¼ oz
12
1/3 cup
2 2/3 oz
16
¼ cup
2 oz
20
3 1/3 T
1 2/3 oz
24
2 2/3 T
1 1/3 oz
30
2 1/5 T
1 1/16 oz
40
1¾T
¾ oz
Determine the number of portions for each of the following:
1. How many hush puppies can be made from 3 ½ pounds of batter
using a #30 scoop for each hush puppy? a #24 scoop?
2. How many portions can be served from 12 pounds of mashed
potatoes using a #8 scoop? a #10 scoop?
3. How many servings of butter can be obtained from a ½ gallon
container of butter using a #40 scoop? a #30 scoop?
4. How many blueberry muffins can be made from 1½ gallons of
batter using a #16 scoop for each muffin? a #12 scoop?
5. How many crab cakes can be made from 5 pounds of batter using a
#12 scoop for each crab cake? a #16 scoop?
6. How many tuna salad sandwiches can be made from 1 gallon of
tuna salad if each is made using a #10 scoop? a #12 scoop?
7. How many servings of blueberry syrup can be obtained from 2
gallons using a #24 scoop? a #30 scoop?
Culinary Math
2-59
2-60
Culinary Math
The Mill
Goal:
One-tenth
of one cent!
Students will be able to identify the mill and use it in
solving problems dealing with money.
Materials:
•
Handout: Dollars, Cents, and Mills
•
Teaching notes: What is a Mill?
•
Calculators
Preparation:
1. Review the “What is a Mill?” teaching notes and decide how you will
present the information to your students.
2. Make copies of the handout, one for each student.
Procedure:
1. Introduce what a mill is using the “What is a Mill?” information
sheet. Allow time for questions and discussion.
2. Distribute the “Dollars, Cents, and Mills” handout and calculators.
3. Demonstrate how to solve one or more of the problems.
4. Allow time for students to work in pairs or small groups to
complete the questions on the handout, then discuss and share
their results.
Assessment:
•
In addition to observing students’ efforts and participation, you
can choose several problems to grade for correctness.
Extension:
•
Have students identify any other areas where mills may be used in
dealing with money.
Culinary Math
2-61
Answers for Handouts:
1a. $0.236
1b. $0.24
1c. $1.168 or $1.17
1d. $0.71
2a. $4.32, 4.23
2b. $0.09
2c. $16,425
Reference:
Strianese, A. J. and Strianese, P. P. (2001). Math principles for food service
occupations, 4th ed. Albany, NY: Delmar Publishing.
2-62
Culinary Math
What is a Mill?
When dealing with monetary numbers, cent is used to represent the value
of the hundredth part of a dollar. The third place to the right of the
decimal is called a mill and represents the value of the thousandths part
of a dollar, or one tenth of one cent.
When the final result of a monetary number includes a mill, it is usually
rounded to a whole number of cents. If the mill is 4 or less, round down.
If the mill is 5 or more, round up.
The mill is important in the food service industry because the production
cost of an item and the cost of menu food items must be figured to the
mill to obtain the exact cost or selling price of an item. The mill can make
a difference in the amount of profit over time.
For example, it is important to know that a roll costs $0.144 to produce,
thus making the cost for 1 dozen $1.728 or $1.73 to produce. If we had
rounded off at the per roll cost ($.14) then the cost of making 1 dozen
($1.68) would be undervalued. Five cents may not seem like much if you
are producing only 1 dozen. What if you are in the bakery business and
producing 120 dozen or more per day? The loss on 120 dozen per day
would amount to a $6.00 per day loss which amounts to $2,190 per year.
This rounding could cost a large business lots of money over time.
Don’t forget the rule for rounding mills: 4 or less, round down; 5 or more,
round up.
Ask your students the following questions:
1. How many mills are in 1 cent?
2. How many mills are in 10 cents?
3. How many mills are in $1.00?
4. Round each of the following to the nearest cent:
a. $0.012
b. $0.537
c. $4.485
d. $2394.934
Answers:
1. 10 mills
4a. $0.01
Culinary Math
2. 100 mills
4b. $0.54
3. 1,000 mills
4c. $4.49
4d. $2,394.93
2-63
Dollars, Cents, and Mills
Complete the following problems.
1. The total cost for ingredients for a recipe of
blueberry muffins came to a total of $16.98.
The recipe yields 6 dozen muffins.
a. What is the cost per muffin to the
nearest mill?
b. What is the cost per dozen to the nearest cent?
c. If the bakery sells the muffins for $4 per dozen, how much
profit is made per dozen?
d. To make a profit, the bakery needs to charge customers
triple the cost of the ingredients. How much should they
charge for individual muffins?
2. A soup recipe calls for the following ingredients and the owner
figured the costs per serving for the ingredients two ways.
Ingredient
tomatoes
corn
carrots
peas
potatoes
onions
green beans
ground beef
Total Cost
Cost per serving
not rounded
$0.194
$0.132
$0.184
$0.163
$0.144
$0.074
$0.114
$0.434
$1.439
Cost per serving
rounded to nearest cent
$0.19
$0.13
$0.18
$0.16
$0.14
$0.07
$0.11
$0.43
$1.41
a. To break even, they must charge customers triple their cost.
What is the charge per serving if the cost is figured without
rounding until the total cost is found? What is the charge per
serving if each ingredient is rounded individually?
b. How much less does the company make per serving by
rounding each individual ingredient instead of rounding after
they determine the total cost?
c. If they serve on average 500 servings per day, 365 days a
year, how much less profit per year do they make if they
ignore the mills?
2-64
Culinary Math
Markup for Menu Pricing
Goal:
Students will be able to calculate markup based on
percents to determine selling prices.
Materials:
•
Handout: Determining Menu Pricing
•
Calculators
Preparation:
1. Review the handout and make additions or deletions so that it
meets the needs of your students.
2. Make copies of the handout, one for each student.
Procedure:
1. Discuss how businesses determine the selling prices of items. If
any of your students have worked in retail, they may have
firsthand experience. Ask them to share their knowledge and
experience.
2. Explain that food service industries compute selling prices much
the same way as any other business. When a menu is made, the
selling price is based on the actual cost with markup added.
3. Distribute the “Determining Menu Pricing” handout and calculators.
4. Discuss some of the markup rates, e.g., What does 100%, 200%, ¾,
or 2 ½ mean?
5. Demonstrate how to find selling/menu prices based on the markup
rates using several examples from the handout and the
equation/formula:
Selling Price = (cost) + (cost x markup rate)
6. Allow students to work collaboratively to complete the handout.
7. Allow time for questions and discussion.
Culinary Math
2-65
Assessment:
•
Assign GED practice questions that involve markup percents.
•
Have students write and solve a word problem involving finding
the selling price when given the cost and percent markup.
Extension:
•
Have students design a menu using the items on the handout.
•
Discuss other areas in the real world where one must know how to
calculate selling prices based on markup percents.
•
Have students solve other problems where they know two things
and must find the third, i.e. find cost when markup and selling
price are known or find the markup rate when cost and selling
price are known.
Answers for Handout:
Item
Appetizer: Shrimp Cocktail
Appetizer: Buffalo Wings
Appetizer: Maryland Crab Cake
Soup: Clam Chowder
Soup: French Onion Soup
Salad: Tossed Green Salad
Salad: Caesar Salad
Entrée: Ribeye (10 oz)
Entrée: New York Strip (12 oz)
Entrée: Prime Rib (12 oz)
Entrée: Shrimp Grille
Entrée: Lobster Tails
Children: Junior Steak
Children: Chicken Tenders
Dessert: Chocolate Cheesecake
Dessert: Key Lime Pie
Beverage: Coffee & Tea
Beverage: Milk, Plain, Chocolate
Beverage: Sodas
Beverage: Apple & Orange Juice
2-66
Cost per
Item
$3.25
$2.83
$3.58
$1.65
$1.12
$0.78
$1.13
$8.46
$7.59
$8.38
$5.24
$9.95
$3.00
$2.00
$2.25
$1.35
$0.22
$0.42
$0.55
$0.42
Markup
Rate
150%
100%
¾
½
50%
2½
1¾
175%
200%
200%
250%
2½
50%
35%
150%
175%
400%
2¼
3½
225%
Selling
Price
$8.13
$5.66
$6.27
$2.48
$1.68
$2.73
$3.11
$23.27
$22.77
$25.14
$18.34
$34.83
$4.50
$2.70
$5.63
$3.71
$1.10
$1.37
$2.48
$1.37
Culinary Math
Determining Menu Pricing
Find the selling price for each menu item based on the given markup rate.
Item
Cost per
Item
Markup
Rate
Appetizer: Shrimp Cocktail
$3.25
150%
Appetizer: Buffalo Wings
$2.83
100%
Appetizer: Maryland Crab Cake
$3.58
¾
Soup: Clam Chowder
$1.65
½
Soup: French Onion Soup
$1.12
50%
Salad: Tossed Green Salad
$0.78
2½
Salad: Caesar Salad
$1.13
1¾
Entrée: Ribeye (10 oz)
$8.46
175%
Entrée: New York Strip (12 oz)
$7.59
200%
Entrée: Prime Rib (12 oz)
$8.38
200%
Entrée: Shrimp Grille
$5.24
250%
Entrée: Lobster Tails
$9.95
2½
Children: Junior Steak
$3.00
50%
Children: Chicken Tenders
$2.00
35%
Dessert: Chocolate Cheesecake
$2.25
150%
Dessert: Key Lime Pie
$1.35
175%
Beverage: Coffee & Tea
$0.22
400%
Beverage: Milk, Plain, Chocolate
$0.42
2¼
Beverage: Sodas, Coke, Sprite
$0.55
3½
Beverage: Apple & Orange Juice
$0.42
225%
Culinary Math
Selling
Price
2-67
2-68
Culinary Math
Percent Loss, Portions, and Cost
Goal:
Students will be able to find the percent of food
loss due to cooking, convert decimal weights into
ounces, find portion sizes, and find the cost per
serving for different foods.
Materials:
•
Handout: Percent Lost, Portions, and Cost
Preparation:
1. Review the procedure and handout for this lesson. Determine if
you will complete the entire lesson in one class or if you will use
two or more classes.
2. Make copies of the handout, one for each student.
Procedure:
1. To get students involved, ask questions such as:
a. Have you ever roasted a ham or turkey?
b. How much does the uncooked weight differ from the cooked
weight? Why do you think there is a difference?
c. In a restaurant, do you think the serving portion of steaks is
based on cooked or uncooked weights, i.e. when you order a
12 ounce steak, are you actually served 12 ounces or was
that the weight before cooking?
d. How do you think a restaurant determines how many hams
or pork loins to buy?
2. Explain that the activities today include being able to solve word
problems involving the percent lost when an item is cooked and
the cost per portion based on the cooked weight.
3. Distribute the “Percent Lost, Portions, and Cost” handout and
calculators. Demonstrate how to solve several problems.
Culinary Math
2-69
4. Allow students to complete the handout, individually or in groups.
Assessment:
•
Observe students as they complete the handout. Offer individual
help as needed. When a student is having difficulty, ask questions
to guide their work.
Extension:
•
When fresh meat is purchased, it is most often weighed in decimal
pounds. The chef must convert the decimal pounds into ounces to
determine portion sizes. Have students convert decimal pounds
into ounces to determine portion sizes. Consider problems such as:
153.36 pounds of chicken with 6-ounce servings, 22.74 pounds of
beef ribs with 12-ounce servings, etc.
Answers for Handouts:
2-70
1. 18.75%
10.
21
2. 16.61%
11.
43
3. 14.47%
12.
36
4. 133
13.
62
5. 23
14.
32
6. 20
15.
$0.945
7. 43
16.
$0.328
8. 102
17.
$0.23
9. 34
18.
$0.20
Culinary Math
Percent Lost, Portions, and Cost
Percent Lost Through Shrinkage, Boning, and Trimming
1. A 48-pound beef round lost 9 pounds through
shrinkage when roasted. What is the percent lost?
2. 38 pounds of steak lost 6 pounds, 5 ounces
through boning, trimming, and cooking. What is
the percent lost?
3. A 19-pound rib eye lost 2 ¾ pounds through shrinkage in roasting.
What is the percent lost?
Finding Portions
4. How many 5-ounce swiss steaks can be cut from 48 pounds if 6
pounds, 5 ounces are lost in boning and trimming?
5. How many 12-ounce strip steaks can be cut from a 20-pound short
loin of beef if 2 ¾ pounds is lost in trimming?
6. How many 6-ounce filet mignons can be cut from an 8-pound beef
tenderloin if 8 ounces is lost in trimming?
7. How many 5-ounce pork chops can be cut from a pork loin
weighing 17 pounds if 3 pounds, 5 ounces is lost in trimming?
8. How many servings of 1.25-ounce Swedish meatballs can be made
from 32 pounds of ground beef and veal if each serving contains 4
meatballs?
9. How many 6-ounce ham steaks can be cut from a
14-pound ham if 15 ounces is lost in trimming?
Culinary Math
2-71
Percent Lost, Portions, and Cost, continued
10. How many 12-ounce prime ribs can be cut from a 19-pound rib
eye if 2 ¾ pounds is lost in trimming?
11. How many 6-ounce veal cutlets can be cut from a 22-pound leg of
veal if 5 pounds, 4 ounces is lost through trimming and boning?
12. How many 6 ½-ounce chopped steaks can be made from 15
pounds of ground chuck?
13. How many 3-ounce servings can be obtained from a 13-pound
pork roast if 1 pound, 6 ounces is lost through shrinkage when
roasted?
14. How many 2 ½-ounce servings can be obtained from a 6-pound
beef tenderloin if 14 ounces are lost through shrinkage when
roasted?
Portion Cost
15. What is the cost of a 6-ounce portion if 15 pounds of beef round
cost $37.78?
16. A 3 ½-pound bag of frozen mixed vegetables
costs $4.59. How much does a 4-ounce serving
cost?
17. A 3-pound bag of corn costs $3.39. How much
does a 3¼-ounce serving cost?
18. A 5-pound bag of frozen green beans costs
$6.39. How much does a 2½-ounce serving cost?
2-72
Culinary Math
Cooking with Ratios
Goal:
Students will be able to use ratios to solve problems
related to food preparation.
Materials:
•
Handouts: Food Preparation with Ratios
•
Food preparation labels that use ratios, e.g., instant rice, stuffing
mix, bulk dry beans, regular rice, etc.
•
Calculators
Preparation:
1. Review the procedure and handout to determine if your students
will need access to a chart for equivalent measures and weights. If
so, consider using the “Equivalent Measures and Weights” handout
from the Standard English Equivalent Measures and Weights lesson.
2. Make copies of the handout, one for each student.
3. Collect food labels. You may want to ask students to bring in
empty boxes or food labels that show ratios.
Procedure:
1. Review ratios and proportions.
2. Ask students how they use ratios in their daily life. Allow time for
discussion.
3. Show students the food labels that use ratios as part of the
directions. Allow students to complete several problems based on
the food labels. For example, on the instant rice box it shows the
ratio of water to rice as 1 to 1. For 1 serving you use ½ cup rice.
How much rice and water would you use to make 3 servings? Allow
time for students to discuss different ways of solving the problem,
e.g., make a list, set it up as a proportion, etc.
Culinary Math
2-73
4. Distribute the “Food Preparation with Ratios” handout, the
equivalency chart (if you decide to use it), and calculators.
5. Allow time for students to work collaboratively to discuss and
complete the problems on the handout.
Assessment:
•
Ask students to individually complete practice problems similar to
the one on the handout.
•
Find and assign GED-type ratio questions.
Extension:
•
Allow students to make up a practice sheet with ratio problems.
Answers for Handouts:
1. 5 quarts
2. 1 ½ quarts
3. 2 ¼ gallons
4. 5 ¼ quarts
5. 6 pints
6. 2 ½ quarts
7. 1 ½ gallons
8. 6 ¼ pints
9. See below.
To Make
2-74
Add Gelatin
Add Water
2 cups
¼ cup
2 cups
3 pints
¾ cup
3 pints
1 ½ quarts
¾ cup
1 ½ quarts
3 quarts
1 ½ cups
3 quarts
2 gallons
4 cups
2 gallons
2 ½ gallons
5 cups
2 ½ gallons
Culinary Math
Food Preparation with Ratios
1. How much water should be added to 1¼ quarts of barley if the
ratio of water to barley is 4 to 1?
2. How much water should be added to ¾ quart of rice if the ratio of
water to rice is 2 to 1?
3. How much water should be added to ¾ gallon of navy beans if the
ratio of water to navy beans is 3 to 1?
4. How much water should be added to 1¾ quarts of
orange juice concentrate to make orange juice if
the ratio of water to concentrate is 3 to 1?
5. How much water should be added to 1½ pints of
lemonade concentrate to make lemonade if the
ratio of water to concentrate is 4 to 1?
6. How much chicken stock should be added to 1¼ quarts of rice if
the ratio of chicken stock to rice is 2 to 1?
7. How much water should be added to ½ gallon of red beans if the
ratio of water to red beans is 3 to 1?
8. How much water should be added to 1¼ pints fruit punch
concentrate if the ratio of water to concentrate is 5 to 1?
9. To make 1 quart of flavored gelatin, the ratio is ½ cup powdered
gelatin to 1 quart of water. Use this information to complete the
chart below:
To Make
Add Gelatin
Add Water
2 cups
3 pints
1 ½ quarts
3 quarts
2 gallons
2 ½ gallons
Culinary Math
2-75
2-76
Culinary Math
Finding Percents of Meat Cuts
Goal:
Students will be able to practice and understand
percents by calculating total weight and percent of
different meat cuts for a side of beef and pork.
Materials:
•
Handout: Sides of Meat
•
Calculators
Preparation:
1. Review the handout and decide how you will present this lesson.
2. Make copies of the handout, one for each student.
Procedure:
1. Begin with a discussion of the different cuts of meat students
regularly purchase. Do they know where bacon comes from? What
is the difference between chuck steak and flank steak? You may
have students who have taken part in butchering hogs or deer or
who work or have worked in the meat department of a grocery
store. Allow these students to share their personal experience and
knowledge about the different cuts of meat. Allow time for
discussion.
2. Distribute the “Sides of Meat” handout and calculators.
3. Explain that a “side” is one half of the complete carcass. Discuss
the handout, including the different cuts of meat that come from
the different areas.
4. Demonstrate how to find the percent of individual blocks, i.e. the
individual block divided by the total weight. Advise students to
round their answers to the nearest tenth of a percent. Tell students
the total percent will hardly ever add up to exactly 100% due to
rounding, however it should be 99% plus some tenths.
Culinary Math
2-77
5. Allow time for students to work collaboratively to complete the
handout.
6. Allow time for questions and discussion. Consider beginning a
discussion with questions such as, “How does learning about the
percent of cuts of meat help you to pass the GED, get a job, or get
into college?,” and “What math concepts did you practice?”
Assessment:
•
Observe student participation and interaction. Encourage questions
when students have difficulty.
Extension:
•
Have students get the grocery store price per pound for each cut
of meat and determine the total cost for each side of meat.
Answers for Handout:
Beef
Side 1
Side 2
495 lbs
466 lbs
Brisket
7.1%
7.3%
Chuck
24.8%
27%
5.1%
4.9%
Loin
10.1%
10.3%
Rib
10.9%
11.2%
Round
21.0%
20.2%
Rump
7.1%
7.1%
Shank
6.1%
4.3%
Short Plate
7.9%
7.7%
100.1%
100.0%
Total Weight
Flank
Total Percent
2-78
Culinary Math
Answers for Handout, continued
Pork
Total Weight
Side 3
Side 4
158.5 lbs
175 lbs
17.7%
17.1%
9.5%
8.0%
30.9%
29.7%
Feet
2.5%
2.3%
Ham
12.6%
14.3%
Hock
1.3%
2.3%
Jowl
6.3%
6.9%
Loin
10.1%
10.3%
Picnic
6.3%
6.3%
Ribs
2.8%
2.9%
100.0%
100.1%
Bacon
Boston Butt
Fat Back
Total Percent
Reference:
Strianese, A. J. and Strianese, P. P. (2001). Math principles for food service
occupations, 4th ed. Albany, NY: Delmar Publishing.
Culinary Math
2-79
Sides of Meat
A side is half of the complete carcass. Find the percentage of each cut
that makes up the cuts for each side of beef shown below. Record
answers in the chart.
Side 1
Chuck
123 lbs
Rib
54 lbs
Shank Brisket
30 lbs 35 lbs
Rump
35 lbs
Loin
50 lbs
Round
104 lbs
Short Plate
39 lbs
Beef
Flank 25 lbs
Side 1
Side 2
Brisket
Total Weight
Side 1 ____________
Chuck
Flank
Loin
Rib
Round
Rump
Shank
Total Weight
Short Plate
Side 2 ___________
Total Percent
Rump
33 lbs
Loin
48 lbs
Rib
52 lbs
Round
94 lbs
Flank 23 lbs
Side 2
2-80
Short Plate
36 lbs
Chuck
126 lbs
Brisket Shank
34 lbs
20 lbs
Culinary Math
Sides of Meat, continued
Find the percentage of each cut that makes up the cuts for each side of
pork shown below. Record answers in the chart.
Side 3
Jowl
10 lbs
Boston Butt
15 lbs
Fat Back 49 lbs
Loin 16 lbs
Ham
20 lbs
1 lb hock
Ribs 4.5 lbs
Picnic
10 lbs
Bacon 28 lbs
2 lb feet
Hock 1 lb
Feet 2 lb
Pork
Side 3
Side 4
Bacon
Total Weight
Boston Butt
Side 3 __________
Fat Back
Feet
Ham
Hock
Jowl
Loin
Picnic
Total Weight
Side 4 _________
Ribs
Total Percent
Side 4
Jowl
12 lbs
Boston Butt
14 lbs
Fat Back 52 lbs
Loin 18 lbs
Ham
25 lbs
2 lb hock
Ribs 5 lbs
Picnic
11 lbs
Bacon 30 lbs
2 lb feet
Hock 2 lb
Feet 2 lb
Culinary Math
2-81
2-82
Culinary Math
Check, Please
Goal:
Students will be able to read a menu, place an
order, and figure the total cost and tip for food
orders.
Materials:
•
Menus
•
Calculators
•
Scrap paper (1/4 sheets)
Preparation:
1. Collect menus from several restaurants, enough so that each pair
of students can have a menu. Try to have a variety of food types
and prices.
2. Obtain scrap paper or cut sheets in fourths.
Procedure:
1. Ask students if they have ever worked as a waitress or waiter. If
they have, ask them to share their experience with taking food
orders and figuring the total check. Allow time for sharing and
discussion.
2. Let students know this activity consists of placing orders for food
and determining the total cost.
3. Allow students to choose a partner.
4. Distribute a menu and several pieces of scrap paper to each pair of
students.
5. Tell students that one of the pair is to act as the waitress/waiter
and the other a hungry customer. The waitress/waiter is to take a
food order from the customer, being careful to record the order
accurately. The customer is to order their favorite meal from the
menu. The waitress/waiter should also write the name of the
Culinary Math
2-83
restaurant and customer (student placing the order) on the back of
the food order.
6. Students should then switch roles and place/take another food
order. They may use the same menu or choose a different menu if
there are extras. Be sure all students get to place at least one food
order.
7. Collect food orders.
8. Distribute calculators and 2 food orders to each pair of students.
Advise students they are to figure the total cost of the food order
including taxes at the local sales tax rate using the menu prices.
9. Allow students to discuss the math used during this activity.
Assessment:
•
Allow students to trade food orders and check the total costs.
Extension:
•
2-84
Allow students to figure tips on the food orders.
Culinary Math
Ordering Food for Large Groups
Goal:
Students will be able to figure the total amount of
food needed to fulfill large orders.
Materials:
•
Handout: Food Order for Banquet
•
Calculators
Preparation:
1. Review the handout to see if it meets the needs of your students.
Adjust as necessary.
2. Make copies of the handout, one for each student.
Procedure:
1. Ask students if they have ever planned a party or event on a budget
for a large group of people. If so, how did they determine what
food they could afford to purchase?
2. Explain that in the food service industry, controlling the amount of
food to order for an event and ordering the right amount helps
control cost and waste. Explain that today’s activity involves
calculating food orders for large events.
3. Distribute calculators and the “Food Order for Banquet” handout.
4. Demonstrate the steps required to determine the amount of each
item to order using an example from the handout:
a. Multiply the amount of the serving size by the number of
people to be served to get the total number of ounces
required.
b. Find the number of ounces in each product.
c. Divide the total ounces required by the ounces per container
to get the number of containers to order.
5. Allow students to work in small groups to complete the handout.
Culinary Math
2-85
Assessment:
•
Observe participation and interaction.
Extension:
•
Assign a cost for each product and have students figure a total cost
for food to serve the indicated number of people.
•
Allow students to plan and prepare food for a fundraiser for a class
trip.
Answers for Handouts:
Food Item, Container Size, and
Serving Size
Baked Beans
1 lb 10 oz cans
5 oz servings
Peas
5 lb box
3 oz servings
Meatballs - 2 ¼ oz each
7 lb box
3 meatballs per serving
Whole Rib Eye
23 lbs
8 oz servings
Frozen Corn
2 ½ lb bag
3 ½ oz serving
Potato Salad
3 ½ lb container
4 oz serving
Fruit Salad
4 lb 4 oz cans
3 oz serving
Chocolate Cheesecake
12 slices per cheesecake
1 slice per serving
Tea
2 gallon containers
8 oz serving
2-86
Servings
per
Container
Purchase Required for
50 people
75 people
5.2
10
15
26.7
2
3
16.6
4
5
46.0
2
2
11.4
5
7
14.0
4
6
22.7
3
4
12.0
5
7
32.0
2
3
Culinary Math
Food Order for Banquet
Determine the number of servings per container or item
and the number of each item to purchase to serve 50 and
75 people. Remember, you cannot buy fractions of cans,
boxes, meat cuts, etc., therefore always round up to the
nearest whole number.
Food Item, Container Size,
and Serving Size
Servings
per
Container
Purchase Required for
50 people
75 people
Baked Beans
1 lb 10 oz cans
5 oz servings
Peas
5 lb box
3 oz servings
Meatballs - 2 ¼ oz each
7 lb box
3 meatballs per serving
Whole Rib Eye
23 lbs
8 oz servings
Frozen Corn
2 ½ lb bag
3 ½ oz serving
Potato Salad
3 ½ lb container
4 oz serving
Fruit Salad
4 lb 4 oz cans
3 oz serving
Chocolate Cheesecake
12 slices per cheesecake
1 slice per serving
Tea
2 gallon containers
8 oz serving
Culinary Math
2-87
2-88
Culinary Math
Healthcare Math
3-2
Healthcare Math
Healthcare Math
Table of Contents
Introduction
3-5
Counting Tablets
3-7
All About Measurement
3-13
Measurement: Terms and Abbreviations
3-17
Measurement and Approximate Equivalents
3-23
Conversion Practice & Dosage Calculations
3-31
Projecting the Need for Nurses
3-39
Estimated Shortages for Registered Nurses
3-43
Healthcare Occupation Growth
3-47
How Satisfied are Registered Nurses?
3-51
Heart Rate, Age, and Gender
3-55
Lung Capacity
3-59
Understanding Medicine Labels
3-63
Healthcare Math
3-3
3-4
Healthcare Math
Introduction
The lesson plans in this chapter offer the
opportunity to inspire student interactions on
some very vital issues, and to incorporate math
into those discussions. As students learn about
matters ranging from heart health to career
opportunities in healthcare professions, they
get to practice and enhance math skills in a
context that makes the importance of those
skills obvious to all. Once students see how
math is used in the contexts addressed by some
of the lesson plans in this chapter, they are
likely to remember the value of those particular
math applications.
With the continuing aging of the American population, job opportunities
in healthcare professions are expected to increase dramatically. Students
may not be aware of the variety of careers in the healthcare industry, or
of the educational requirements for those careers. By putting math
practice in the framework of healthcare careers, you can also educate
students about those career opportunities.
Healthcare math incorporates measuring calculations and skills that can
benefit students in other aspects of life. Conversions between units of
measurement are required in other professions, as well as in healthcare.
The phrase, “math drill and practice,” invariably evokes an “Oh no! How
boring!” reaction, so please don’t tell anyone that these lesson plans
incorporate math with drill and practice. Students need the mental math
and paper and pencil practice, as well as the calculator practice involved
in completing the activities. Students will actually find the math
applications interesting, challenging, and even fun.
Whereas the preceding paragraph could be used as an introduction to any
chapter in this training manual, it seems particularly applicable to this
chapter. If you, the Adult Basic Skills instructor, inspire interesting
discussions, and possibly debates, about healthcare as part of classes
using these lesson plans and activities, student interest should be piqued
to the point that completing these math exercises becomes fun.
Healthcare Math
3-5
3-6
Healthcare Math
Counting Tablets
Goal:
Students will be able to count, add, subtract, multiply
and/or divide using the context of filling
prescriptions.
Materials:
•
Dry beans, beads, or tablet-size candy
•
A variety of empty medicine bottles
•
Bottle labels, provided or make your own
•
Tape
•
Two envelopes
Preparation:
1. Obtain 8 different kinds of dry beans, beads, and/or candy
(Skittles™, M&M’s™, or other tablet-size candy), in sufficient
quantities to fill bulk size medicine bottles. Refer to the labels
provided with this activity to determine the approximate amount
you will need of each.
2. Obtain medicine bottles in several different sizes. Your local
pharmacy may donate or supply these at a nominal charge. Be sure
you have larger sizes to use as bulk containers and smaller sizes
for filling prescriptions. You will need 8 bulk size bottles and 48
smaller size bottles.
3. Make 1 copy of the bulk labels provided and 2 copies of the
prescription labels provided. Cut the labels apart. Put all the bulk
labels in one envelope and the prescription labels in another
envelope.
Procedure:
1. Advise students that today they are going to simulate two jobs: (1)
working in a company that supplies medicine to the local
pharmacies and (2) working as a pharmacist to fill prescriptions.
Healthcare Math
3-7
2. If needed, demonstrate the entire process (Steps 3-7) to the class
prior to students beginning to fill the prescriptions.
3. Give each student (or pair of students) a bulk label and access to
the larger medicine bottles and tablets (beans, beads, or candy).
4. Advise students to pay careful attention to the label instructions as
they fill their prescriptions.
5. Allow time for students to choose a bottle and fill it with the
indicated number of tablets.
6. Once the bulk prescription is filled, the student should initial the
“filled by” line and tape the label to the bottle. The filled bottle
should be placed at the front of the class.
7. After the bulk bottles are filled, students use the bulk bottles of
tablets to fill individual prescriptions.
8. Give each student (or pair of students) several prescriptions to fill.
Be sure the prescriptions given to each student are for different
medicines and have different instructions.
9. Allow time for students to fill their prescriptions, tape the label to
the bottle, and return their filled prescription to the front of the
room.
Assessment:
•
Observe the methods students choose to count the correct number
of tablets for each bottle.
•
After all prescriptions are filled, allow students to randomly check
other prescriptions to see if they were correctly filled. Bottles with
errors should be kept separate for discussion. Discuss the errors
found, if any. Ask questions such as:
•
3-8
•
Why is it important to fill prescriptions correctly?
•
What might happen if the wrong medication is given?
•
What might happen if the incorrect number of tablets is
given?
Discuss different counting techniques observed or suggested by
students in terms of accuracy and reliability.
Healthcare Math
Extension:
•
Ask if any students think they would like to become a pharmacist
or pharmacist’s assistant and why or why not. Discuss duties of a
pharmacist other than filling prescriptions.
•
Do the same exercise using liquid (colored water) as the medicine.
Have students determine the number of teaspoons or tablespoons
needed to fill prescriptions. Students complete the task by
measuring and then checking their results mathematically.
Healthcare Math
3-9
Labels for Bulk Bottles
Make a copy and cut apart each label. Be sure bottles are large enough to
hold the indicated amounts.
Medicine
Q
Medicine
R
400 tablets
400 tablets
Filled by: _______________________
Filled by: _______________________
Medicine
S
Medicine
T
600 tablets
600 tablets
Filled by: _______________________
Filled by: _______________________
Medicine
U
Medicine
V
840 tablets
840 tablets
Filled by: _______________________
Filled by: _______________________
Medicine
W
Medicine
X
1008 tablets
1008 tablets
Filled by: _______________________
Filled by: _______________________
3-10
Healthcare Math
Labels for Prescription Bottles
Take 1 tablet 4 times per
Take 2 tablets 3 times per
Take 1 tablet 3 times per
day for 15 days.
day for 2 weeks.
day for 15 days.
Medicine Q
Medicine Q
Medicine Q
Quantity _____
Quantity _____
Quantity _____
Take 1 tablet 4 times per
Take 2 tablets 3 times per
Take 1 tablet 3 times per
day for 2 weeks.
day for 12 days.
day for 2 weeks.
Medicine R
Medicine R
Medicine R
Quantity _____
Quantity _____
Quantity _____
Take 1 tablet 3 times per
Take 2 tablets twice per
Take 2 tablets 4 times per
day for 24 days.
day for 2 weeks.
day for 3 weeks.
Medicine S
Medicine S
Medicine S
Quantity _____
Quantity _____
Quantity _____
Take 1 tablet 3 times per
Take 2 tablets twice per
Take 2 tablets 4 times per
day for 24 days.
day for 2 weeks.
day for 3 weeks.
Medicine T
Medicine T
Medicine T
Quantity _____
Quantity _____
Quantity _____
Take 1 tablet 4 times per
Take 2 tablets 3 times per
Take 2 tablets twice per
day for 30 days.
day for 30 days.
day for 30 days.
Medicine U
Medicine U
Medicine U
Quantity _____
Quantity _____
Quantity _____
Take 1 tablet 4 times per
Take 2 tablets 3 times per
Take 2 tablets twice per
day for 30 days.
day for 30 days.
day for 30 days.
Medicine V
Medicine V
Medicine V
Quantity _____
Quantity _____
Quantity _____
Take 2 tablets 4 times per
Take 2 tablets 3 times per
Take 2 tablets 2 times per
day for 4 weeks.
day for 4 weeks.
day for 4 weeks.
Medicine W
Medicine W
Medicine W
Quantity _____
Quantity _____
Quantity _____
Take 2 tablets 4 times per
Take 2 tablets 3 times per
Take 2 tablets 2 times per
day for 4 weeks.
day for 4 weeks.
day for 4 weeks.
Medicine X
Medicine X
Medicine X
Quantity _____
Quantity _____
Quantity _____
Healthcare Math
3-11
3-12
Healthcare Math
All About Measurement
Goal:
Students will be able to see, work with, and
recognize differences between units of
measurement and their equivalents.
Materials:
•
Variety of containers in different sizes and measuring instruments
•
Tea or other colored liquid, 1-2 gallons
•
Tables to hold the containers and measuring instruments
•
One display table
•
Handout: Systems of Measurement and Approximate Equivalents
•
Index cards
•
Markers
•
Tape
Preparation:
1. Collect a variety of containers, medicine bottles, and objects that
would hold or simulate the different measurements. Try to have
containers or objects for all of the measurements listed on the
handout.
2. Collect a variety of measuring instruments for each of the
measurements listed on the handout. Note: If you do not have the
instruments to actually allow students to do all of the
measurements, make samples of each measurement so students
can see exactly how much each measurement is, then adjust the
remainder of the activity.
3. Make 1-2 gallons of colored liquid, such as tea.
4. Set up a table in front of the class that has all the different
containers, measuring instruments, and colored water. If you have
a large class, you may want to set up different tables/stations
Healthcare Math
3-13
around the classroom so that all students will have a place to work
in a small group.
5. Set up an empty display table.
6. Make copies of the “Systems of Measurement and Approximate
Equivalents” handout for each student.
Procedure:
1. Begin by advising students that class today is about measurement.
Ask students questions such as, “How much is a cup? a teaspoon?
a quart?” Then ask about common metric measurements such as a
liter and a kilogram.
2. Allow students to choose from the table a container they think is
the closest to the size of each measurement.
3. After discussing some of the more familiar measurements, ask
about some of the less familiar ones used in healthcare
professions. Less familiar measurements may include 1 milliliter, 5
milliliters, 15 milliliters, 30 milliliters, cubic centimeters (cc’s), or
10 milligrams. Ask students if they have “mental images” of what
these measurements look like. Ask if they can identify containers
that would hold these approximate amounts or objects that would
be about that size. Note that most students will not be able to do
this.
4. Advise students that by the end of class today everyone will have a
better understanding of these measurements and will have “mental
images” to take with them.
5. Demonstrate how to make each of the measurements discussed
and share with students how these measurements might be used
when administering medicine.
6. Distribute the “Systems of Measurement & Approximate
Equivalents” handout. Remind students that the table shows
approximate equivalents, meaning they are not exact; however,
they are used in the healthcare industry as given on the table. For
example, the table states 1 liter is equivalent to 1 quart, however a
more accurate measurement would be 1.1 quarts to 1 liter for
liquid measurements. Also, the table is more accurate with weight,
i.e., 1 kilogram is equivalent to 2.2 pounds. Discuss why the degree
3-14
Healthcare Math
of accuracy for converting liters and quarts may not be as
important as converting kilograms and pounds.
7. Advise students to make a display table showing the measurements
listed on the handout.
8. Allow students to form pairs and assign each pair several
measurements to make and display on the table.
9. Advise students to make their assigned measurement(s) then make
a label for their measurement(s) using the index cards, markers,
and tape.
Assessment:
•
Observe students as they make the assigned measurements.
•
Keep watch on the displays. If something is in question, ask
students to discuss and measure again until all measurements are
accurately displayed.
•
Allow time for students to reflect on what they learned from this
activity.
Healthcare Math
3-15
Systems of Measurement & Approximate Equivalents
There are three measurement systems commonly used in
healthcare: the metric, apothecary, and household
systems. Approximate equivalents were developed so
healthcare professionals can more easily compare
measured amounts between the systems.
VOLUME
Metric
Apothecary
Household
1 milliliter (ml) (cc)*
15-16 gtts (gtts = drops)
5 milliliters (ml)
1 teaspoon (t)
75 drops (gtts)
15 milliliters (ml)
1 tablespoon (T)
3 teaspoons (t)
30 milliliters (ml)
1 ounce (oz)
2 tablespoons (T)
240 milliliters
8 ounces (oz)
1 cup (c)
1000 milliliters (1 liter)
1 quart (q)
1 quart (q)
*Cubic centimeters (cc’s) and milliliters (ml’s) are the same equivalents.
Weight
Metric
Apothecary
60 milligrams (mg)
Household
1 grain (gr)
16 ounces (oz)
1 kilogram (kg)
1 pound (lb)
2.2 pounds (lb)
Metric Weight
1 milligram (mg) = 1000 micrograms (mcg)
1 gram (g or gm) = 1000 milligrams (mg)
1 kilogram (kg) = 1000 grams (g or gm)
Metric Weight to Volume
1 gram (g or gm) = 1 milliliter (ml) (approximately)
3-16
Healthcare Math
Measurement: Terms and Abbreviations
Goal:
Students will be able to play games that require the
matching of common measurement terms with their
abbreviations. Through playing the games students
will learn and review the correct abbreviations used
for measurement terms.
Materials:
•
Sets of “Measurement Terms and Abbreviations” cards
Preparation:
1. Review the measurement terms and abbreviations provided on the
cards at the end of this activity. You may wish to delete or add
cards to the set given. Blank cards are provided.
2. Make a copy of the “Measurement Terms and Abbreviations” cards
on cardstock. Cut the cards apart to make one set. Make enough
sets of cards so each group of 2-4 students can have a set.
3. Be sure each card set is thoroughly shuffled.
4. Decide which game (Matching or Concentration) the students will
play. Rules are given on the following page.
Procedure:
1. Briefly review the measurement terms and abbreviations students
will be using to play the game.
2. Explain the rules for the game.
3. Allow students to form groups of 2-4 players. Give each group one
set of the “Measurement Terms and Abbreviations” cards.
4. Allow students to play until all groups finish at least one game.
5. Be sure to collect the cards for future use.
Healthcare Math
3-17
Assessment:
•
As students play the game, observe their involvement.
Extension:
•
Allow students to make different rules for the games.
•
Allow students to make rules for a new game.
Rules for Matching Card Game:
1. Tell the students that when you say “GO,” they are to spread the
cards on the table, face up, so that all students can look for
matches.
2. Students within each group work together to pair up each term
with its correct abbreviation as quickly as possible. When they
have finished, they should announce they are done.
3. When a team announces they have finished, all groups stop
working while their matches are checked for correctness. If there
are errors, all groups begin to pair up their cards again.
4. Repeat until one group has correctly matched all their cards. This
team is the winner.
Rules for Concentration Card Game:
1. Have one student place the cards face down on the table so the
rows and columns of cards make a rectangle. Space should be left
between rows and columns so that cards can easily be turned over.
2. Students take turns choosing two cards. For each turn, the student
turns two cards face up to see if they match. If the cards match, the
student keeps the two cards. If not, the student replaces the cards
face down in the same position.
3. Students continue to take turns until all the cards have been
matched.
4. The winner is the student with the most pairs.
3-18
Healthcare Math
Measurement Terms and Abbreviations
milliliter
ml
cubic centimeter
cc
drops
gtts
teaspoon
t
Healthcare Math
3-19
Measurement Terms and Abbreviations
3-20
tablespoon
T
ounce
oz
cup
c
quart
q
Healthcare Math
Measurement Terms and Abbreviations
liter
l
milligram
mg
grain
gr
pound
lb
Healthcare Math
3-21
Measurement Terms and Abbreviations
3-22
kilogram
kg
microgram
mcg
Healthcare Math
Measurements and Approximate
Equivalents
Goal:
Students will be able to play games that require
matching approximate equivalent measurements.
Through playing the games students learn and
review equivalencies used in the healthcare industry.
Materials:
•
Sets of “Equivalent Measurements” cards
Preparation:
1. Review the measurements and approximate equivalents provided
on the cards at the end of this activity. You may wish to delete or
add cards to the set given. Blank cards are provided.
2. Make a copy of the “Equivalent Measurements” cards on cardstock.
Cut the cards apart to make one set. Make enough sets of cards so
that each group of 2-4 students can have a set.
3. Be sure each card set is thoroughly shuffled or have students mix
up the cards prior to using them.
4. Decide which game (Matching or Concentration) the students will
play. Rules are included on the following page.
Procedure:
1. Briefly review the measurements and approximate equivalents
students will be using to play the game.
2. Explain the rules for the game.
3. Allow students to form groups of 2-4 players. Give each group one
set of the “Equivalent Measurements” cards.
4. Allow students to play until all groups finish at least one game.
5. Be sure to collect the cards for future use.
Healthcare Math
3-23
Assessment:
•
As students play the game, observe their involvement.
Extension:
•
Allow students to make different rules for the games.
•
Allow students to make rules for a new game.
Rules for Matching Card Game:
1. Tell the students that when you say “GO,” they are to spread the
cards on the table, face up, so that all students can look for
matches.
2. Students within each group work together to pair up each
equivalent with a different measurement as quickly as possible.
When they have finished, they announce they are done. Note: Do
not pair cards with same measurements.
3. When a team announces they have finished, all groups stop
working while their matches are checked for correctness. If there
are errors, the game continues.
4. Repeat until one group has correctly matched all their cards. This
team is the winner.
Rules for Concentration Card Game:
1. Have one student place the cards face down on the table so the
rows and columns of cards make a rectangle. Space should be left
between rows and columns so that cards can easily be turned over.
2. Students take turns choosing two cards. The student turns two
cards face up to see if they match. If the cards match (different
measurement but equivalent), the student keeps the two cards. If
not, the student replaces the cards face down in the same position.
3. Students continue to take turns until all the cards have been
matched.
4. The winner is the student with the most equivalent pairs.
3-24
Healthcare Math
Equivalent Measurements
Healthcare Math
1 ml
15-16 gtts
1 ml
1 cc
5 ml
1t
1t
75 gtts
3-25
Equivalent Measurements
3-26
15 ml
1T
1T
3t
30 ml
1 oz
30 ml
2T
Healthcare Math
Equivalent Measurements
240 ml
8 oz
8 oz
1c
1000 ml
1l
1l
1 qt
Healthcare Math
3-27
Equivalent Measurements
3-28
60 mg
1 gr
16 oz
1 lb
1 kg
2.2 lbs
1 mg
1000 mcg
Healthcare Math
Equivalent Measurements
Healthcare Math
1g
1000 mg
1 kg
1000 g
1g
1 ml
3-29
3-30
Healthcare Math
Conversion Practice and Dosage
Calculations
Goal:
Students will be able to read, interpret, and use a
table to set up ratios and proportions to solve
problems involving conversions.
Materials:
•
Handouts: (1) Systems of Measurement & Approximate Equivalents
(2) Conversion Practice
(3) Dosage Calculations
•
Measuring containers and samples of different measurements
•
Calculators
Preparation:
1. Make copies of the handouts for each student.
2. Obtain measuring containers and samples of different
measurements so students can see the similarities and differences.
Procedure:
1. Give each student a copy of the “Systems of Measurement &
Approximate Equivalents” handout.
2. Explain the different measurements used on the handout. Use the
measuring containers and samples to demonstrate the different
measurements.
3. Demonstrate that 1 liter is closer to 1.1 quarts than to 1 quart. Ask
why that might not be considered significant in medical applications.
4. Discuss the importance of accurate conversions and calculations in
the healthcare industry.
5. Give each student a copy of the “Conversion Practice” handout.
Review the concepts of ratio and proportion. Demonstrate several
Healthcare Math
3-31
examples and then allow students to work together or
independently to solve the remainder of the problems.
6. Give each student a copy of the “Dosage Calculations” handout.
Demonstrate several examples then allow students to work
together or independently to solve the remainder of the problems.
7. Allow students to share solutions and discuss areas of difficulty in
solving the problems.
Assessment:
•
Ask students to write and solve a word problem similar to the
problems on the handout. Collect, review, and give feedback.
Extension:
•
Use the student-written word problems for more practice and
review in a future class.
•
Bring in news stories or news clips of people who have suffered
injury or death due to errors in the amount or kind of medication
given. Share and discuss the stories.
•
Allow students to search the Internet for information about people
who have suffered injury or death due to errors in the amount or
kind of medication given. Allow students to share their findings.
•
Invite a guest speaker (nurse and/or pharmacist) to visit the class
to discuss how they use math to complete tasks on the job. Allow
time for students to ask the guest speaker(s) about other aspects of
their job. You may want to have students decide on a list of
questions ahead of time.
Answers for Handouts:
•
An answer key is provided at the end of this lesson.
Reference:
Melton, C., Gaffney, B., McAlister, C. & Shapiro, S. (2006). Fundamentals of
mathematics for nursing. Retrieved January 15, 2007, from
http://www.adn.eku.edu/math.pdf
3-32
Healthcare Math
Systems of Measurement & Approximate Equivalents
There are three measurement systems commonly used in
healthcare: the metric, apothecary, and household systems.
So that healthcare professionals can more easily compare
measured amounts in the systems, approximate equivalents
have been developed. Because the measures are not exactly
equal, a conversion that takes more than one step will not
produce as accurate a value as a conversion that takes only one step.
Rule: Always convert from one unit of measure to another by the
shortest number of steps possible.
VOLUME
Metric
Apothecary
Household
1 milliliter (ml) (cc)*
15-16 gtts (gtts = drops)
5 milliliters (ml)
1 teaspoon (t)
75 drops (gtts)
15 milliliters (ml)
1 tablespoon (T)
3 teaspoons (t)
30 milliliters (ml)
1 ounce (oz)
2 tablespoons (T)
240 milliliters (ml)
8 ounces (oz)
1 cup (c)
1000 milliliters (1 liter)
1 quart (q)
1 quart (q)
*Cubic centimeters (cc’s) and milliliters (ml’s) are the same equivalents.
Weight
Metric
Apothecary
60 milligrams (mg)
Household
1 grain (gr)
16 ounces (oz)
1 kilogram (kg)
1 pound (lb)
2.2 pounds (lb)
Metric Weight
1 milligram (mg) = 1000 micrograms (mcg)
1 gram (g or gm) = 1000 milligrams (mg)
1 kilogram (kg) = 1000 grams (g or gm)
Metric Weight to Volume
1 gram (g or gm) = 1 milliliter (ml) (approximately)
Healthcare Math
3-33
Conversion Practice
Review: One way to solve conversion problems is to set
up a proportion problem. There are four basic steps to
solving proportion problems:
1. Set up a known ratio.
2. Set up a proportion with known and desired
(unknown) units. Use x for the quantity that is unknown.
3. Cross multiply.
4. Solve for x.
Directions: Set up a ratio and proportion to solve each of the following
problems.
1.
0.5 gm = ______ mg
11. 3 t = ________ ml
2.
3000 mcg = _______ mg
12. 1.25 l = ________ml
3.
1.34 kg = ________ mg
13. 320 mg = ________ g
4.
0.05 l = ________ ml
14. 60 lbs = ________ kg
5.
5.07 kg = ________ g
15. 45 ml = ________ oz
6.
3 t = ______ gtts
16. 750 mcg = ________ mg
7.
1 ½ T = ________ t
17. 1 T = ________ oz
8.
5 T = ________ oz
18. 4 kg = ________ lbs
9.
12 t = _______ T
19. 3 gr = ________ mg
10.
8 oz = _______ T
20. 300 gtts = ________ t
3-34
Healthcare Math
Dosage Calculations
Medications may be ordered in a form or amount
different from what is available. The pharmacist,
nurse, or parent must then calculate the right dosage.
It is important that healthcare professionals are
100% correct 100% of the time.
1.
60 mg of medication are ordered. Tablets are available which have
30 mg of medication in each of them. How many tablets are needed
to give 60 mg?
2.
2 tablespoons of a liquid every 2 hours for a 12-hour period are
ordered. How many mls of the drug will the patient receive over the
12-hour period?
3.
A patient is to receive 2 gm of a drug. The drug comes 500 mg/5ml.
Each vial contains 10 mls. How many vials would you need?
4.
3 gm of medication are ordered. The tablets available have 1 gm per
tablet. How many tablets should be given?
5.
.25 mg of medication are ordered. The medication comes in 0.05
mg/ml. How many mls will the patient receive?
6.
An order reads: Give “Drug A” 3 mg/kg per day in two divided doses.
The patient weighs 22 lbs. How many mgs should the patient receive
per dose?
7.
1 oz of Maalox is ordered. The only measuring instrument available
is a tablespoon. How many tablespoons should be given?
8.
A patient is ordered to drink 1 gallon of fluid per day. The only
measuring instrument available is an 8 oz cup. How many cups
should the patient drink per day?
Healthcare Math
3-35
Dosage Calculations, continued
9.
Ordered Digoxin 0.125 mg by mouth. Have Digoxin 0.25 mg per
tablet. How many tablets should be given?
10. Ordered Cipro 500 mg by mouth. Have Cipro 250 mg per tablet. How
many tablets should be given?
11. Ordered Nystalin 400,000 units. Have Nystalin 200,000 units per
teaspoon. How many teaspoons
should be given?
12. The patient is to receive Phenegran
Expectorant 2 t po qid. How many ml
should the patient receive per dose?
How many ml per day?
Note:
13. The doctor orders 15 cc po tid. How
many tablespoons should you give
per dose? How many tablespoons per
day?
tid = 3 times per day
14. You must give your patient gr 0.5 po
stat. How many mg should the
patient receive?
prn = as needed
po = by mouth
qid = 4 times per day
stat = immediately
q4hrs = every 4 hours
scored = tablets made to
be cut in half as needed
15. The order is for Tylenol gr 10 po
q4hrs prn for headache. How many mg should you give per dose?
16. Ordered Lasix 60 mg po stat. You have scored tablets that contain
Lasix 40 mg. What will you give?
17. Ordered Atropine gr 1/300 po before surgery. You have tablets that
contain Atropine gr 1/150. What will you give?
3-36
Healthcare Math
Conversion Practice Answer Key
1.
0.5 g = 500 mg
11. 3 tsp = 15 ml
2.
3000 mcg = 3 mg
12. 1.25 l = 1,250 ml
3.
1.34 kg = 1,340,000 mg
13. 320 mg = .32 g
4.
0.05 l = 50 ml
14. 60 lbs = 27.23 kg
5.
5.07 kg = 5070 g
15. 45 ml = 1.5 oz
6.
3 t = 225 gtts
16. 750 mcg = .75 mg
7.
1 ½ T = 4.5 t
17. 1 T = ½ oz
8.
5 T = 2 ½ oz
18. 4 kg = 8.8 lbs
9.
12 t = 4 T
19. 3 gr = 180 mg
10. 8 oz = 16 T
20. 300 gtts = 4 t
Dosage Calculations Answer Key
1.
2.
3.
4.
5.
6.
2 tablets
180 ml
2 vials
3 tablets
5 ml
weight: 10 kg, daily dosage:
30 mg, 15 mg per dose
7. 2 T
8. 16 cups
Healthcare Math
9.
10.
11.
12.
13.
14.
15.
16.
17.
½ tablet
2 tablets
2t
10 ml per dose, 40 ml per day
1 T per dose, 3 T per day
30 mg
600 mg
1 ½ tablets
½ tablet
3-37
3-38
Healthcare Math
Projecting the Need for Nurses
Goal:
Students will be able to read and interpret a
line graph that discusses national trends for
registered nurses. Through discussion and
working with the graph, students will gain
insight into the field of nursing as a career.
Materials:
•
Handout: Supply and Demand for Registered Nurses
•
Index cards, one for each student
Preparation:
1. Review the handout.
2. If desired, add additional questions.
3. Make copies of the handout for each student.
Procedure:
1. Distribute the “Supply and Demand for Registered Nurses”
handout.
2. Allow a few minutes for students to look at the graph and discuss
it in small groups. Ask students to share what they think the graph
shows. Facilitate the discussion by asking questions such as:
a. What are some reasons the number of nurses is projected to
decrease over the years? Discussion might include ideas such
as lower pay since many jobs pay more, the stress level of
the job, the risk of being exposed to disease, retirement, not
enough training programs, etc.
b. Why do you think there is such an increase in the number of
needed nurses? Discussion might include ideas such as a
larger older population needing nursing care, people living
longer, more illness, etc.
Healthcare Math
3-39
c. Do you think that nursing would be a good career choice for
you? Other adult students? Why or why not?
3. After discussing the graph, allow time for students to answer the
questions on the handout and discuss their answers with each
other.
Assessment:
•
Give each student an index card. Ask students to write their
multiple-choice question (from number 5 on the handout) on the
card and record the answer on the back.
•
Collect the index cards. Choose from the student-written multiplechoice questions to make practice sheets, quizzes, and/or tests for
future assessment.
•
If students are studying for the GED, have them complete several
GED-type practice questions that address similar concepts.
Extension:
•
Have students conduct research on the Internet to investigate
answers to the three questions asked in #2 of the Procedure section
above. Allow students to share their findings.
Answers for Handout:
1. approximately 2.8 million or 2,800,000
2. decrease (beginning @ 2012)
3. approximately 2.8-2= 0.8 million or 800,000
4. Yes, demand exceeds supply and the difference will increase
5. Answers will vary
Reference:
Biviano, M. (2003, April 23). The nursing crisis: Improving job satisfaction
and quality of care. (Slide presentation). Rockville, MD: Agency for
Healthcare Research and Quality. Retrieved January 15, 2007, from
www.ahrq.gov/news/ulp/workforctel/sess1/bivianotxt.htm
3-40
Healthcare Math
Supply and Demand for Registered Nurses
The graph below shows supply and demand projections for full-time
registered nurses in the United States from the year 2000 to 2020.
Based on the above graph:
1. Approximately how many nurses will be needed by 2020?
2. Is the supply of nurses projected to increase or decrease between
2010 and 2020?
3. What is the projected shortfall of nurses in 2020, i.e. approximately
how many nurse positions will be unfilled?
4. Do you believe jobs will be available for new registered nurses for
the next 5 years?
5. Write one multiple-choice question with four answers. One of your
answers should be the correct answer and the other three should
be distracters that you think others might choose if they did not
understand the graph.
Healthcare Math
3-41
3-42
Healthcare Math
Estimated Shortages for Registered
Nurses
Goal:
Students will be able to read and interpret
picture graphs that depict the states with and
without shortages for registered nurses for the
years 2000 and 2020. Through discussion and
working with the graphs, students gain insight into the availability of
nurses now and in the future.
Materials:
•
Handout: Shortages for RNs
Preparation:
1. Review the graphs and questions included on the handout.
2. If desired, add additional questions.
3. Make copies of the handout for each student.
Procedure:
1. Distribute the “Shortages for RNs” handout.
2. Discuss the graphs.
3. Allow students to pair up to complete the handout.
4. After discussing the graph, allow time for students to answer the
questions on the handout and discuss their answers with each
other.
Assessment:
•
If students are studying for the GED, have them complete several
GED-type practice questions that address similar concepts.
Healthcare Math
3-43
Extension:
•
Allow students to choose one of the states with a shortage both in
2000 and 2020. Then have students conduct research on the
Internet to investigate the nursing shortage in their chosen state,
i.e. find actual statistics on the estimated shortages.
•
Have students write a short summary of their findings to share.
•
Allow students who chose the same state to work together to
research and write their summary.
Answers for Handout:
1. No, NC did not have a nurse shortage in 2000.
2. 20 states did not have nurse shortages in 2000.
3. 60%
4. West, every West Coast state had a shortage, but 5 East Coast states
did not.
5. 6 are shown (Kansas, Iowa, Kentucky, Ohio, Vermont, and Hawaii)
6. Yes, NC is projected to have a shortage in 2020.
7. 88% (44 out of 50 states)
Reference:
Biviano, M. (2003, April 23). The nursing crisis: Improving job satisfaction
and quality of care. (Slide presentation). Rockville, MD: Agency for
Healthcare Research and Quality. Retrieved January 15, 2007, from
www.ahrq.gov/news/ulp/workforctel/sess1/bivianotxt.htm
3-44
Healthcare Math
Shortages for RNs
Based on the graphs on the
right, answer the following
questions:
1. In 2000, was North
Carolina one of the states
estimated to have a
shortage of RNs?
2. In 2000, how many states
were not estimated to
have a shortage of RNs?
3. What percent of states
were estimated to have a
shortage of RNs in 2000?
In 2000, 30 states were estimated
to have shortages for RNs.
4. In 2000, did the percent
of states with a shortage
of RNs seem to be higher
on the East Coast or
West Coast?
5. In 2020, how many
states are not expected
to have a shortage of
RNs?
6. Is North Carolina
projected to have a
shortage of RNs in 2020?
7. What is the percentage of
states projected to have a
shortage of RNs in 2020?
Healthcare Math
By 2020, the number of states to
have shortages will grow to 44.
3-45
3-46
Healthcare Math
Healthcare Occupation Growth
Goal:
Students will be able to read, interpret, and
answer questions about a table depicting
healthcare job openings from 2000 to 2010.
Through discussion students gain insight into
possible demands for increased healthcare
professionals in the future.
Materials:
•
Handout: Healthcare Occupation Growth from 2000 to 2010
Preparation:
1. Review the handout.
2. If desired, add additional questions.
3. Make copies of the handout for each student.
Procedure:
1. Brainstorm with students about jobs in the healthcare industry
that might be impacted by the aging population and list the jobs on
the board.
2. Ask students to choose one of the jobs and share how and why
they feel that job will be impacted to a greater extent than some of
the other jobs listed.
3. Distribute and discuss the “Healthcare Occupation Growth from
2000 to 2010” handout.
4. Allow time for students to complete the questions and share their
answers.
5. Allow students to self-assess their work. Be sure those who failed
to answer correctly understand their errors and/or workable
solution procedures.
Healthcare Math
3-47
Assessment:
•
Have students complete similar type questions from GED
workbooks or practice tests.
Extension:
•
Allow students to research the healthcare jobs to find additional
information about the job openings. They might research salary
information such as current and estimated future salaries. They
may also look at the role demographics play in salaries, i.e., do
people who have similar jobs in other states make similar salaries?
What about rural areas versus cities?
•
Ask them to keep a list of their findings to share with the class.
Answers for Handout:
1. Registered nurses
2. LPN and personal/home care aides
3. 2,516,000
4. 39.9% or 40%
Reference:
Biviano, M. (2003, April 23). The nursing crisis: Improving job satisfaction
and quality of care. (Slide presentation). Rockville, MD: Agency for
Healthcare Research and Quality. Retrieved January 15, 2007, from
www.ahrq.gov/news/ulp/workforctel/sess1/bivianotxt.htm
3-48
Healthcare Math
Healthcare Occupation Growth from 2000 to 2010
The Bureau of Labor Statistics (BLS) forecasts that employment in all
healthcare occupations will grow by 29% between 2000 and 2010, twice
as fast as the rest of the economy.
Forecast of Total Job Openings Due to Growth
and Replacements Between 2000 and 2010
Healthcare Occupation
Registered Nurses
Number of Job
Openings
1,004,000
Nurse Aides, Orderlies, Attendants
498,000
Home Health Aides
370,000
Personal and Home Care Aides
322,000
Licensed Practical Nurses
322,000
Of the healthcare jobs listed in the table above:
1. Which is expected to have the largest number of job openings?
2. Which is expected to have the least number of job openings?
3. What is the total projected number of job openings?
4. What percent of the total job openings are for registered nurses?
Healthcare Math
3-49
3-50
Healthcare Math
How Satisfied are Registered Nurses?
Goal:
Students will be able to read and interpret a bar
graph that shows job satisfaction for registered
nurses.
Materials:
•
Handout: Registered Nurses’ Job Satisfaction
Preparation:
1. Review the graphs and questions included on the handout.
2. If desired, add additional questions.
3. Make copies of the handout for each student.
Procedure:
1. Distribute the “Registered Nurses’ Job Satisfaction” handout.
2. Discuss the graph and allow students to ask questions.
3. Allow students to pair up, discuss, and complete the handout.
Assessment:
•
Allow students to check their work and discuss correct answers.
Extension:
•
Have students discuss other ways the same information could have
been shown.
•
Have students write a newspaper article to go with the graph.
•
Have students research job satisfaction data for other careers, such
as public service, teaching, self-employment, etc.
Healthcare Math
3-51
Answers for Handout:
1. Index x-axis from 0, label the x-axis, title the graph, label the y-axis
(percents)
2. Ambulatory care and student health
3. 71.7 – 66.6 = 5.1%
4. 100-65.4 = 34.6%
5. Student health, only 20.8% are dissatisfied
Reference:
Biviano, M. (2003, April 23). The nursing crisis: Improving job satisfaction
and quality of care. (Slide presentation). Rockville, MD: Agency for
Healthcare Research and Quality. Retrieved January 15, 2007, from
www.ahrq.gov/news/ulp/workforctel/sess1/bivianotxt.htm
3-52
Healthcare Math
Registered Nurses’ Job Satisfaction
The graph below shows the percent of registered nurses who are satisfied
in their jobs, by employment setting. This graph is based on data
collected in 2000.
1. Examine the graph above. State at least two things that should be
done to improve the graph.
Answer the following questions based on the graph above:
2. In what two settings are registered nurses most likely to be
satisfied with their jobs?
3. How much more likely are public health nurses to be satisfied with
their jobs than hospital nurses, i.e., what is the difference in
percentages?
4. What percent of nursing home nurses are not satisfied with their
jobs?
5. What area has the least number of dissatisfied nurses?
Healthcare Math
3-53
3-54
Healthcare Math
Heart Rate, Age, and Gender
Goal:
Students will be able to collect, organize, and
analyze data relating to age and heart rate at rest,
walking, and running. Data analysis includes
graphing, finding equation of a line, making
predictions based on “line of best fit,” finding mean,
and interpreting results.
Materials:
•
Handouts: (1) Heart Rate Data Collection
(2) Heart Rate Data Analysis
•
3-4 clocks or watches with second hand
•
Graph paper
•
Calculators
Preparation:
1. Plan two classes to complete this activity. Day 1 for data collection
and Day 2 for data analysis.
2. Make copies of the handouts, one for each student.
Procedure:
1. Day 1-Collecting Data: Discuss heart rates and what happens when
you exercise. Tell students that today’s class will involve them
collecting data with relation to gender, age, and heart rates after
resting, walking, and running.
2. Demonstrate how to take heart rates (pulse). Be sure students have
access to watches or clocks with second hands. Have all students
take their heart rate while resting, i.e. find pulse, count beats for 15
seconds and multiply by 4 to get beats per minute. Stress the
importance of accurate data collection.
3. Distribute the “Heart Rate Data Collection” handout. Have students
collect and record data on the handout. Allow time for students to
Healthcare Math
3-55
collect some of the data during class. If time does not permit
students to collect all the data during class, make the assignment
for students to collect data on several adult (16+ years of age)
family members or friends.
4. Day 2-Analyzing Data: Allow students to share the data collected so
that each student has their chart complete, i.e. data on 20 different
individuals. Remind students their charts will be different since
they collected data on different individuals.
5. Distribute the “Heart Rate Data Analysis” handout, graph paper,
and calculators. One per student if working individually or one per
group if working together. If working together, the group chooses
one data set to analyze.
6. Advise students to analyze the data, plot graphs, and answer the
questions. Allow students to work in small groups to help each
other and compare results. Remind students results will vary since
they have collected data from different people.
7. Allow students to discuss their findings. Make note of areas where
students need additional practice. Be sure to point out how this
lesson ties back into GED Mathematics and Science.
Assessment:
•
Collect graphs and provide individual feedback to students on what
they did well and where they need improvement.
Extension:
•
Have students analyze their data using a spreadsheet program on
the computer.
Answers for Handouts:
•
3-56
Answers will vary since students are collecting their own data.
Healthcare Math
Heart Rate Data Collection
Person
Male or
Female
Age
Resting
Rate
Walking
Rate
Running
Rate
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Healthcare Math
3-57
Heart Rate Data Analysis
Part 1:
1. Use the sheet of graph paper provided to make a
graph of “age” and “resting heart rate.” Be sure to
carefully label your graph.
2. Does your graph show a trend? If yes, does the heart rate increase,
decrease, or stay the same with age?
3. Draw a line of best fit on your graph.
4. Find the equation of the line of best fit you drew on your graph.
5. Based on the equation of the line of best fit, predict the resting
heart rate for a 40 year old.
6. Outliers are data points that do not fit the trend very well. Outliers
on a graph are points that “lay outside of the other data points.”
Are there any outliers in your data set? If yes, why do you think
those data points do not fit the trend? Do you think health could
be a reason?
Part 2:
7. Calculate the mean (average) heart rate for each of the following
groups. Record answers in the chart below:
Mean Heart Rates
Males
Females
Resting
Walking
Running
8. Describe any differences you see in the means. Do males have
higher, lower, or the same heart rates as females when resting,
walking, or running?
3-58
Healthcare Math
Lung Capacity
Goal:
Students will be able to collect, organize, and analyze
data pertaining to lung capacity. Data analysis
includes calculating mean, median, and range and
interpreting the results to answer questions such as
“Do nonsmokers have greater lung capacity than
smokers?” and “Do males have greater lung capacity
than females?”
Materials:
•
Handouts: (1) Lung Capacity Data Collection
(2) Lung Capacity Data Analysis
•
Timers or watches that can easily display seconds
•
Calculators
Preparation:
1. You may want to plan for two class periods to complete this lesson;
Day 1 for data collection and Day 2 for data analysis.
2. Make copies of the handouts, one for each student.
Procedure:
1. Day 1-Collecting Data: Tell students today’s class will involve them
collecting data on smokers, nonsmokers, gender, and lung capacity,
i.e., How long can individuals hold their breath?
2. Demonstrate how to collect the data. Time, in seconds, how long a
person can hold their breath and record the result, along with their
gender and whether or not they smoke.
3. Distribute the “Lung Capacity Data Collection” handout and timers.
Have one student time, in seconds, how long another student can
hold his or her breath and record the result along with whether or
not the student is a smoker. Have students share the data with
each other until all lines on their handout are filled. Ask students
Healthcare Math
3-59
to collect data so they have a mixture of males and females and
smokers and nonsmokers. If additional data is needed, have
students collect data on other adult students and/or adult family
members.
4. Day 2-Analyzing Data: Ask students to share the data collected so
that every student has their chart complete, i.e. data on 20
different individuals. Remind students their charts will be different
since they collected data on different individuals.
5. Distribute the “Lung Capacity Data Analysis” handout and
calculator, one per student. Advise students to organize and
analyze their data and answer the questions. Allow students to
work in small groups to help each other and compare results.
Remind students that results will vary if they have collected data
from different sources.
6. Discuss the findings. Ask questions such as, “Can we say the
findings are true for all adults?,” “Why or why not?,” and “What
would we have to do to have results that would better represent all
adults?”
Assessment:
•
Observation and participation.
Extension:
•
Have students analyze their data using a spreadsheet program on
the computer.
•
Have students collect and analyze other data, such as length of arm
span versus height or fist measurement versus foot length.
Answers for Handout:
•
3-60
Answers will vary since students are collecting and analyzing data
from different people.
Healthcare Math
Lung Capacity Data Collection
Person
Male or
Female
Smoker
Yes or No
Breath Held
# of Seconds
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Healthcare Math
3-61
Lung Capacity Data Analysis
1. Organize your data and calculate the mean, median,
and range for length of time all males could hold
their breath. Do the same for all females, all
smokers, all nonsmokers, and the complete data set.
2. Record results in the chart below:
Mean
Median
Range
Males
Females
Smokers
Nonsmokers
Total Data Set
3. Based on the information in the above chart:
a. Do males have greater lung capacity than females? Explain
your answer.
b. Do nonsmokers have greater lung capacity than smokers?
Explain your answer.
3-62
Healthcare Math
Understanding Medicine Labels
Goal:
Students will be able to read label directions and
make decisions on dosage for over-the-counter
medicines.
Materials:
•
Handouts: (1) Alavert™
(2) Dimetapp™ ND
(3) Benadryl™
(4) Understanding Medicine Labels
Preparation:
1. Make copies of the handouts, one for each student or each group of
students if they are working together.
Procedure:
1. Discuss the use of over-the-counter medicines. Ask students to
share their experiences and knowledge about over-the-counter
medicines.
2. Advise students the focus today is on reading and understanding
labels for some over-the-counter medicines.
3. Distribute the “Alavert™,” “Dimetapp™ ND,” “Benadryl™,” and
“Understanding Medicine Labels” handouts.
4. Allow time for students to review the three medicine label
handouts. Tell students they will be using the three labels to
answer questions from the “Understanding Medicine Labels”
handout.
5. Allow time for students to complete the handout, share their
answers, and ask questions.
Healthcare Math
3-63
Assessment:
•
Observe student answers to determine if students have grasped
reading and understanding labels.
Extension:
•
Have students bring in over-the-counter medicines they use. Read
and discuss the labels.
Answers for Handout:
Alavert™
Dimetapp™ ND
Benadryl™
1.
Loratadine 10
mg
Loratadine 10
mg
Diphenhydramine
HCL 25 mg
2.
1
1
2
3.
1
1
6
4.
1
1
12
5.
$.62
$.99
$.74
6.
$.56
$.99
$.27
7.
Answers may vary since all 3 medications are
approved for a 10 year-old child. Students may base
their answer on (1) the number of doses per day since
most children do not like to take medicine, (2) the one
that is labeled for children, (3) the cost, or (4) any
other reason.
8.
No
References:
Alavert™ Label. Retrieved February 25, 2007, from
http://www.alavert.com/products/swallows_labeling.asp
Benadryl™ Label. Retrieved February 25, 2007, from
http://www.pfizerch.com/product.aspx?id=248
Dimetapp™ ND Label. Retrieved February 25, 2007, from
http://www.dimetapp.com/allergy/lbl_allergytabs.asp
3-64
Healthcare Math
Alavert™
24 tablets for $14.88, 30 tablets for $18.90
48 tablets for $26.88
Active ingredient (in each tablet)
Loratadine 10 mg
Purpose
Antihistamine
Uses
Temporarily relieves these symptoms due to hay fever or other upper respiratory
allergies: •runny nose •sneezing •itchy, watery eyes •itching of the nose or throat
Warnings
Do not use if you have ever had an allergic reaction to this product or any of its
ingredients.
Ask a doctor before use if you have liver or kidney disease. Your doctor should
determine if you need a different dose.
When using this product do not use more than directed. Taking more than
recommended may cause drowsiness.
Stop use and ask a doctor if an allergic reaction to this product occurs. Seek
medical help right away.
If pregnant or breast-feeding, ask a health professional before use.
Keep out of reach of children. In case of overdose, get medical help or contact a
Poison Control Center right away.
Directions
Age
adults and children 6 years and over
children under 6 years of age
consumers with liver or kidney disease
Other information
Dose
1 tablet daily; do not use more than
1 tablet in 24 hours
ask a doctor
ask a doctor
store at 15-30ºC (59-86ºF)
Inactive ingredients: lactose monohydrate, magnesium stearate, microcrystalline
cellulose, sodium starch glycolate
Questions or comments? Call weekdays from 9 am to 5 pm EST at 1-800-252-8378
Source: http://www.alavert.com/products/swallows_labeling.asp
Healthcare Math
3-65
Dimetapp™ ND
12 Tablets for $11.88
Active ingredient (in each tablet)
Loratadine 10 mg
Purpose
Antihistamine
Uses
Temporarily relieves these symptoms due to hay fever or other upper respiratory
allergies: •runny nose •sneezing •itchy, watery eyes •itching of the nose or throat
Warnings
Do not use if you have ever had an allergic reaction to this product or any of its
ingredients.
Ask a doctor before use if you have liver or kidney disease. Your doctor should
determine if you need a different dose.
When using this product do not use more than directed. Taking more than
recommended may cause drowsiness.
Stop use and ask a doctor if an allergic reaction to this product occurs. Seek
medical help right away.
If pregnant or breast-feeding, ask a health professional before use.
Keep out of reach of children. In case of overdose, get medical help or contact a
Poison Control Center right away.
Directions
Tablet melts in mouth. Can be taken with or without water.
Age
Dose
adults and children 6 years and over
1 tablet daily; do not use more than
1 tablet in 24 hours
children under 6 years of age
ask a doctor
consumers with liver or kidney disease ask a doctor
Other information:
• Pheynlketonurics: Contains Phenylalanine 8.4 mg per tablet
• store at 15-30ºC (59-86ºF)
• keep in a dry place
Inactive ingredients: artificial & natural flavor, aspartame, citric acid, colloidal silicon
dioxide, corn syrup solids, crospovidone, magnesium stearate, mannitol,
microcrystalline cellulose, modified food starch, sodium bicarbonate
Questions or comments? Call weekdays from 9 am to 5 pm EST at 1-800-762-4675
Source: http://www.dimetapp.com/allergy/lbl_allergytabs.asp
3-66
Healthcare Math
Benadryl™
24 tablets for $8.88 48 tablets for $12.96
Active ingredient (in each tablet)
Diphenhydramine HCL 25 mg
Purpose
Antihistamine
Uses
Temporarily relieves these symptoms due to hay fever or other upper respiratory allergies:
•runny nose •sneezing •itchy, watery eyes •itching of the nose or throat
Temporarily relieves these symptoms due to the common cold: •runny nose •sneezing
Warnings
Do not use with any other product containing diphenhydramine, even one used on skin.
Ask a doctor before use if you have
• glaucoma
• trouble urinating due to an enlarged prostate gland
• a breathing problem such as emphysema or chronic bronchitis
Ask a doctor or pharmacist before use if you are taking sedatives or tranquilizers
When using this product
• marked drowsiness may occur
• avoid alcoholic drinks
• alcohol, sedatives, and tranquilizers may increase drowsiness
• be careful when driving a motor vehicle or operating machinery
• excitability may occur, especially in children
If pregnant or breast-feeding, ask a health professional before use.
Keep out of reach of children. In case of overdose, get medical help or contact a Poison
Control Center right away.
Directions
• take every 4 to 6 hours
• do not take more than 6 doses in 24 hours
o adults and children 12 years of age and over: 25 mg to 50 mg (1 to 2 tablets)
o children 6 to under 12 years of age: 12.5 mg** to 25 mg (1 tablet)
• children under 6 years of age: ask a doctor
**12.5 mg dosage strength is not available in this package. Do not attempt to break tablets.
Other information:
•each tablet contains: calcium 15 mg •store at 59° to 77°F in a dry place •protect from light
Inactive ingredients: candelilla wax, crospovidone, dibasic calc ium phosphate
dihydrate, D&C red no. 27 aluminum lake, hypromellose, magnesium stearate,
mi crocrystalline cellulose, polyethylene glycol, polysorbate 80, pregelatinized starch,
stearic acid, and titanium dioxide
Questions or comments? Call weekdays from 9 am to 5 pm EST at 1-800-524-2624
Source: http://www.pfizerch.com/product.aspx?id=248
Healthcare Math
3-67
Understanding Medicine Labels
1. What is the active ingredient?
________ Alavert™ ________ Dimetapp™ ND ________ Benadryl™
2. What is the maximum number of tablets per dose?
________ Alavert™ ________ Dimetapp™ ND ________ Benadryl™
3. How many times per day (24 hours) is it recommended each
medication be taken?
________ Alavert™ ________ Dimetapp™ ND ________ Benadryl™
4. What is the maximum number of tablets (dosage) in a 24-hour
period?
________ Alavert™ ________ Dimetapp™ ND ________ Benadryl™
5. If purchased in the smallest quantity available, what is the cost
per dose if the maximum dose is taken?
________ Alavert™ ________ Dimetapp™ ND ________ Benadryl™
6. If purchased in the largest quantity available, what is the cost
per dose if the maximum dose is taken?
________ Alavert™ ________ Dimetapp™ ND ________ Benadryl™
7. Which of the three medications would you choose for a 10 yearold child with a common cold, runny nose, and sneezing?
Explain why you chose that particular medication.
8. Should any of these medications be stored in the refrigerator?
3-68
Healthcare Math
Horticulture Math
4-2
Horticulture Math
Horticulture Math
Table of Contents
Introduction
4-5
Landscape Geometry: Perimeter and Area
4-7
Volume of Planting Containers
4-17
Landscaping with Bricks, Blocks, and Pavers
4-25
Soil, Mulch, and Stone
4-29
Seeding a Lawn
4-37
Hands-on Seed Mixtures
4-43
Grass Seed Mixtures
4-47
Cost of Seed Mixtures
4-53
Sod for an Instant Lawn
4-59
Insecticides and Herbicides
4-63
All About Fertilizer
4-69
Horticulture Math
4-3
4-4
Horticulture Math
Introduction
Horticulture is a growing industry
that offers career opportunities some
Adult Basic Skills students may find
interesting. One goal of this chapter
is to provide lesson plans and
activities that focus on basic math
skills using content from the
horticulture and landscaping
industry.
Students who want to complete
landscaping projects around their home or start their own greenhouse,
lawn care, or landscaping business will find these activities to be a
valuable learning experience. Students who have helped maintain homes,
lawns, and gardens will be able to relate to many of the ideas presented
in this chapter. These students will be able to contribute insights from
their own knowledge and experience. Those who aspire to home
ownership will be intrigued by this discussion and the lesson plans and
activities in this chapter. Instructors may also inspire students’ interest in
developing math skills by relating those math skills to their dreams and
aspirations.
As they work on these activities, students will see the value of math as a
tool for solving problems. Math will become less boring and less
threatening because it will be viewed as helpful, and even essential to
achieving their goals and dreams.
The instructor who keeps in mind the goal of making math interesting
and relevant is able to inspire students to learn the math skills in many
contexts. Remember to draw on the students’ experiences and their
aspirations. Lesson plans can be modified to fit specific situations and
enhanced for interesting and challenging class projects.
Working with these lesson plans may lead some students to propose
other learning activities based on their own experiences. Getting this type
of input from students is a dramatic way to demonstrate real-life math
applications. Any student who wants to modify a lesson plan to a
situation from their own experience, or to help develop a learning activity
from that experience, will have additional inspiration and opportunity to
learn about applications of math skills and to practice those skills.
Horticulture Math
4-5
The math used in horticulture offers many
opportunities for collaborative learning, which
produces more learning by students than most
other teaching strategies. Instructors should not
only use the collaborative learning applications
included in these lesson plans, but should look
for ways to increase collaborative learning
opportunities when using this chapter, as well
as other chapters in this training manual.
4-6
Horticulture Math
Landscape Geometry: Perimeter and
Area
Goal:
Students will be able to calculate the perimeter and
area of basic geometric shapes and real-life geometric
shapes including partitioning to find area.
Materials:
•
Handouts: (1) Perimeter and Area Review
(2) Perimeter and Area – Perfect Shapes
(3) Perimeter and Area – Real Life
(4) Planning a Flower Garden
(5) Greenhouse Floor Plan
•
Calculators, at least one for each pair of students
•
Poster board (to make squares, rectangles, triangles, and circles)
•
Measuring tools: rulers and tape measures with inches and
centimeters, one for each pair of students
•
Markers, one for each pair of students
•
Extension activity materials: “Perimeter and Area in the Workplace”
handout, markers, and flipchart paper
Preparation:
1. Review the procedure for this lesson. It is broken into 3 different
activities. Determine if you will complete the entire lesson in one
class or if you will use several classes. The author suggests you
plan to complete the entire lesson over several class periods.
2. Make copies of the handouts, one for each student.
3. Make poster board cutouts of varying size squares, rectangles,
triangles (different types), and circles. Make two of each size.
4. For any right triangles, mark the right angle on both sides.
Horticulture Math
4-7
Procedure, Activity 1:
1. Review what the students know about areas and perimeters of
squares, rectangles, triangles, and circles. Allow students to
describe the characteristics of each.
2. Distribute and review the “Perimeter and Area Review” handout. As
needed, explain vocabulary and show examples of how to use the
formulas. Advise students that pi is approximately equal to 3.14
and that answers may vary slightly depending upon whether
computations are done using 3.14 or 22/7 for pi or using the pi
function on a calculator. Allow students to ask questions.
3. Facilitate a brainstorm session/discussion of the different jobs
within the field of horticulture and how area and perimeter are
used in each job.
4. Explain the focus of this activity is finding area and perimeter in
general and that it will be extended into finding area and perimeter
in relation to landscape jobs.
5. Allow students to choose partners.
6. Distribute measuring tools, poster board shapes, calculators, and
markers. Be sure each pair gets 4 different shapes.
7. Advise students they are to find and label the measurements of
each of the shapes. One side should be measured in inches and the
other side measured in centimeters. After they complete the
measurements, they should calculate the perimeter and area of
each shape. Advise students that for the triangles they should draw
a dotted line for the height of the triangle (if not a right triangle)
and measure the height; advise students you have marked all right
angles. Ask students to record the area and perimeter on the shape.
8. As students finish this activity, have them sort the shapes and put
the matches together. Let students check to see if they have the
same measurements on each side. If discrepancies are found, allow
the students who made the measurements to get together to find
the error(s).
4-8
Horticulture Math
Procedure, Activity 2:
1. Distribute the “Perimeter and Area – Perfect Shapes” handout and
calculators.
2. Allow students to complete the handout individually or work in
pairs.
3. Discuss times in real life that students deal with perfect shapes, i.e.
rectangular and round table tops, rectangular rooms, etc. Ask how
many live in a house that is a perfect shape. If some students do
not, allow them to sketch their house on the board. Use this
discussion to lead into the next handout.
4. Distribute the “Perimeter and Area – Real Life” handout. Allow
students to complete the problems. Discuss any difficulties
students had in completing the handout.
Procedure, Activity 3:
1. Advise students that today’s activity is a continuation of their
study of perimeter and area with a focus on reading sketches and
completing calculations that would be required for a person
working in a horticulture occupation.
2. Distribute the “Planning a Flower Garden” and “Greenhouse Floor
Plan” handouts and calculators.
3. Advise students whether they will work in pairs or small groups.
4. Allow students to compare and discuss answers.
Assessment:
•
Activity 1: Allow students to self-check their work by comparing
the like shapes. Mastery can be determined by the accuracy of their
answers. See #7 in the procedure section.
•
Activities 2 and 3: Allow students to compare and discuss answers.
•
Allow students to draw a diagram, write similar problems, and then
make an answer key. Collect for review. Choose several for future
practice.
•
Find and assign GED-type perimeter and area practice questions.
Horticulture Math
4-9
Extension:
•
Distribute the “Perimeter and Area in the Workplace” handout.
Allow students to work in pairs and choose one of the job
situations to present to the class. List chosen jobs on the flipchart
paper so that other students can choose a different job and/or
situation. Give each pair a sheet of flipchart paper and markers to
use as they prepare for and make their presentation.
Answers for Handouts:
Perimeter and Area – Perfect Shapes
7’ square
P = 28 ft, A = 49 ft2
7’ x 5’ rectangle
P = 24 ft, A = 35 ft2
15’ x 13’ x 18’ triangle
P = 46 ft, A = 108 ft2
8’ x 6’ right triangle
3rd side = 10’, P = 24 ft, A = 24 ft2
9’ circle
Radius = 4.5’, P = 28.3 ft, A = 63.6 ft2
Perimeter and Area – Real Life
Irregular “L” shape
P = 46 ft, A = 82 ft2 (missing sides 11’ & 9’)
Rectangle with ½ circle
P = 67.7 ft, A = 164.5 ft2
Irregular “C” shape
P = 100 ft, A = 176 ft2
Planning a Flower Garden
1. 134 ft
6. 1,120 ft2
2. 150 ft
7. 630 ft2
3. 220 ft
8. 37.3%
4. 110 ft
9. 696 ft2
5. 3,000 ft2
Greenhouse Floor Plan
1. 300 ft
4. 2,860 ft2
2. 126 ft
5. 4,970 ft2
3. 1,300 ft2
Perimeter and Area in the Workplace
Answers will vary.
4-10
Horticulture Math
Perimeter and Area Review
Perimeter and area play an important role in
horticulture jobs whether you are a worker or designer.
You need to be familiar with the terms listed below:
Perimeter (P) – the distance around
Example: If you were to walk around the outside of a garden, you would
be walking the perimeter. Perimeter is measured in linear units.
Area (A) – the space contained inside the perimeter
Example: If you were to lay squares of cardboard to cover the entire
garden completely, you would be covering the area. Area is measured in
square units.
Circumference (C) - the perimeter of a circle
Diameter (d) – the line that divides a circle into two equal parts. It passes
through the center and intersects the circle in two places.
Radius (r) – one half of the diameter
Pi (π) – the equivalent of 3.14 or 22/7
Height – the line segment that shows how tall a triangle is
Base – the side of the triangle to which the height is drawn
Rules to Remember
Perimeter of a rectangle:
Perimeter (P) = sum of sides
Perimeter of a triangle:
Perimeter = side 1 + side 2 + side 3
Perimeter of a circle:
Circumference (C) = d x π
Area of a square:
Area (A) = side x side or s2
Area of a rectangle:
Area (A) = length x width
Area of a circle:
Area = radius x radius x π or πr2
Area of a triangle:
Area (A) = (height x base) ÷ 2
Horticulture Math
4-11
Perimeter and Area – Perfect Shapes
Calculate the perimeter and area for each figure.
Write your answers in the space provided.
7’
7’
5’
7’
P = ________
A = ________
P = ________
A = ________
15’
13’
12’
18’
P = ________
A = ________
8’
9’
6’
P = ________
A = ________
4-12
P = ________
A = ________
Horticulture Math
Perimeter and Area – Real Life
In real life, you seldom find projects composed of one
geometric shape. Often, these projects consist of two or
more shapes. To find the perimeter and area you need to
examine each drawing carefully, divide it into parts, and
determine the required measurements. Find the
perimeter and area of each of the following drawings.
14’
5’
P = ________
12’
4’
A = ________
9’
3’
P = ________
22’
A = ________
10’
4’
24’
18’
2’
P = ________
A = ________
2’
Horticulture Math
4-13
Planning a Flower Garden
Refer to the flower garden drawing below to answer the
following questions:
1. How much fencing will be needed to surround
the rose garden?
2. How much fencing is needed to surround the hostas and zinnias as
one garden?
3. How much fencing is needed to surround the outside of the entire
garden?
4. How much fencing is
needed to separate the
inside areas of the 4
different kinds of
flowers?
60 ft
zinnias
5. What is the area of the
entire garden?
6. What is the area of the
rose garden?
32 ft
roses
50 ft
hostas
30
ft
35
ft
petunias
7. What is the area of the
petunia garden?
8. What percent of the garden is being planned for roses?
9. Calculate the area of a 3-foot walkway that is being planned to go
around the outside of the entire garden.
4-14
Horticulture Math
Greenhouse Floor Plan
House 2
House 1
House 3
35’
20’
25’
70’
18’
House 4
45’
Refer to the floor plan above to calculate the:
1. perimeter of the entire greenhouse.
__________
2. perimeter of House 4.
__________
3. area of House 3.
__________
4. combined area of Houses 1 and 2.
__________
5. total area of the entire greenhouse.
__________
Horticulture Math
4-15
Perimeter and Area in the Workplace
It is important to know how finding perimeter and area
of squares, rectangles, triangles, and circles relates to
actual job situations.
Part 1: Brainstorm with your partner about different jobs
and situations where perimeter and area are used. List
those jobs and situations below.
Job
Description of Situation
Part 2: Choose one of the jobs listed above. Plan a short (2-3 minute)
presentation to explain or demonstrate finding perimeter and area in the
job situation you chose.
4-16
Horticulture Math
Volume of Planting Containers
Goal:
Students will be able to calculate the volume of
geometric shapes and planting containers as well as
apply the concept to horticulture in the workplace.
Materials:
•
Handouts: (1) Volume Review
(2) Volume in Horticulture
(3) Volume in the Workplace
(4) Planting Containers
•
Calculators
•
6-12 Planting containers of different sizes, shapes, and colors
•
Bag of potting soil
•
Plants (optional)
•
Rulers and/or tape measures
Preparation:
1. Review the procedure for this lesson. It is broken into 2 different
activities. Determine if you will complete the entire lesson in one
class or if you will use several classes.
2. Make copies of the handouts, one for each student.
3. Tape a label to each planting container, i.e., A, B, C, D etc. This will
allow easy reference of individual containers during the activity.
Procedure, Activity 1:
1. Begin with a discussion of volume. Distribute and use the “Volume
Review” handout as a guide for discussion. Demonstrate how to
use the formulas. Also review how to convert cubic inches into
cubic feet (1 cubic foot = 1, 728 cubic inches).
2. Allow students to brainstorm about how volume is used in the
horticulture industry.
Horticulture Math
4-17
3. Distribute the “Volume in Horticulture“ and “Volume in the
Workplace” handouts. Allow students to complete the handouts
individually or in groups.
Procedure, Activity 2:
1. Distribute the “Planting Containers” handout, calculators, and
measuring instruments.
2. Let students choose and measure a container to find the amount of
potting soil it would take to completely fill the container. Then
have students exchange containers with another student to find the
volume of a second container. If both agree on the volume, they
should record the volume on the handout. If not, they should
discuss the inconsistency and make corrections as necessary.
3. Observe students and offer help and/or advice as they complete
this task.
4. As students complete their measurements, have them list the
volume for each container on their handout and then complete the
handout, i.e. convert each volume to cubic feet and answer the
questions.
5. Discuss the questions from the handout.
6. Optional: if you have plants, allow students to plant them in the
containers.
Assessment:
•
Observe students as they complete the handout. Offer individual
help as needed. When a student is having difficulty, instead of just
telling them what to do, ask questions to guide their work.
•
Allow students to share and compare their answers. When answers
are inconsistent, students should discuss how they solved that
problem and work to resolve the inconsistencies.
•
Provide GED-type practice questions involving volume.
4-18
Horticulture Math
Extension:
•
For Activity 2, give students the price of the potting soil,
containers, and plants so they can figure the total cost.
•
Students need to know how volume is used in the workplace. Allow
students to brainstorm other occupations and situations where
volume is used. Let students present different scenarios to the
class where volume is used in the workplace.
Answers for Handouts:
Volume in Horticulture
Part 1: 216 in3, 141.43 in3, 381.86 in3
Part 2: 28.3 ft3, .88 ft3, 12.5 ft3
Part 3: 50,914.3 in3, 29.4 ft3
11,520 in3, 6.67 ft3
Volume in the Workplace
1. 432 in3
2. 324 in3
3. 15,552 in3 = 9 ft3
4. 1.125 bags, therefore you would need to purchase 2 bags
5. 18.75 in3
6. 61.25 in3
7. 71,500 in3 = 41.38 ft3 = 6.9 bags, therefore you would need to
purchase 7 bags
Horticulture Math
4-19
Volume Review
Volume describes how much a container holds. Containers used in the
horticulture industry generally involve three basic types: box, cylinder,
and sphere. Volume is measured in cubes, i.e. cubic inches, cubic feet, or
cubic yards. When calculating volume, think of it as, “How many cubes
will it take to fill the container?” Remember, all units must be expressed
as the same unit of measure prior to
calculating volume.
Volume of a Box
Length (l) – longest side
h
w
Width (w) – shorter side
l
Height (h) – how deep the container is
Formula: volume (V) = length x width x height or V = lwh or think of
it as, “Volume is the area of the bottom times the height.”
Volume of a Cylinder
To calculate the volume of a cylinder, you need to
know the radius or diameter of the top or bottom
and the height of the cylinder.
Formula: Volume = radius x radius x π x height
or V = πr2h or think of it as,
“Volume is the area of the bottom x the height.”
d
h
r
Volume of a Sphere (ball)
To calculate the volume of a sphere (ball) you must
know the radius or diameter.
d
4-20
Formula: Volume = 4/3 x π x radius x radius x radius
or V = 4/3 π r3
Horticulture Math
Volume in Horticulture
Round all answers to 2 decimal places.
Part 1: Calculate how many cubic inches of soil will be needed to
completely fill each of the containers below.
9”
5”
6”
4.5”
3”
8”
__________
__________
__________
Part 2: Calculate how many cubic feet of soil will be needed to
completely fill each of the containers below.
3’
5’
diameter = 1.5’
4’
1’
__________
__________
2.5’
__________
Part 3: Calculate the amount needed to fill each of these containers
completely. Write your answers in cubic inches and cubic feet.
5’
18”
32”
8”
3.75’
__________ cubic inches
__________ cubic inches
__________ cubic feet
__________ cubic feet
Horticulture Math
4-21
Volume in the Workplace
1. How much germinating mix is
needed to completely fill one
of the row planters?
2. How much germinating mix is
needed to fill one of the row
planters ¾ full?
Row Planters
Dimensions: 6”wide,
4” high, 1.5’ long
3. How much germinating mix would be needed to fill 48 row planters
¾ full?
4. How many bags of germinating mix would be needed to fill 48 row
planters ¾ full if each bag contains 8 cubic feet?
5. How much transplanting mix is needed
to fill the small transplant pot?
6. How much transplanting mix is needed
to fill the large transplant pot?
7. Transplanting mix is sold in 6 cubic
feet bags. How many bags of
transplanting mix should be ordered to
fill 1,200 small and 800 large
transplant pots?
4-22
Transplant Pots
Small: 3” h x 2.5” square
Large: 5” h x 3.5” square
Horticulture Math
Planting Containers
Record the volume of each container below:
Container
Volume
Cubic Inches
Volume
Cubic Feet
A
B
C
D
E
F
G
H
I
J
K
L
TOTAL
1. How much potting soil is in the bag? ______ cubic in _____ cubic ft
2. Which containers would you choose to fill if you wanted to use all
the potting soil (1 bag) and completely fill the chosen containers?
3. How many additional bags of potting soil would you need to
purchase in order to be able to fill all the containers?
Horticulture Math
4-23
4-24
Horticulture Math
Landscaping with Bricks, Blocks, and
Pavers
Goal:
Students will be able to find the number of bricks,
patio blocks, or pavers needed for a landscape or
patio project.
Materials:
•
Handouts: (1) Materials
(2) Patio and Walkway Projects
•
Calculators
Preparation:
1. Review the handouts. Add additional problems (projects) to meet
your students’ needs.
2. Make copies of the handouts, one for each student.
Procedure:
1. Begin with a discussion of how people often incorporate patios and
walkways into their landscape design. Distribute and use the
“Materials” handout as a guide for further discussion.
2. Advise students that today they are going to figure the materials
needed to build a walkway and a patio. Distribute the calculators
and the “Patio and Walkway Projects” handout.
3. Explain that answers will need to be rounded up since the materials
will be ordered in whole number units. Also advise students they
can ignore the need to order extra units in case of breakage and
because blocks may sometimes need to be cut to fit specified
dimensions.
4. Allow students to work in small groups to complete the handout.
Horticulture Math
4-25
Assessment:
•
Observe the students as they work. Encourage discussion about
what they found difficult or easy.
Extension:
•
Determine the cost of bricks, blocks, and pavers at the local
building supply. Have students figure the cost of each project on
the “Patio and Walkway Projects” handout.
Answers for Handout:
Patio and Walkway Projects
1a. 32
1b. 328
1c. 288
1d. 53
2a. 64
2b. 232
3a. 146
3b. 1,491
3c. 1,312
3d. 242
4a. 96
4b. 83
4-26
Horticulture Math
Materials
Many materials are available for landscaping jobs. Patios and walkways
are often built using bricks, patio blocks, or concrete pavers. These
materials are usually sold by the piece. Some stone materials are sold by
weight and will not be discussed.
Bricks
Common building bricks measure a little less
than 4 inches x 8 inches x 2 inches high. However,
for figuring patios and bricks we will use the 4” x
8” dimensions. We are not concerned with the
height of the brick. However, the height would be
important if you were building a wall.
Patio Blocks
Patio blocks come in a range of sizes. Two of the most common sizes are
14-inch and 18-inch square blocks.
Concrete Pavers
Concrete pavers come in a
variety of shapes. The number
needed is commonly figured
at 4 pavers per square foot.
Shapes of Pavers
Figuring the Material Needed
Use the information in the table below to figure project materials.
Remember: 1 square foot = 144 square inches
Square
Inches
Square
Feet
32
.22
1 14” square patio block
196
1.36
1 18” square patio block
324
2.25
36
.25
Material
1
1
Horticulture Math
4” x 8” brick
concrete paver
4-27
Patio and Walkway Projects
You will need information from the “Materials” handout to complete the
problems below. Remember to round answers up since the materials will
need to be ordered in whole number units.
1. Determine the materials required to construct the
walkway using:
a. 18” patio blocks ________
Walkway
b. bricks ________
c. concrete pavers _________
18’
d. 14” patio blocks _________
2. Suppose the customer wants the walkway built
with a single row of bricks installed end to end
around the perimeter and the remainder with
concrete pavers. Determine the materials needed.
4’
a. How many bricks? ________
b. How many concrete pavers? _________
3. Determine the materials
required to construct the
patio using:
a. 18” patio blocks ______
b. bricks ______
18’
12’
Patio
c. concrete pavers _______
d. 14” patio blocks ______
4. Suppose the customer wants
the 12’ x 18’ section of the
patio built using 18” patio
blocks and the 14’ x 8’
section built using 14” patio
blocks. Determine the
materials needed.
a. 18” blocks ________
14’
8’
b. 14” blocks _________
4-28
Horticulture Math
Soil, Mulch, and Stone
Goal:
Students will be able to calculate volume to determine
the amount of mulch, stone, or soil needed for
landscaping projects.
Materials:
•
Handouts: (1) Applying Mulch
(2) Crushed Rock Borders
(3) Root Balls and Soil Weight, Part 1
(4) Root Balls and Soil Weight, Part 2
(5) Volume Review (optional)
•
Calculators
Preparation:
1. Review the procedure for this lesson. It has 4 handouts (5 if you
count the “Volume Review” handout), each of which could easily
take an hour of class time to discuss and complete. Determine how
much you will cover during each class.
2. If students need to review how to find volume, make copies of the
“Volume Review” handout included in the Volume of Planting
Containers lesson or use it as a guide to review volume.
3. Make copies of the handouts, one for each student.
Procedure:
1. Review how to find volume of a rectangle, cylinder, and sphere
using the “Volume Review” handout. If you choose to do so,
distribute copies of this handout to students.
2. To introduce the content of the “Applying Mulch” handout use your
personal knowledge, your students’ knowledge, and information
from the handouts. If some of your students have applied mulch,
ask them to share their personal experiences.
Horticulture Math
4-29
3. Distribute calculators and the “Applying Mulch” handout. Remind
students to pay careful attention to details and directions and to
refer to the “Volume Review” handout as needed if you chose to
distribute it to your students. Allow students to work together to
complete the problems.
4. Allow time for class discussion and sharing when students have
completed the handout.
5. When students complete the first handout, continue the same
procedure for each of the following handouts:
a. Crushed Rock Borders
b. Root Balls and Soil Weight, Part 1
c. Root Balls and Soil Weight, Part 2
Assessment:
•
In addition to observing group interaction and efforts, assess
problems for mathematical correctness.
•
Assess the students’ ability to solve problems formed by other
groups (see Extension).
•
Ask students to share the math skills they reviewed, learned,
and/or practiced. Make a list on the board.
Extension:
•
Ask each group to write an application problem similar to the
problems on the handouts. Each person in the group should
examine the problem for clarity and solve it to be sure it works.
Make copies of the students’ problems, one for each group. Allow
each group to solve the new problems, showing all steps required
to arrive at the answer. When groups finish, collect the papers and
ask each group to “grade” their problem that the other groups
worked. After students have completed the grading, collect the
papers for review and make comments prior to returning them to
the students.
•
Allow students to investigate the different types of mulch and
loose stone available. Have them make a list of the pros and cons
for each and include cost comparisons.
4-30
Horticulture Math
Answers for Handouts:
Applying Mulch
Shaded Area
Depth
Cubic Feet
Cubic Yards
Walkway
5”
16.7
0.62
Flower Garden
3”
50.3
1.86
Outdoor Stage
6”
275.9
10.22
Hedge
4”
70.7
2.62
Crushed Rock Borders
Path: 1.31 cubic yards
Driveway: 7.41 cubic yards
Root Balls and Soil Weight, Part 1
Tree or Shrub
euonymus
mountain ash
Diameter of
Root Ball
6 inches
Volume of Soil
in Cubic Feet
.065 ft3
Weight of Soil
7.2 lbs
8 inches
.155 ft3
17.0 lbs
dogwood
10 inches
.303 ft3
33.3 lbs
willow
11 inches
.403 ft
3
44.4 lbs
buckeye
15 inches
1.02 ft3
112.4 lbs
spruce
18 inches
Horticulture Math
1.767 ft
3
194.4 lbs
4-31
Answers for Handouts:, continued
Root Balls and Soil Weight, Part 2
Quantity
Type
Diameter of
Root Ball
2
mountain ash
8 inches
.31 ft3
34 lbs
15
euonymus
6 inches
.975 ft3
107 lbs
10
buckeye
15 inches
10.23 ft3
1125 lbs
9
dogwood
10 inches
2.727 ft3
300 lbs
spruce
18 inches
35.36 ft3
3890 lbs
20
Total
Volume of Soil
in Cubic Feet
49.602 ft
3
Weight of
Soil
5,456 lbs
2a. No, the total weight of the root balls is 5,456 pounds. This is
more than the truck can hold. The actual tree would add more
weight.
2b. Answers will vary. One option would be 2 loads, i.e., one load to
deliver all the spruce and another load to deliver everything else.
References:
Bianchina, P. (2006). Crushed rock–the ideal solution. Retrieved January
27, 2007, from http://www.doityourself.com/stry/crushedrock
Powell, M. A. (1994). Planting techniques for trees and shrubs. Leaflet No.
601. Retrieved January 28, 2007, from
http://www.ces.ncsu.edu/depts/hort/hil/hil-601.html
4-32
Horticulture Math
Applying Mulch
Mulch is one of the most common materials used when
completing landscaping projects; the other is soil. Mulch
can be used in a variety of areas; the most common, of
course, being in flowerbeds. Mulch can also be used in
play areas, playgrounds, or any other area where you
might find it useful and attractive. Mulch may be
purchased by the bag (measured in cubic feet) or by the
truckload (measured in cubic yards).
Cypress
Mulch
To calculate the amount of mulch you need for a project, you must
know the area to be covered and how deep the mulch should be.
Calculations involve three dimensions: length, width, and depth. In the
volume formulas, height becomes depth.
Remember: 27 cubic feet = 1 cubic yard
Determine the cubic feet and cubic yards of mulch needed to cover the
shaded areas in each sketch. Record answers in the table below.
25’
Walkway
15’
Flower Garden
16’
Outdoor Stage
10’
4’
Shaded Area
Depth
Walkway
5”
Flower Garden
3”
Outdoor Stage
6”
Hedge
4”
Horticulture Math
Cubic
Feet
Cubic
Yards
22’
4’
Hedge
9’
4’
4’
4-33
Crushed Rock Borders
Crushed rock can be an ideal landscape material. It's durable, virtually
maintenance free, reasonably priced, and available in a variety of colors
and sizes.
While just about any crushed rock can be used for just about any
application, some rocks are better choices than others for certain uses.
For example, some rock packs down better than others, making it a better
choice for roads. Others are smooth and rounded, and while they don't
pack as well, they are softer underfoot and may be a better choice for
some walkways and dog runs. Two of the more common rocks include:
1. River rocks, which are rounded and smooth in appearance, drain
water well, and are more attractive than some other types of
crushed rock. Uses include paths, landscaping, drainage areas,
animal runs, and driveways.
2. Crushed grey rock, which is the generic “gravel,” has sharp and
irregular edges, thus it packs down more firmly. Uses include
roads, driveways, paths, and walkways.
To calculate the amount of crushed rock you need for a project, you must
know the area to be covered and how deep the rock should be.
Calculations involve three dimensions: length, width, and depth. In the
volume formulas, height becomes depth. Crushed rock is almost always
sold by the cubic yard. Remember, 27 cubic feet = 1 cubic yard.
Determine the cubic yards of rock that should be ordered to cover the
shaded area in each diagram below:
3’
2.5’
Pond
12’
Path
Hedge
Driveway
20’
2.5’
32’
Depth = 3” Cubic Yards = ________
4-34
Depth = 5” Cubic Yards = ________
Horticulture Math
Root Balls and Soil Weight, Part I
Trees and shrubs purchased from a nursery often
come with the roots “balled and burlapped,” hence the
name root ball. It is helpful to know the approximate
amount and weight of soil in the root ball when it
comes to handling the trees for delivery or planting.
The root ball can be treated as a sphere (ball), so to
calculate the amount of soil use the formula for
finding the volume of a sphere:
Volume = 4/3 x π x radius x radius x radius
or V = 4/3 π r3
Nursery workers make rough estimates of the diameter of the shrubs and
trees since it would be impractical to measure every one being balled and
burlapped. The weight of the soil is another estimate or “educated guess”
since the actual weight varies according to the makeup and moisture
content of the soil. A commonly used estimate is:
1 cubic foot of soil weighs about 110 pounds
Calculate the amount of weight of the soil contained in the root ball of
each tree or shrub listed in the table below.
Tree or
Shrub
Diameter
of Root
Ball
euonymus
6 inches
mountain ash
8 inches
dogwood
10 inches
willow
11 inches
buckeye
15 inches
spruce
18 inches
Horticulture Math
Volume of
Soil in Cubic
Feet
Weight of
Soil
4-35
Root Balls and Soil Weight, Part 2
1. Calculate the total volume and weight of the soil contained in the
root ball of the quantity of trees listed in the table below.
Quantity
Type
Diameter of
Root Ball
2
mountain ash
8 inches
15
euonymus
6 inches
10
buckeye
15 inches
9
dogwood
10 inches
spruce
18 inches
20
Volume of
Soil in
Cubic Feet
Weight of
Soil
Total
2. A landscaper has been hired to deliver and plant the shrubs and
trees listed in problem 1.
a. Can all these trees and shrubs be delivered at the same time
on a truck that has a maximum load limit of 2 tons (4,000
pounds)? Explain how you arrived at your answer.
b. If your answer to 2a was “no,” make a list of
how many loads it would take and which trees
you would put on each load to get all of them
delivered.
4-36
Horticulture Math
Seeding a Lawn
Goal:
Students will be able to determine the area of
different shaped lawns and the number of
pounds of grass seed needed to seed a new
lawn or reseed an existing lawn.
Materials:
•
Handouts: (1) Seed Broadcasting
(2) Perimeter and Area Review (Optional)
•
Calculators
Preparation:
1. Review the handouts included with this lesson. If students need
review in finding area consider using the “Perimeter and Area
Review” handout from the Landscape Geometry: Perimeter and
Area lesson.
2. Make copies of handouts, one for each student.
Procedure:
1. To get students involved, ask questions such as:
a. How much grass seed will I need to plant a new lawn?
b. What additional information do I need to answer that
question?
2. Advise students that after today’s activity they will be able to
calculate the amount of grass seed needed to not only plant a new
lawn, but also reseed an existing lawn.
3. Distribute the “Seed Broadcasting” handout.
4. Discuss the information needed to determine the amount of seeds
required.
5. Note: If students need to review how to find the area of rectangles,
triangles, and circles, provide students with the formulas or the
Horticulture Math
4-37
“Perimeter and Area Review” handout included as part of the
Landscape Geometry: Perimeter and Area lesson.
6. Demonstrate the steps required to determine the amount of seeds
needed for a new or established lawn. The steps are:
a. Calculate the area of the lawn.
b. Divide the area by 1,000 square feet to find the number of
units required.
c. For a new lawn, multiply the number of units by 5 pounds
OR
For an established lawn, multiply the number of units by 4
pounds.
d. If dealing with fractions of pounds, always round up to the
nearest half pound.
7. Allow students to work in small groups to complete the handout.
8. Ask each group to present one of the problems they solved,
including their thinking process to determine how to approach the
problem. Allow time for discussion.
Assessment:
•
Ask students to individually complete practice problems such as:
•
How many pounds of grass seed should be purchased for a new
square lawn that measures 24 feet? (3 lbs)
•
How many pounds of grass seed should be purchased to reseed
an existing rectangular lawn that measures 33’ x 42’? (6 lbs)
•
How many pounds of grass seed should be purchased to seed a
12-foot circular area in the middle of a new flower garden? (1 lb)
Extension:
•
4-38
Ask each student to draw a sketch of their yard and house,
complete with measurements. Allow students to figure the grass
seed needed for the different areas. If they live in an apartment
building, suggest they sketch the apartment building including
green space or sketch their dream home.
Horticulture Math
Answers for Handout:
Seed Broadcasting
Part 1: 14’ x 20’ square
1.5 lbs
16’ circle
1.5 lbs
48’ base triangle
4.5 lbs
Part 2: 48’ high triangle
7.0 lbs
69’ x 76’ lawn
18.0 lbs
lawn with circular ends
2.5 lbs
lawn around walk and flower beds 5.5 lbs
Reference:
Boor, M. A. (1994). Math for Horticulture. Columbus, OH: Ohio
Agricultural Education Curriculum Materials Service, Ohio State
University.
Horticulture Math
4-39
Seed Broadcasting
To establish a new lawn or reseed an existing lawn, seed is broadcast
(spread) over the lawn in pounds per square foot. Often the quote is
given in pounds per 1,000 square feet.
The most common rates are:
new lawns – 5 pounds of grass seed per 1,000 square feet
established lawns – 4 pounds of grass seed per 1,000 square feet
To find the number of pounds of grass seed needed for a new or
established lawn:
1. Calculate the area of the lawn.
2. Divide the area by 1,000 square feet to find the number of units
required.
3. For a new lawn, multiply the number of units by 5 pounds. For an
established lawn, multiply the number of units by 4 pounds.
4. If dealing with fractions of pounds, always round up to the nearest
half pound.
For example, if a new rectangular lawn measured 80 feet x 16 feet, to
calculate the amount of grass seed needed you would:
1. Calculate the area of the lawn:
A = 80 x 16 = 1,280 square feet
2. Divide the area by 1,000 square feet:
3. Multiply units by 5 pounds:
1,280 ÷ 1,000 = 1.28 units
1.28 x 5 pounds = 6.4
4. 6.5 pounds of grass seed would be needed to seed the lawn
Now, it’s your turn.
Part 1: Determine how many pounds of grass seed should be purchased
for each of the new lawns shown below:
14’ x 20’
4-40
16’
h = 37’
b = 48’
Horticulture Math
Seed Broadcasting, continued
Part 2: Determine how many pounds of grass seed should be purchased
for each of the lawns shown below:
68’
new lawn
69’
76’
new house
48’
38’ x 42’
existing lawn
Seed Required _____________
Seed Required _____________
45’
new lawn
25’
flowers
flowers
flowers
15’
walk (6’ wide)
existing lawn
42’
flowers
flowers
flowers
Seed Required ____________
new lawn
All flowerbeds are the same size.
Seed Required _______________
Horticulture Math
4-41
4-42
Horticulture Math
Hands-on Seed Mixtures
Goal:
Students will be able to follow directions and complete
math computations to make seed mixtures. By actually
doing several mixing problems, students will have a
better understanding of pencil and paper examples of
mixture problems.
Materials:
•
4 different kinds of dry beans and/or peas
•
Plastic Ziploc bags, about twice as many as the number of students
participating in the activity
•
Marker or labels (to label grass seed type of each bag)
•
Handout: Making Seed Mixtures, one copy for each student
•
Measuring cups
•
Paper cups
•
Paper plates or box tops (to keep beans from rolling off workspace)
•
Scales (that can measure ounces), preferably 1 for every 4 students
Preparation:
1. Obtain 4 different kinds of beans that are different colors and sizes
so students can easily distinguish between the different kinds. You
need enough so that each student will have access to about a half
cup plus a few extra.
2. Divide the beans into plastic bags, ½ to ¾ cup per bag. Assign a
grass seed type for each kind of bean and label bags accordingly.
Dry Beans/Peas
1st Kind
2nd Kind
3rd Kind
4th Kind
Horticulture Math
Grass Seed Type
Creeping Red Fescue
Kentucky Bluegrass
Perennial Ryegrass
Pennlink Bentgrass
4-43
3. Label additional empty plastic bags as “Mix A,” “Mix B,” “Mix C,”
and “Mix D,” one for each group (3-4 students per group).
4. Make copies of handout, one copy for each student.
5. Gather other materials: plastic bags, paper cups and plates,
measuring cups, and scales (optional).
Procedure:
1. Have students form groups of four. Distribute materials. Each
group needs:
a. 4 bags of “seeds,” one bag of each “grass type” per group
b. 4 empty plastic bags, labeled Mix A, B, C, and D
c. 4 paper cups, one per student
d. 4 paper plates, one per student
2. Explain that each bean/pea represents 1 grass seed. Explain the
basics of seed mixtures, i.e., if a mixture is made up of 40% Fescue,
30% Bluegrass, 20% Ryegrass, and 10% Bentgrass then 40 out of
every 100 seeds will be Fescue, 30 out of every 100 seeds will be
Bluegrass, 20 out of every 100 seeds will be Ryegrass, and 10 out of
every 100 seeds will be Bentgrass. Alternatively, show the same
example based on 10 seeds, i.e., 4 out of 10, 3 out of 10, etc.
3. Distribute the “Making Seed Mixtures” handout, one per student.
4. Have students complete the handout, i.e., determine the number of
each type of seed needed to make the mixture, then have them
actually make the mixture.
5. Ask students why they think actual grass seed mixtures are not
made this way in real life. Answers should include (1) grass seeds
are too small to count and (2) it would be very labor intensive.
Explain that in real life grass seed mixtures are made by weight
(pounds and ounces).
6. Have students put all the seeds into the plastic container. Let each
student get a paper cup full of the seed mixture.
7. Let students form pairs. Have students use the scales to measure
the weight of their mixture in ounces. Once they have recorded the
total weight, they should “take apart” their mixture, calculate the
4-44
Horticulture Math
weight (in ounces) of each different type of seed, and calculate the
percentage of each type of seed (total weight divided by weight of
each individual type seed) contained in the mix. Then they should
determine how the weight percent for each type of seed compares
to the percentages given for that mix on the handout.
8. Allow time for questions and discussion.
Assessment:
•
Observe individual participation and group interaction.
Answers for Handout:
Mix A
100 Seeds
Grass Seed Type
40% Creeping Red Fescue
30% Kentucky Bluegrass
15% Perennial Ryegrass
15% Bentgrass
# of Seeds Required
40
30
15
15
Mix B
200 Seeds
Grass Seed Type
35% Creeping Red Fescue
25% Kentucky Bluegrass
15% Perennial Ryegrass
25% Bentgrass
# of Seeds Required
70
50
30
50
Mix C
150 Seeds
Grass Seed Type
24% Creeping Red Fescue
18% Kentucky Bluegrass
36% Perennial Ryegrass
22% Bentgrass
# of Seeds Required
36
27
54
33
Mix D
250 Seeds
Grass Seed Type
10% Creeping Red Fescue
22% Kentucky Bluegrass
32% Perennial Ryegrass
36% Bentgrass
# of Seeds Required
25
55
80
90
Horticulture Math
4-45
Making Seed Mixtures
Working together with others in your group, make the following mixtures
and put the mixture into the plastic bag labeled for that mixture.
Mix A
100 Seeds
Grass Seed Type
# of Seeds Required
40% Creeping Red Fescue
30% Kentucky Bluegrass
15% Perennial Ryegrass
15% Bentgrass
Mix B
200 Seeds
Grass Seed Type
# of Seeds Required
35% Creeping Red Fescue
25% Kentucky Bluegrass
15% Perennial Ryegrass
25% Bentgrass
Mix C
150 Seeds
Grass Seed Type
# of Seeds Required
24% Creeping Red Fescue
18% Kentucky Bluegrass
36% Perennial Ryegrass
22% Bentgrass
Mix D
250 Seeds
Grass Seed Type
# of Seeds Required
10% Creeping Red Fescue
22% Kentucky Bluegrass
32% Perennial Ryegrass
36% Bentgrass
4-46
Horticulture Math
Grass Seed Mixtures
Goal:
Students will be able to calculate seed mixtures and
analyze, interpret, and complete tables related to seed
mixtures.
Materials:
•
Handouts: (1) Grass Seed Mixtures for Lawns
(2) Grass Seed Mixtures for Pastures
•
Calculators
Preparation:
1. Consider doing the Hands-on Seed Mixtures lesson prior to
completing this lesson.
2. Make copies of handouts, one for each student.
Procedure:
1. Ask students about their knowledge of different kinds of grasses.
Have they noticed how different grasses look, i.e. lawns, pastures,
turf at golf courses, etc.? Do they think these different areas are
planted with only one type of seed or is it a mixture? What are the
advantages and disadvantages of using a seed mixture?
2. Advise students that today they are going to continue their study
of the horticulture industry by learning about seed mixtures. They
will determine the amount of each seed in a mixture when given
the package label information.
3. Distribute the “Grass Seed Mixtures for Lawns” handout.
Demonstrate how to complete the calculations for one of the seed
mixtures.
4. Allow time for students to complete the handout, ask questions,
and discuss activity.
Horticulture Math
4-47
Assessment:
•
Have students complete one of the problems from the “Grass Seed
Mixtures for Pastures” handout for your review and/or grading.
Extension:
•
Allow students to search the Internet for information on the
different types of grasses and their uses in different seed mixtures,
i.e. pastures, playgrounds, etc.
Answers for Handouts:
Shade Plus
Elite Bluegrass
Fine Fescue
Grass Seed Mixtures for Lawns
4-48
Percentages of Grass Seed in a
10 pound Fescue Blend
36% Flyer Creeping Red Fescue
30% Shadow II Chewing Fescue
34% Aurora Gold Hard Fescue
Decimal
Equivalent
.36
.30
.34
Totals
Ounces
per Type
57.6
48
54.4
160
Pounds,
Ounces
3 lbs, 9.6 oz
3 lbs
3 lbs, 6.4 oz
10 lbs
Percentages of Grass Seed in a
25 pound Custom Blend
42% Midnight II Ky Bluegrass
38% Morning Star Ryegrass
20% Boreal Creeping Red Fescue
Decimal
Equivalent
.42
.38
.20
Totals
Ounces
per Type
168
152
80
400
Pounds,
Ounces
10 lbs, 8 oz
9 lbs, 8 oz
5 lbs
25 lbs
Percentages of Grass Seed in a
50 pound Custom Blend
20% Limousine Ky Bluegrass
39% Flyer Creeping Red Fescue
25% Predator Hard Fescue
16% Cascade Chewing Fescue
Decimal
Equivalent
.20
.39
.25
.16
Totals
Ounces
per Type
160
312
200
128
800
Pounds,
Ounces
10 lbs
19 lbs, 8 oz
12 lbs, 8 oz
8 lbs
50 lbs
Horticulture Math
Part Shade
Answers for Handouts, continued
Percentages of Grass Seed in a
5 pound Custom Blend
30% Moonlight Ky Bluegrass
28% Prosperity Ky Bluegrass
30% Boreal Creeping Red Fescue
12% Morning Star Ryegrass
All Shade
Percentages of Grass Seed in a
3 pound Custom Blend
10%
28%
32%
10%
20%
Midnight II Ky Bluegrass
Flyer Creeping Red Fescue
Boreal Creeping Red Fescue
Silverlawn Red Fescue
Shining Star Ryegrass
Decimal
Equivalent
.30
.28
.30
.12
Totals
Ounces
per Type
24
22.4
24
9.6
80
1
1
1
5
Pounds,
Ounces
lb, 8 oz
lb, 6.4 oz
lb, 8 oz
9.6 oz
lbs
.10
.28
.32
.10
.20
Totals
Ounces
per
Type
4.8
13.4
15.4
4.8
9.6
48
0
0
0
0
0
3
Decimal
Equivalent
.35
.25
.20
.20
Totals
Ounces
per Type
140
100
80
80
400
Pounds,
Ounces
8 lbs, 12 oz
6 lbs, 4 oz
5 lbs
5 lbs
25 lbs
Decimal
Equivalent
Pounds,
Ounces
lbs,
lbs,
lbs,
lbs,
lbs,
lbs
4.8 oz
13.4 oz
15.4 oz
4.8 oz
9.6 oz
Cattle Pasture Mix
Horse Pasture Mix
Grass Seed Mixtures for Pastures
Percentages of Grass Seed in
a 25 pound Custom Blend
35% Potomac Orchardgrass
25% Climax Timothy
20% Perennial Ryegrass
20% Fawn Tall Fescue
Percentages of Grass Seed in a
50 pound Custom Blend
25% Annual Ryegrass
20% Perennial Ryegrass
20% Climax Timothy
20% Fawn Tall Fescue
10% Alsike Clover
5% Medium Red Clover
Horticulture Math
Decimal
Equivalent
.25
.20
.20
.20
.10
.05
Totals
Ounces
per Type
200
160
160
160
80
40
800
Pounds,
Ounces
12 lbs, 8 oz
10 lbs
10 lbs
10 lbs
5 lbs
2 lbs, 8 oz
50 lbs
4-49
Grass Seed Mixtures for Lawns
Grass seed mixtures are a blend of various
percentages of different grasses relative to total
weight. The individual seed types are packaged in
bulk containers. The worker must calculate how
many pounds or ounces of each type are needed
for the desired total amount.
To calculate the number of ounces of a particular type contained in a
mixture:
1. Convert the number of pounds desired to ounces.
2. Multiply each percent by the total number of ounces in the mixture.
3. For answers greater than 16 ounces, convert to pounds and ounces.
Note: Total may not be exact due to rounding.
Fine Fescue
Calculate how much of each type is needed for the following mixtures.
Percentages of Grass Seed in a
10 pound Fescue Blend
Decimal
Ounces
Equivalent per Type
(Step 1)
(Step 2)
Pounds,
Ounces
(Step 3)
36% Flyer Creeping Red Fescue
30% Shadow II Chewing Fescue
34% Aurora Gold Hard Fescue
Elite Bluegrass
Totals
Percentages of Grass Seed in a
25 pound Custom Blend
Decimal
Ounces
Equivalent per Type
(Step 1)
(Step 2)
Pounds,
Ounces
(Step 3)
42% Midnight II Kentucky
Bluegrass
38% Morning Star Ryegrass
20% Boreal Creeping Red Fescue
Totals
4-50
Horticulture Math
Shade Plus
Grass Seed Mixtures for Lawns, continued
Percentages of Grass Seed in a
Decimal
50 pound Custom Blend
Equivalent
20% Limousine Kentucky
Bluegrass
Ounces Pounds,
per Type Ounces
39% Flyer Creeping Red Fescue
25% Predator Hard Fescue
16% Cascade Chewing Fescue
Part Shade
Totals
Percentages of Grass Seed in a
5 pound Custom Blend
30% Moonlight Kentucky
Bluegrass
28% Prosperity Kentucky
Bluegrass
30% Boreal Creeping Red
Fescue
Decimal
Equivalent
Ounces Pounds,
per Type Ounces
12% Morning Star Ryegrass
All Shade
Totals
Percentages of Grass Seed in a
3 pound Custom Blend
10% Midnight II Kentucky
Bluegrass
Decimal
Ounces Pounds,
Equivalent per Type Ounces
28% Flyer Creeping Red Fescue
32% Boreal Creeping Red
Fescue
10% Silverlawn Red Fescue
20% Shining Star Ryegrass
Totals
Horticulture Math
4-51
Grass Seed Mixtures for Pastures
Horse Pasture Mix
Calculate how much of each type seed is needed
for the following mixtures.
Percentages of Grass Seed
in a 25 pound Custom Blend
Pounds,
Ounces
35% Potomac Orchardgrass
25% Climax Timothy
20% Perennial Ryegrass
20% Fawn Tall Fescue
Totals
Percentages of Grass Seed
in a 50 pound Custom Blend
Cattle Pasture Mix
Decimal
Ounces
Equivalent per Type
Decimal
Equivalent
Ounces
per Type
Pounds,
Ounces
25% Annual Ryegrass
20% Perennial Ryegrass
20% Climax Timothy
20% Fawn Tall Fescue
10% Alsike Clover
5% Medium Red Clover
Totals
4-52
Horticulture Math
Cost of Seed Mixtures
Goal:
Students will be able to determine the costs for different
seed mixtures. Students will be able to analyze, interpret,
and complete tables related to grass seed mixtures.
Materials:
•
Handouts: (1) Calculating Prices for Seed Mixtures
(2) Grass Seed – Prices by Weight
(3) Grass Seed Mixtures – Total Costs
•
Calculators
Preparation:
1. Consider doing the Grass Seed Mixtures lesson prior to completing
this lesson.
2. Make copies of handouts, one for each student.
Procedure:
1. Remind students that in the Grass Seed Mixtures lesson they
learned to mix grass seeds and when in business, it is just as
important to be able to calculate the prices for custom blend seed
mixtures.
2. Distribute the “Calculating Prices for Seed Mixtures,” “Grass Seed –
Prices by Weight”, and “Grass Seed Mixtures – Total Costs”
handouts and calculators.
3. Explain and demonstrate how to use the “Grass Seed – Prices by
Weight” table and how to calculate the total cost for a grass seed
mixture.
4. Allow students to complete the “Grass Seed Mixtures – Total Costs”
handout.
5. Allow time for questions and discussion.
Horticulture Math
4-53
Assessment:
•
Have students find the price for one of the seed mixtures on the
“Grass Seed Mixtures for Lawns” handout from the Grass Seed
Mixtures lesson.
Extension:
•
Allow students to search the Internet and/or call local businesses
to obtain information on the individual seeds and seed blends
available and the actual costs in their local area.
Answers for Handout:
Grass Seed Mixtures – Total Costs
Mix 1
Ounces in Price per
15 pounds Part Shade
Mixture
Ounce
Moonlight Kentucky Bluegrass
72.0
.152
Prosperity Kentucky Bluegrass
57.6
.141
Boreal Creeping Red Fescue
72.0
.225
Morning Star Ryegrass
38.4
.118
Total Cost of 15 pounds
Price for
Type
10.94
8.12
16.20
4.53
$39.79
10%
30%
32%
08%
20%
Mix 2
5 pounds All Shade
Midnight II Kentucky Bluegrass
Flyer Creeping Red Fescue
Boreal Creeping Red Fescue
Silverlawn Red Fescue
Shining Star Ryegrass
Ounces in Price per
Mixture
Ounce
8.0
.188
24.0
.103
25.6
.250
6.4
.500
16.0
.313
Total Cost of 5 pounds
Price for
Type
1.50
2.47
6.40
3.20
5.01
$18.58
35%
25%
20%
20%
Mix 3
25 pounds Horse Pasture
Potomac Orchardgrass
Climax Timothy
Perennial Ryegrass
Fawn Tall Fescue
Ounces in Price per
Mixture
Ounce
140
.105
100
.115
80
.091
80
.058
Total Cost of 25 pounds
Price for
Type
14.70
11.50
7.28
4.64
$38.12
30%
24%
30%
16%
4-54
Horticulture Math
Calculating Prices for Seed Mixtures
In business, it is just as important to know how to calculate
the price for a seed mixture as it is to be able to determine
the amount of each type in a mixture.
To calculate the price of a seed mixture:
1. Find the number of ounces in the seed mixture.
2. Find the number of ounces of each type of seed in the mixture.
3. Find the price of one ounce of each type of seed using the “Grass
Seed - Prices by Weight” table (on the next page). If the mixture is
for:
a. 1-9 pounds, divide the price by 16 to get the price/ounce.
b. 10-19 pounds, divide the price by 160 to get the price/ounce.
c. 20 or more pounds, divide the price by 320 to get the
price/ounce.
4. Multiply the ounces of each type by the price per ounce. Add these
to find the total price.
Example: Calculate the cost of 25 pounds of the Elite Bluegrass Mixture
containing the following:
42% Midnight II Kentucky Bluegrass
38% Morning Star Ryegrass
20% Boreal Creeping Red Fescue
Type
(Step 1: ounces in
25 lbs = 400)
Midnight II
Kentucky Bluegrass
Morning Star
Ryegrass
Boreal Creeping
Red Fescue
Ounces in
Mixture
(Step 2)
Price per Ounce
(Step 3)
Price for Type
(Step 4)
.42 x 400=168
$48.00 ÷ 320=0.15
168 x .15=$25.20
.38 x 400=152
$33.60 ÷ 320=0.105
152 x .105=$15.96
.20 x 400=80
$64.00 ÷ 320=0.20
80 x .20=$1.60
(Step 5) Total Cost of 25 Pounds of Elite Bluegrass
Horticulture Math
$42.76
4-55
Grass Seed - Prices by Weight
Type & Variety
1 - 9 lbs
10 – 19
lbs
20 lbs or
more
Alsike Clover
$1.10
$9.90
$17.60
Annual Ryegrass
$1.05
$9.45
$16.80
Aurora Gold Hard Fescue
$1.65
$14.85
$26.40
Bentgrass
$12.00
$108.00
$192.00
Boreal Creeping Red Fescue
$4.00
$36.00
$64.00
Cascade Chewing Fescue
$2.50
$22.50
$40.00
Climax Timothy
$2.30
$20.70
$36.80
Flyer Creeping Red Fescue
$1.65
$14.85
$26.40
Fawn Tall Fescue
$1.15
$10.35
$18.40
Florentine Creeping Red Fescue
$1.90
$17.10
$30.40
Limousine Kentucky Bluegrass
$5.50
$49.50
$88.00
Medium Red Clover
$3.85
$34.65
$61.60
Midnight II Kentucky Bluegrass
$3.00
$27.00
$48.00
Moonlight Kentucky Bluegrass
$2.70
$24.30
$43.20
Morning Star Ryegrass
$2.10
$18.90
$33.60
Potomac Orchardgrass
$2.10
$18.90
$33.60
Perennial Ryegrass
$1.82
$16.38
$29.12
Predator Hard Fescue
$2.40
$21.60
$38.40
Prosperity Kentucky Bluegrass
$2.50
$22.50
$40.00
Shadow II Chewing’s Fescue
$2.60
$23.40
$41.60
Shining Star Ryegrass
$5.00
$45.00
$80.00
Silverlawn Red Fescue
$8.00
$72.00
$128.00
4-56
Horticulture Math
Grass Seed Mixtures – Total Costs
Calculate the cost for each of the following grass seed mixtures:
Mix 1
15 pounds Part Shade
30% Moonlight Kentucky Bluegrass
Ounces in
Mixture
Price per
Ounce
Price for
Type
24% Prosperity Kentucky Bluegrass
30% Boreal Creeping Red Fescue
16% Morning Star Ryegrass
Total Cost of 15 pounds
Mix 2
5 pounds All Shade
10% Midnight II Kentucky Bluegrass
Ounces in
Mixture
Price per
Ounce
Price for
Type
30% Flyer Creeping Red Fescue
32% Boreal Creeping Red Fescue
08% Silverlawn Red Fescue
20% Shining Star Ryegrass
Total Cost of 5 pounds
Mix 3
25 pounds Horse Pasture
35% Potomac Orchardgrass
Ounces in
Mixture
Price per
Ounce
Price for
Type
25% Climax Timothy
20% Perennial Ryegrass
20% Fawn Tall Fescue
Total Cost of 25 pounds
Horticulture Math
4-57
4-58
Horticulture Math
Sod for an Instant Lawn
Goal:
Students will be able to calculate areas to
determine the amount of sod needed to complete
landscaping projects involving rectangles,
triangles, circles, and other area configurations
that include one or more regular areas.
Materials:
•
Handouts: (1) Sod Installation
(2) GED Formula Sheet (optional)
•
Calculators
Preparation:
1. Review the complete lesson. Make adjustments to meet the needs
of your students.
2. Make copies of the handouts, one for each student.
Procedure:
1. Facilitate a discussion on sod, what it is and why it is used. Be sure
that at the end of the discussion, students know (1) sod is a
commercially grown grass that is cut and rolled much like
carpeting, and (2) it provides an “instant” lawn.
2. Explain that sod comes in rolls measuring: 1 foot x 9 feet or 1.5
feet x 6 feet. Each roll covers 9 square feet, which equals 1 square
yard.
3. Review the formulas for finding areas of rectangles, triangles, and
circles using examples requiring the second step of finding the
number of rolls of sod. The number of rolls needed is always
rounded up since sod can only be bought in full rolls. Consider the
following examples for class demonstration:
a. Find the number of yards (or rolls) of sod needed to cover an
area measuring 25 ft x 50 ft. (Answer: 139 yards or rolls)
Horticulture Math
4-59
b. Find the number of yards/rolls of sod needed to cover a
triangular area measuring 50 ft. at the base with a height of
54 ft. (Answer: 150 yards or rolls)
c. Find the number of yards/rolls of sod needed to cover a 12
ft. diameter circle. (Answer: 13 yards or rolls)
4. Distribute the “Sod Installation” handout and calculators.
Demonstrate several examples that require multiple steps.
5. Allow students to work together in pairs or small groups to
complete the handouts.
Assessment:
•
Observe interaction.
•
Ask students to demonstrate to the class their procedure for
solving one of the problems from the handout.
•
Allow students to make their own practice sheet, i.e. each pair or
group of students submits one question that requires finding area.
Extension:
•
Facilitate a discussion of the math involved in completing the
handout and other areas of landscaping (and other occupations)
where similar math is used.
•
Have students figure the amount of sod needed for each of the
lawns given in the “Seed Broadcasting” handout from the Seeding a
Lawn lesson provided earlier in this chapter.
Answers for Handout:
1.
27
5a. 24 yards or rolls
6b. $8,472.80
2. 79
3. 144
5b. $240
7a. 5,334
4. 68
6a. 623 yards or rolls
7b. $72,542.40
Reference:
Turfgrass America. (2005). Retrieved February 3, 2007, from
http://www.turfgrassamerica.com/
4-60
Horticulture Math
Sod Installation
Remember: 1 roll of sod = 1 square yard = 9 square feet
Sod is sold by the square yard; partial rolls cannot be purchased. Round
answers to full rolls.
Determine how many rolls of sod should be purchased for each of the
sod areas shown below.
10’
28’
12’
roses
roses
6’
8’
sod
14’
deck
sod
16’
sod
60’
1. __________ rolls of sod
14’
roses
30’
roses
3. __________ rolls of sod
24’
sod
12’
2’ wide mulch bed
2. __________ rolls of sod
24’
Pool
sod
30’
4. __________ rolls of sod
Horticulture Math
4-61
Sod Installation, continued
1 roll of sod = 1 square yard = 9 square feet
Sod is only sold by the square yard
Sod sells for $3.60 per square yard
Installation is $10 per square yard
5. A neighbor has decided to quit gardening. She wants to cover the
12 feet x 18 feet garden area with sod. She plans to install the sod.
a. How much sod will it take to cover the garden?
b. How much will she save by doing it herself?
6. A customer who is building a new home wants sod installed on all
the lawn areas. The three areas to be covered measure 60 feet x 60
feet, 40 feet x 20 feet, and 120 feet x 10 feet.
a. How many yards of sod will be needed?
b. How much will it cost (before tax) to purchase the sod and
have it installed?
7. All the trees on both sides of Main Street were torn up when a new
sewage line was laid. The city has contracted your landscape
company to sod these areas. There are 8 city blocks, each 750 feet
long. The sod will be 4 feet wide.
a. How many yards of sod will you need for both sides of the
street?
b. How much will your company charge (before tax) the city for
the sod and having it installed?
4-62
Horticulture Math
Insecticides and Herbicides
Goal:
Students will be able to read a product label and
determine the amount of chemical needed to mix
insecticides and herbicides.
Materials:
• Handouts: (1) Mixing Herbicide
(2) Mixing Insecticide
•
Calculators
Preparation:
1. Preview the procedure and handouts. Determine if you want to
include additional information and/or product labels.
2. Make copies of the handouts, one for each student.
Procedure:
1. Ask students if they have ever applied chemicals around the house.
Did they have to mix them? Discuss the different kinds of
chemicals they have used.
2. If not already discussed, talk about insecticides and herbicides that
are used in horticulture, agriculture, and homes. Be sure students
understand the difference between insecticides and herbicides:
a. An insecticide is a pesticide used against insects in all
developmental forms. Insecticides are used in agriculture,
medicine, industry, and the household.
b. An herbicide is a pesticide used to kill unwanted plants.
Herbicides are widely used in agriculture and landscape turf
management.
3. Discuss the importance of mixing chemicals correctly for the stated
purpose. For example, a stronger mixture does not necessarily
mean a better job, but it does mean more chemicals in the
environment.
Horticulture Math
4-63
4. Distribute the “Mixing Herbicide” and “Mixing Insecticide”
handouts. Discuss the label on each handout. Allow time for
students to ask questions.
5. Review household measurement equivalencies pertaining to ounces
and cups, i.e., 1 ounce = 1/8 cup, 8 ounces = 1 cup, 16 ounces = 1
pint, 32 ounces = 1 quart, etc.
6. Work cooperatively as a class to complete several examples from
the handouts, and then allow students to work individually or in
small groups to finish the handouts.
Assessment:
•
Have students complete a few chemical mixture problems to be
turned in for grading. Problems could be:
⇒ How much water should be mixed with an herbicide that is
applied 2 pints per acre to make a 6-gallon solution? (Answer: 6
gallons = 48 pints – 2 pints chemical = 46 pints water to make a
6-gallon solution.)
⇒ The label on an insecticide states that you should mix 2 cups of
chemical per 6 gallons of water. Suppose you only wanted to
mix about 1 gallon of water, how much chemical would you use?
(Answer: 2 cups ÷ 6 = 2/6 or 1/3 cup per gallon of water.)
Extension:
•
Bring in chemical labels from household and/or lawn care products
to discuss how to mix the chemicals according to the mixing
directions provided on the label.
•
Use plain water and colored water to allow students to simulate
mixing different chemicals according to label directions.
•
Have students conduct research and make a list of the pros and
cons of using insecticides and herbicides.
•
Have students figure the amount of insecticide or herbicide needed
for each of the lawns given in the “Seed Broadcasting” handout
from the Seeding a Lawn lesson and/or the “Sod Installation”
handout from the Sod for an Instant Lawn lesson provided earlier
in this chapter.
4-64
Horticulture Math
Answers for Handouts:
Mixing Herbicide
Weed Killer
Water
Coverage
¼ ounce
1 gallon
1,000 sq ft
½ ounce
2 gallons
2,000 sq ft
½ cup
16 gallons
16,000 sq ft
1 cup
32 gallons
32,000 sq ft
3 gallons
3,000 sq ft
2 ½ ounces
10 gallons
10,000 sq ft
3 ¾ ounces
15 gallons
15,000 sq ft
12 ½ ounces
50 gallons
50,000 sq ft
3/8 ounce
1.5 gallons
1,500 sq ft
1/8 ounce
0.5 gallons
500 sq ft
1 ¼ ounce
5 gallons
5,000 sq ft
10 gallons
10,000 sq ft
¾ ounce
2 ½ ounces
Mixing Insecticide
1. 3 fluid ounces to 5 gallons of water, 2 weeks before 2nd treatment
2. 18 fluid ounces to 3 gallons of water, 4 ft. diameter circle
3. 3 fluid ounces to 4 ½ gallons of water for each lawn
Reference:
Pesticide use. (n.d.). Retrieved February 2, 2007, from South Dakota
Department of Agriculture Website:
http://www.state.sd.us/doa/das/hp-pest.htm
Horticulture Math
4-65
Mixing Herbicide
WEED KILLER
MIXING INSTRUCTIONS
¼ ounce per gallon of water
Covers 1,000 square feet
Based on the label above, complete the table below:
Weed Killer
¼ ounce
Water
1 gallon
Coverage
1,000 sq ft
½ ounce
½ cup
1 cup
3 gallons
10 gallons
15 gallons
50 gallons
1,500 sq ft
500 sq ft
5,000 sq ft
10,000 sq ft
4-66
Horticulture Math
Mixing Insecticide
LAWN INSECT CONTROL
TREATMENT
AREAS
Bent,
Bermuda,
Bluegrass,
Dichondra,
Fescue,
Irish Moss,
Merion,
St. Augustine
PESTS
REMARKS
Armyworms, Brown dog
ticks, Chiggers, Chinch
bugs, Cutworms, Fleas,
Japanese beetle grubs,
Sod Mole crickets,
Mosquitoes, Webworms,
Ticks, including Deer
Ticks
Ants (including foraging
fire ants), Crickets,
Grasshoppers
Fire ants
Thoroughly wet down grass a few hours
before applying. Home lawns should be no
taller than 3 inches at time of application.
For heavy infestations, repeat application
after 2 weeks.
Apply 1 gallon of solution as a gentle rain
to each fire ant mound using a sprinkler
can. Thoroughly wet the mound and
surrounding area to a 4-foot diameter. For
best results, apply in cool weather, 65-80
degrees.
USE RATE
6 fl. oz. in 10 gals.
of water to cover
1,000 sq. ft.
2 fl. oz. in 3 gals. of
water to cover 1,000
sq. ft.
6 fl. oz. in 1 gallon
of water to treat one
fire ant mound
Use the Lawn Insect Control table above to answer the questions below.
1. A customer has a small lawn area measuring 25 feet x 20 feet that
she wants sprayed with insecticide to control mosquitoes. How
much insecticide and water should be used to make an insecticide
mixture to cover just this area? How long after the first treatment
should a second treatment be applied?
2. A customer has a problem with fire ants. He has three fire ant
mounds to be treated. How much insecticide and water should be
used to make an insecticide mixture to cover just this area? How
much of the area around each mound should be treated?
3. The neighbors are having problems with ants (not fire ants) in their
lawns. There are three lawns that need to be sprayed. Each lawn
measures 50 feet x 30 feet. How much insecticide and water should
be used to make an insecticide mixture to spray each lawn?
Horticulture Math
4-67
4-68
Horticulture Math
All About Fertilizer
Goal:
Students will be able to calculate how many
bags of fertilizer are needed for a project; the
amounts of nitrogen, phosphorus, potassium,
and filler in a bag of fertilizer and the amount
of fertilizer needed to feed a tree.
Materials:
•
Handouts: (1) Understanding Fertilizer Labels
(2) Dealing With Fertilizer
•
A fertilizer bag (empty or full), several bags for large classes
•
Calculators
Preparation:
1. Review the handouts and the information provided about fertilizer.
Conduct further research if additional information is desired.
2. Make copies of handouts, one for each student.
Procedure:
1. Most adults have had some experience with using fertilizer for
their lawns, gardens, and/or houseplants. Ask students to share
what they know about fertilizer. To facilitate discussion, ask
questions such as:
a. Has anyone ever used fertilizer?
b. If so, for what purpose?
c. How did you decide what to buy?
d. How did you know how much to use?
2. Allow students to examine the fertilizer bag and discuss important
information about the label. During the discussion, be sure
students gain an understanding of the meaning of the three bold
Horticulture Math
4-69
numbers on the bag. An explanation is given on the “Understanding
Fertilizer Labels” handout.
3. Explain that another important component of fertilizer application,
especially for those in business, is determining the amount of
fertilizer needed to cover a specified area. Examine the fertilizer
bag again to see what the bag says about how much area it will
cover.
4. Distribute the “Understanding Fertilizer Labels” and “Dealing With
Fertilizer” handouts and calculators. Demonstrate several examples
and then allow students to work collaboratively to complete the
handout.
5. When students have completed the handout, allow time for
questions and discussion. Consider beginning the discussion with a
question such as, “How does learning about fertilizer help you to
pass the GED math test?” Students need to see how what they are
doing in real life and in class relates to the GED test and future
career goals.
Assessment:
•
Observe student participation and interaction.
Extension:
•
4-70
Have students figure the amount of fertilizer needed for each of
the lawns given in the “Seed Broadcasting” handout from the
Seeding a Lawn lesson and/or the “Sod Installation” handout from
the Sod for an Instant Lawn lesson provided earlier in this chapter.
Horticulture Math
Answers for Handout:
1.
Size
Formula
Nitrogen
5 lbs
5-10-5
.25 lbs
Phosphate/
Phosphorus
.5 lbs
Potash/
Potassium
.25 lbs
Filler
10 lbs
5-10-10
.5 lbs
1 lb
1 lb
7.5 lbs
15 lbs
10-10-10
1.5 lbs
1.5 lbs
1.5 lbs
10.5 lbs
25 lbs
8-0-24
2 lbs
0
6 lbs
17 lbs
50 lbs
6-6-18
2. a. 15 bags
3 lbs
3 lbs
9 lbs
35 lbs
4 lbs
b. No
3. a. 11 bags
b. ¼ bag, 12 ½ pounds
4. a. 5-10-5
b. 40 pounds
c. 1 bag
5. a. 5-10-10
b. 120 pounds
c. 720 bags
References:
Homeowner’s guide to fertilizer. (n.d.). Retrieved February 3, 2007, from
http://www.agr.state.nc.us/cyber/kidswrld/plant/label.htm
Understanding fertilizer labels. (2003). Retrieved February 3, 2007, from
LESCO Website: http://www.lesco.com/default.aspx?PageID=76
Horticulture Math
4-71
Understanding Fertilizer Labels
The three bold numbers on all fertilizer bags refer to
the percentage of primary nutrients in the fertilizer.
Primary nutrients are: nitrogen (N), phosphorous (P)
and potassium (K). The first number indicates the
percentage of nitrogen, the second number indicates
the percentage of phosphate which includes
phosphorus, and the last number indicates the
percentage of potash which includes potassium.
Fertilizer
For example, the bag pictured is a 24-5-11 blend. It contains 24%
nitrogen, 5% phosphate/phosphorus, and 11% potash/potassium. The
remaining 60% is filler, usually sand or granulated limestone.
To calculate the amount of fertilizer nutrients in a given bag:
Multiply the bag weight x the percentage of each nutrient.
For example, the calculations for the amount of nutrients in a 50-pound
bag of 24-5-11 fertilizer would be calculated as follows:
1. 50 x 24% = 12, therefore the bag contains 12 pounds of nitrogen.
2. 50 x 5% = 2.5, therefore the bag contains 2 ½ pounds of
phosphate/phosphorus.
3. 50 x 11% = 5.5, therefore the bag contains 5 ½ pounds of
potash/potassium.
4. 50 x 60% = 30, therefore the bag contains 30 pounds of filler.
Fertilizer comes in many different nutrient mixtures. Some of the most
common include the following:
•
5-10-5
•
5-10-10
•
10-10-10
•
8-0-24
•
6-6-18
4-72
Horticulture Math
Dealing With Fertilizer
1. Use the information on the “Understanding
Fertilizer Labels” handout to determine the
number of pounds of nitrogen,
phosphate/phosphorus, potash/ potassium,
and filler that makeup the contents of each bag
of fertilizer listed in the table below.
Size
Formula
5 lbs
5-10-5
10 lbs
5-10-10
15 lbs
10-10-10
25 lbs
8-0-24
50 lbs
6-6-18
Nitrogen
Phosphate/
Phosphorus
Potash/
Potassium
Filler
2. A customer has a lawn area measuring 75 feet x 40 feet that she
wants to fertilize. She has decided to purchase 5-pound bags of 1010-10 lawn fertilizer. The label on the bag states that one bag
covers 200 square feet.
a. How many 5-pound bags will she need to purchase?
b. Will she have any fertilizer left over? If so, how much?
3. A customer wants to fertilize all the lawn areas around his house.
The four areas to be fertilized measure 40 feet x 120 feet, 60 feet x
120 feet, 30 x 12 feet, and 30 feet x 18 feet. He has decided to
purchase 50-pound bags of 6-6-18 lawn fertilizer. The label on the
bag states that one bag covers 1200 square feet.
a. How many 50-pound bags will he need to purchase?
b. Will he have any fertilizer left over? If so, how much?
Horticulture Math
4-73
Dealing With Fertilizer, continued
4. A soil test indicates that a garden needs 2 pounds of nitrogen, 4
pounds of phosphate, and 2 pounds of potash per 1000 square
feet.
a. What fertilizer ratio would be ideal?
b. How many pounds of that fertilizer should be applied to
1000 square feet?
c. How many 50-pound bags should be purchased for a 50’ x
50’ garden?
5. A group of parents is working together to
create a 500’ x 600’ community
playground. A soil test shows that 6
pounds of nitrogen, 12 pounds of
phosphate, and 12 pounds of potash per
1000 square feet should be applied before
grass is seeded.
a. What fertilizer ratio would be ideal?
b. How many pounds of that fertilizer should be applied to
1000 square feet?
c. How many 50-pound bags should be purchased to fertilize
the entire playground?
4-74
Horticulture Math
Resources
and
Bibliography
5-2
Resources and Bibliography
Internet Resources
This section is an annotated list of useful Internet resources related to teaching and
learning math and numeracy in Adult Basic Skills. These resources were selected to
complement the other chapters of this manual for those professionals who want
additional research-based information and materials to enhance their teaching, learning,
and training endeavors. All listed websites were functional as of March, 2007.
Adult Education Resource and Information Service (ARIS)
http://www.saalt.com.au
Australia is an international voice in adult numeracy education. This site gives an
overview of recent developments in numeracy and literacy education in Australia. It is a
“one-stop” information service for materials, resources, articles, and related links in
numeracy and literacy.
Adults Learning Math Newsletter
http://www.alm-online.org/Newsletters/ALM-Newsletter.htm
This electronic newsletter, published three times per year, contains a variety of items
related to mathematics for Adult Basic Skills. It includes papers, articles,
announcements, book reviews, and other entries relevant to adults learning
mathematics. The editorial staff consists of representatives from Australia, the
Netherlands, and Denmark.
Adult Numeracy Core Curriculum
http://www.basic-skills.co.uk
In late winter of 2001, the United Kingdom published its new curriculum documents for
adult numeracy. The entire document is available at this site. The site links to features of
the new standards and guidelines for Adult Basic Education in the United Kingdom.
Adult Numeracy Instruction: A New Approach
http://www.literacyonline.org/products/ncal/pdf/PR9404.pdf
This is the participant packet from the videoconference Adult Numeracy Instruction: A
New Approach authored by Gal Iddo (1994) and published by The National Center on
Adult Literacy. It contains a wealth of materials, including a list of instructional principles,
sample classroom activities, suggestions for staff development, background information
on reform trends, and lists of key printed and electronic resources on numeracy
instruction.
Resources and Bibliography
5-3
Adult Numeracy and Maths On-line Project (ANAMOL)
http://www.saalt.com.au/numeracy/anamol
ANAMOL is an Australian site dedicated to providing a forum for adult numeracy
practitioners to exchange information, resources, and opinions. Links include Teaching
Ideas and Conversations About Teaching.
Adult Numeracy Network
http://shell04.theworld.com/std/anpn//
This site is devoted exclusively to numeracy. It is for numeracy practitioners around the
world. It includes a discussion group, activities, and resources.
Adult Numeracy Network, Boston Branch
http://www2.wgbh.org/MBCWEIS/LTC/CLC/numintro.html
This site contains resources and learning activities for Adult Basic Skills practitioners. It
would be worthwhile to investigate the activities and resources available at this site.
Algebra Lab
http://www.algebralab.org/
This online learning environment focuses on topics and skills from high school math that
students must be able to use in introductory science courses.
Allmath.com
http://www.allmath.com
This website covers mathematics principles and applications for multiple grade levels.
AlphaPlus Center
http://www.alphaplus.ca/mainframe.htm
A wealth of items from Ontario and abroad form this comprehensive collection of
resources, materials, links, discussions, and current events for numeracy and literacy.
Assessing Mathematical Knowledge of Adult Learners: Are We Looking at What
Counts? NCAL Technical Report TR98-05
http://literacyonline.org/products/ncal/pdf/TR9805
The authors of this report advance a set of principles that reflect psychometric concerns
and current research policies on assessment. These principles can be used to evaluate
existing assessment practices and guide the development of new assessment models.
5-4
Resources and Bibliography
Coping with Math Anxiety
http://www.mathacademy.com/pr/minitext/anxiety/index.asp
Coping with Math Anxiety is written by a math instructor for students and instructors.
This site defines math anxiety, suggests strategies to overcome math anxiety, examines
the roots of math anxiety, and dispels some commonly believed myths about math.
EdHelper.com
http://www.edhelper.com/
This site includes resources, games, and activities for different levels of math.
Education Resources for Adults
http://www.fodoweb.com/erfora/index.asp
This site includes numerous resources focusing on communications and numeracy. The
materials are suitable for adults with functioning levels between 6.0 and 12.0.
ESPN Sports Figures
http://sportsfigures.espn.com/sportsfigures/
This site has a wealth of lesson plans and activities that combine sports, math, and
science.
Explore Math.com
http://www.explorelearning.com/
This site provides interactive math activities with lesson plans.
Florida TechNet
http://floridatechnet.org/
This site offers lesson plans, professional development, and an Internet library.
Framework for Adult Numeracy Standards
http://www.literacynet.org/ann/framework01.html
This paper, authored in 1996 by the Adult Numeracy Network, was funded by the
National Institute for Literacy and is subtitled, The Mathematical Skills and Abilities
Adults Need to Be Equipped for the Future. It contains the research and methodology
behind the creation of the adult numeracy content, and process themes built upon the
Massachusetts Adult Basic Education Math Standards.
Resources and Bibliography
5-5
Funbrain
http://www.funbrain.com
This site provides activities, games, and puzzles in basic mathematics.
Gameaquarium.com
http://www.gameaquarium.com/math.htm
Many online games in different areas of mathematics.
GED Resources for Adult Educators
http://www.aceofflorida.org/ged
This site offers extensive information and materials such as a printable Teachers’
Handbook and extensive lesson plans using realia for all five GED testing areas. It offers
two formats: view materials online or a printer-friendly version.
Inclusive Teaching
http://depts.washington.edu/cidrweb/inclusive/diversify.html
Need to diversify your teaching style? This website gives teachers helpful hints on how
to change their teaching style and lists resources for instructors to first assess their
teaching style, then diversify it.
Issues and Challenges in Adult Numeracy NCAL Technical Report TR9315
http://www.literacyonline.org/products/ncal/pdf/TR9315.pdf
This technical report presents a study that addresses the need for a strong numeracy
component in adult literacy programs. It has four major sections: Mathematics Education
for Adults; Perspectives on Numeracy; Toward Defining Numeracy; and Conclusions
and Implications.
Learning Styles
http://www.d.umn.edu/student/loon/acad/strat/lrnsty.html
This is a web page from the University of Minnesota’s Handbook. It has a summary of
learning styles. It also delves into the theories behind different learning styles. It includes
a brief article that describes students’ learning styles.
LINCS Science and Numeracy Collection
http://literacynet.org/sciencelincs/studentlearner-num.html
This site contains numerous links to science and mathematics materials and resources.
5-6
Resources and Bibliography
Math Anxiety
http://www.math.com/students/advice/anxiety.html
This website has numerous study tips and practical advice needed to overcome math
anxiety. It links to other sites that have helpful tools such as formulas and tables.
Math in Daily Life
http://www.learner.org/exhibits/dailymath/
This site provides text-based commentary on applications of numeracy in everyday
situations, including savings and credit, home decorating, population growth, etc. Some
hands-on activities are included.
Math Forum
http://forum.swarthmore.edu
The Math Forum is an extensive site with many links including Student Center,
Teachers’ Place, and Parents and Citizens. It is not directed specifically to adult
educators, but it has some interesting generic information. The link to Ask Dr. Math
offers explanations to frequently asked questions in multi-level mathematics. Also, there
is a section on “classic” problems suitable for group work.
Math Goodies
http://www.Mathgoodies.com
This site is a source of interactive lessons, puzzles, homework help, message boards,
and much more. The website links to both topic-specific resources and subtopics: Real
World Connections, Parent’s Place, Teacher Talk, etc. Adult learners and instructors will
benefit from visiting this interesting site.
Math Power
http://www.mathpower.com
This site provides information and links about basic math, algebra, study skills, math
anxiety and learning styles and gives students access to tutorials, algebra assignments,
math videos, and a forum for discussing with the professor a variety of math topics.
Mathematics Resources on the Internet
http://mathres.kevius.com/
This website contains hundreds of links to math websites.
Resources and Bibliography
5-7
Math Word Problems
http://www.mathstories.com
Though some of the worksheets available on this site are aimed at children, many are
suitable for use with learners of any age. The worksheets contain solutions.
Measure 4 Measure
http://www.wolinskyweb.com/measure.htm
This site offers students and instructors the opportunity to explore a collection of Internet
math sites that estimate, calculate, evaluate, and translate. It has three main areas:
Science Math, Health Math, and Finance Math.
National Adult Literacy Database (NALD)
http://www.nald.ca
This site is a comprehensive Canadian site for adult educators devoted to adult literacy
and numeracy. It includes events, newsletters, articles, resource lists, and more. It is
easy to navigate and provides a forum for literacy discussion.
National Council of Teachers of Mathematics
http://www.nctm.org/
NCTM is a professional organization for teachers of mathematics. Research,
publications, national standards, and general information are available at the site.
North Carolina Online
http://ncbsonline.net/Directory.htm
This is the North Carolina Basic Skills online resource directory. This site provides links
to other sites as well as numerous math lesson plans.
Ohio Mathematical Planning Committee
http://archon.educ.kent.edu/Oasis/Resc/Educ/numthe.html
This paper investigates each of the seven content and process themes developed by the
Adult Numeracy Network. Included under each theme is a description and commentary
on the related implications for teaching and learning.
PBS Teacher Source
http://www.pbs.org/teachersource/math.htm
This site includes lesson plans and lots of activities for all math levels.
5-8
Resources and Bibliography
Professor Freedman’s Math Help
http://www.mathpower.com/
This site includes information on basic math and algebra written for the adult audience.
Project Based Teaching and Learning Links
http://www.michaelmino.com/links/external.html
This site has numerous links and resources for teachers interested in project-based
teaching and learning. There is also a list of ideas for teacher projects.
PurpleMath.com
http://www.purplemath.com/modules/modules.htm
If you’re looking for practical algebra lessons, then look no further. This site has great
practical tips, hints, and algebra examples and points out common math mistakes.
Quantitative Literacy Bibliography
http://www.stolaf.edu/other/ql/publ.html
This site includes a chronological list of publications related to numeracy.
Quia Top 20 Math Games
http://www.quia.com/dir/math/
Check out the games and other areas provided at this site.
Science and Numeracy Special Collection
http://literacynet.org/sciencelincs
This site originates from the Literacy Information and Communication System, a network
affiliated with the National Institute for Literacy. It includes a link to a student/learner
section that contains interactive activities for all levels of Adult Basic Skills learners.
Sure Math: Teaching Problem-Solving Techniques
http://www2.hawaii.edu/suremath
This site offers “reliable problem solving in all subjects that use mathematics … Algebra,
Physics, Chemistry – from grade school to grad school and beyond.”
Resources and Bibliography
5-9
Books and Articles:
This section is a list of publications related to teaching and learning math and numeracy.
These resources were selected for those professionals who want additional researchbased information and to enhance their teaching, learning, and training endeavors. All
listed websites were functional as of March, 2007.
Adult Numeracy Network. (2005, August 16). Teaching and Learning Principles.
American Council on Education. (2005, July). Who Passed the GED Tests? 2003
Statistical Report. Washington, DC: GED Testing Service.
Ahlstrom, C. (2003). Collaborating with students to build curriculum that incorporates
real-life materials. Focus on Basics, 6C. Cambridge, MA: National Center for the
Study of Adult Learning and Literacy. Retrieved January 3, 2007, from
http://www.gse.harvard.edu/%7Encsall/fob/2003/ ahlstrom.html
Ball, D.L. (2000). Bridging Practices: Intertwining Content and Pedagogy in Teaching
and Learning to Teach. Journal of Teacher Education, 51(3): 241–247.
Buck Institute for Education. (2002). Buck institute for education project based learning
handbook. Retrieved June 9, 2006, from Buck Institute for Education Web site:
http://www.bie.org /pbl/pblhandbook/intro.php
Burchfield, P.C., Jorgensen, P.R., McDowell, K.G., and Rahn, J. (1993). Writing in the
Mathematics Curriculum. Retrieved July 24, 2006, from
http://www.geocities.com/kaferico/writemat.htm
California State Board of Education. (1998, December). Criteria for Evaluating
Mathematics Instructional Resources. Retrieved January 13, 2006, from
http://www.cde.ca.gov/ci/ma/im/documents/math98criteria.pdf
Ciancone, T. (1996). Numeracy in the adult ESL classroom. (ERIC Document
Reproduction Service No. ED392316). Retrieved September 25, 2006, from
http://www.ericdigests.org/1996-4/adult.htm
Countryman, J. (1992). Writing to Learn Mathematics. Portsmouth, NH: Heinemann.
Daviau, J. Steiner, R., Pappas, M., Zabrocki, V. & Jackson, K. (1993). Method to your
mathness: A teacher resource manual. Billings, Montana: Department of Adult
Education.
5-10
Resources and Bibliography
Davidson, N. (1985). Small group cooperative learning in mathematics: A selective view
of the research. In R. Slavin (Ed), Learning to Cooperate: Cooperating to Learn.
NY: Plenum.
Deubel, P. (2006). Math Manipulatives. Computing Technology for Math Excellence.
Retrieved May 21, 2006, from http://www.ct4me.net/math_manipulatives.htm
Dingwall, J. (2000). Improving numeracy in Canada. Ottawa: National Literacy
Secretariat.
Eades, C. (2001). A mingling of minds: Collaboration and modeling as transformational
teaching techniques. Focus on Basics, 5B, 26-29.
Edmonds, K. (2005, Spring). Can numeracy and technology work together? Literacies,
5, 9-11. Retrieved March 1, 2007, from http://www.literacyjournal.ca
The Education Alliance. (2006, Spring). Closing the Achievement Gap: Best Practices in
Teaching Mathematics. Charleston, WV: Author. Retrieved May 31, 2006, from
http://www.educationalliance.org/Downloads/Research/TeachingMathematics.pdf
Gal, I. (1993). Issues and challenges in adult numeracy. Philadelphia, PA: National
Center on Adult Literacy. (ERIC Document Reproduction Service No. ED366746)
Gal, I. (1995). Big picture: What does “numeracy” mean? GED Items, 12, 4-5.
Gal, I., van Groenestign, M., Manly, M., Schmitt, J. J., & Tout, D. (1999). Adult literacy
and lifeskills survey numeracy framework working draft. Ottawa: Statistics
Canada.
Green, A. M.. (2006, July). NCSALL seminar guide: Activity-based instruction: Why and
how. Retrieved April 5, 2007, from http://www.ncsall.net/fileadmin/resources/
teach/GED_inst.pdf
Green, A. M. (1998, June). Project-based learning and the GED. Focus on Basics, 2B,
6-10.
Grouws, D. A. & Cebulla, K. J. (2000a). Improving student achievement in mathematics,
part 1: Research findings. Eric Digest. Columbus, OH: ERIC Clearinghouse for
Science, Mathematics, and Environmental Education. (ERIC Document
Reproduction Service No. ED463952)
Resources and Bibliography
5-11
Grouws, D. A. & Cebulla, K. J. (2000b). Improving student achievement in mathematics,
part 2: Research findings. Eric Digest. Columbus, OH: ERIC Clearinghouse for
Science, Mathematics, and Environmental Education. (ERIC Document
Reproduction Service No. ED463953)
Hanselman, C.A. (1996). Using brainstorming webs in the mathematics classroom.
Mathematics Teaching in the Middle School, 1(9), 766–770. NCTM.
Hiebert, J. (1999). Relationship between research and the NCTM standards. Journal of
Research in Mathematics Education, 30, 1.
Hasselbring, A. C. & Zydney, J. M. (2006). Technology-supported math instruction for
students with disabilities: Two decades of research and development. Retrieved
June 27, 2006, from LDOnline Website: http://www.ldonline.org/article/6291
Huntington, L. (2000, September). Focus on teaching: Beginning math for beginning
readers. Focus on Basics, 4B. Retrieved April 5, 2007, from
http://www.ncsall.net/?id=324
Imel, S. (1998). Teaching adults: is it different? Columbus, OH: ERIC Clearinghouse on
Adult, Career, and Vocational Education, Center on Education and Training for
Employment. Retrieved April 13, 2004, from http://www.otan.us
Jacobson, E., Degener, S., & Purcell-Gates, V. (2003). Creating authentic materials and
activities for the adult literacy classroom: A handbook for practitioners.
Cambridge, MA: National Center for the Study of Adult Learning and Literacy.
Jacobson, E., Degener, S., & Purcell-Gates, V. (2003). The impact of use of authentic
materials and activities. Focus on Basics, 6C. Cambridge, MA: National Center
for the Study of Adult Learning and Literacy. Retrieved October 8, 2004, from
http://www.nscall.gse.harvard.edu/fob/2003/research.html
Kerka, S. (1995). Not just a number: critical numeracy for adults. (ERIC Document
Reproduction Service No. ED385780). Retrieved March 2, 2007, from
http://eric.ed.gov/ERICDocs/data/ericdocs2/content_storage_01/0000000b/80/2a/
23/e8.pdf
Kraft, N. (2003). Criteria for authentic project-based learning. Retrieved June 8, 2006,
from http://www.rmcdenver.com/useguide/ pbl.htm
Leonelli, E. D. (1999). Teaching to the math standards with adult learners. Focus on
Basics, 3C. Cambridge, MA: National Center for the Study of Adult Learning and
Literacy. Retrieved March 21, 2007, from http://www.ncsall.net/?id=771&pid=348
5-12
Resources and Bibliography
Marr, B. & Helm, S. (1991). Breaking the math barrier: A kit for building staff
development skills in adult literacy. Canberra, Australia: Department of
Employment, Education, and Training.
Meader, P. (2000). The effects of continuing goal-setting on persistence in a math
classroom. Focus on Basics, 4A. Cambridge, MA: National Center for the Study
of Adult Learning and Literacy. Retrieved January 29, 2007, from
http://www.gseweb.harvard.edu/~7ncsall/fob/2000/ meader.html
Ngeow, K. Y. (1998). Enhancing student thinking through collaborative learning. (Eric
Document Reproduction Service No. ED422586). Retrieved October 8, 2006,
from http://www.ericfacility.net/databases/ERIC_Digests/ed422586.html
Nonesuch, K. (2005, Spring). Working with student resistance to math tools. Literacies,
5. Retrieved January 5, 2007, from http://www.literacyjournal.ca
Nowlan, D. (2004). Principles of adult education as related to instructional development.
EDER 657 Principles of Adult Education (Concept Paper). Retrieved June 12,
2006, from http://www.ucalgary. ca/uofc/faculties/EDUC/jdnowlan/adult.html
Railsback, J. (2002). Project-based instruction: Creating excitement for learning.
Retrieved June 8, 2006, from http://www.nwrel.org/request/2002aug/benefits.html
Saskatchewan Education. (1991). Chapter 2: Instructional Models, Strategies, Methods,
and Skills. In Instructional Approaches: A Framework for Professional Practice.
Regina, Saskatchewan: Author. Retrieved January 7, 2006, from
http://www.sasked.gov.sk.ca/docs/policy/approach/instrapp03.html
Schmitt, M. J. (2000). Developing adults numerate thinking: Getting out from under the
workbooks. Focus on Basics, 4B. Cambridge, MA: National Center for the Study
of Adult Learning and Literacy. Retrieved January 3, 2007, from
http://www.gse.harvard.edu/%7Encsall/fob/2000/schmit.html
Secretary of Labor’s Commission on Achieving Necessary Skills (SCANS). (1991). What
work requires of schools: A SCANS report for America 2000. Washington, DC:
U.S. Government Printing Office.
Secretary of Labor’s Commission on Achieving Necessary Skills (SCANS). (1992).
Learning a living: A blueprint for high performance. Washington, DC: U.S.
Government Printing Office.
Resources and Bibliography
5-13
Tout, D. (2000, July). Having some fun with math-the Aussie way. Paper presented at
the Adults Learning Mathematics Conference. Retrieved September 11, 2006,
from http://www.alm-online.org/ALM7/abstracts.html
Tout, D. & Schmitt, M. J. (2002). The inclusion of numeracy in adult basic education.
Review of Adult Learning and Literacy, 3. Retrieved September 21, 2006, from
http://www.ncsall.net/?id=771&pid=573
Van Groenestijn, M. (2001). Assessment of math skills in ABE: A challenge. ALM-7
Conference Proceedings. (ERIC Document Reproduction Service No ED478890)
Whitin, Phyllis and Whitin, David J. (2000). Math is language too: Talking and writing in
the mathematics classroom. Urbana, IL: National Council of Teachers of English,
and Reston, VA: National Council of Teachers of Mathematics.
Why Do Project-Based Learning. (2004). The multimedia project: Project-based learning
with multimedia. Retrieved June 8, 2006, from http://pblmm.k12.ca.us/PBLGuide
Wrigley, H. S. (1998). Knowledge in action: The promise of project-based learning.
Focus on Basics, 2D. Cambridge, MA: National Center for the Study of Adult
Learning and Literacy. Retrieved June 8, 2006, from
http://www.gse.harvard.edu/%7Encsall/fob/1998.wrigley/htm
5-14
Resources and Bibliography
Bibliography
Alavert™ Label. Retrieved February 25, 2007, from http://www.alavert.com
Barber, D., Kitchens, A. & Barber, W. (1997). Mastering the mind for math. Boone, NC:
Appalachian State University.
Benadryl™ Label. Retrieved February 25, 2007, from http://www.pfizerch.com
Bianchina, P. (2006). Crushed rock–the ideal solution. Retrieved January 27, 2007, from
http://www.doityourself.com/stry/crushedrock
Biviano, M. (2003, April 23). The nursing crisis: Improving job satisfaction and quality of
care. (Slide presentation). Rockville, MD: Agency for Healthcare Research and
Quality. Retrieved January 15, 2007, from
www.ahrq.gov/news/ulp/workforctel/sess1/bivianotxt.htm
Boor, M. A. (1994). Math for Horticulture. Columbus, OH: Ohio Agricultural Education
Curriculum Materials Service, Ohio State University.
Cooking by numbers. (2007). Retrieved February 11, 2007, from
http://www.learner.org/exhibits/dailymath/meters_liters.html
Curtain-Phillips, M. (2004). The causes and prevention of math anxiety. Retrieved
February 26, 2007, from MathGoodies Website:
http://www.mathgoodies.com/articles/mathanxiety.html
Dimetapp™ ND Label. Retrieved February 25, 2007, from http://www.dimetapp.com
Dingwall, J. (2000). Improving numeracy in Canada. Ottawa: National Literacy
Secretariat.
Gal, I. (1993). Issues and challenges in adult numeracy. Philadelphia, PA: National
Center on Adult Literacy. (ERIC Document Reproduction Service No.
ED366746).
Gal, I., van Groenestign, M., Manley, M., Schmitt, J. J., & Tout, D. (1999). Adult Literacy
and lifeskills survey numeracy framework working draft. Ottawa: Statistics
Canada.
Gardner, H. (1999). The disciplined mind. New York: Simon & Schuster.
Resources and Bibliography
5-15
Glass, B. (2001). Numbers talk: A cross-sector investigation of best practices in LS
numeracy. Ottawa: National Literacy Secretariat.
Homeowner’s guide to fertilizer. (n.d.). Retrieved February 3, 2007, from
http://www.agr.state.nc.us/cyber/kidswrld/plant/label.htm
Imel, S. (1998). Teaching adults: Is it different? Columbus, OH: ERIC Clearinghouse on
Adult, Career, and Vocational Education, Center on Education and Training for
Employment. Retrieved April 13, 2004, from http://www.otan.us
Johnes, T. (2004). Culinary calculations: Simplified math for culinary professionals.
Hoboken: NJ: John Wiley & Sons.
Liebowitz, M. & Taylor, J. C. (2004, November). Breaking through: Helping low-skilled
adults enter and succeed in college and careers. (Electronic Copy). Retrieved
February 25, 2007, from
http://www.ncwe.org/documents/report_2004_ncweJff_breakingThrough.pdf
Leonelli, E. D. & Schwendeman, R. (Eds.). (1994). The Massachusetts ABE math
standards. Retrieved September 9, 2004, from
http://www2.wgbh.org/Mcweis/LTC/CLC/abemathhomepage.html
Melton, C., Gaffney, B., McAlister, C. & Shapiro, S. (2006). Fundamentals of
mathematics for nursing. Retrieved January 15, 2007, from
http://www.adn.eku.edu/math.pdf
Numeracy in Focus (1). (1995). Melbourne, Australia: Adult Basic Education Resource
and Information Service.
Pesticide use. (n.d.). Retrieved February 2, 2007, from South Dakota Department of
Agriculture Website: http://www.state.sd.us/doa/das/hp-pest.htm
Powell, M. A. (1994). Planting techniques for trees and shrubs. Leaflet No. 601.
Retrieved January 28, 2007, from http://www.ces.ncsu.edu/depts/hort/hil/hil601.html
Schmitt, M. J. (2000). Developing adult numerate thinking: Getting out from under the
workbooks. Focus on Basics, 4B. Cambridge, MA: National Center for the Study
of Adult Learning and Literacy. Retrieved January 31, 2007, from
http://www.gse.harvard.edu/%7Encsall/fob/2000/schmitt.html
5-16
Resources and Bibliography
Strianese, A. J. and Strianese, P. P. (2001). Math principles for food service
occupations, 4th ed. Albany, NY: Delmar Publishing.
Turfgrass America. (2005). Retrieved March 3, 2007, from
http://www.turfgrassamerica.com/
Understanding fertilizer labels. (2003). Retrieved February 3, 2007, from
http://www.lesco.com/default.aspx?PageID=76
Withnall, A. (1995). Older adults’ needs and usage of numerical skills in everyday life.
Lancaster, England: Lancaster University.
Yasukawa, K., Johnston, B. & Yates, W. (1995). Numeracy as a critical constructivist
awareness of maths: Case studies from engineering and adult basic education.
Regional Collaboration in Mathematics Education, (Proceedings from ICMI
Conference), 815-825.
Zemke, R. & Zemke, S. (1981). 30 things we know for sure about adult learning. Council
for Christian Colleges and Universities. Retrieved April 13, 2004, from
http://www.cccu.org/resourcecenter
Resources and Bibliography
5-17