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MATH AND YOUTH
Center for Educator Recruitment, Retention, & Advancement
INTRODUCTION TO MAY CURRICULUM
Teacher Cadet instructors and the Center for Educator Recruitment, Retention, and Advancement (CERRA) staff
members helped to develop the lessons in this Math and Youth (MAY) curriculum. CERRA also gratefully
acknowledges the work of current and former Teacher Cadet instructors, Anne Ledford, Kathy Richardson, and
Cindy Alford. The South Carolina State Board of Education labeled mathematics as a critical shortage in 1984,
the first year that subject shortage areas were identified statewide.
As part of CERRA’s mission to recruit teachers for the “critical need” subject area of math, Teacher Cadets will
enhance students’ mathematical skills in elementary and middle school classes as well as enhance their own
ability to conduct math lessons. The MAY lessons make learning fun for both the students and the Teacher
Cadets, and, hopefully, will inspire some young people to pursue a career in teaching math.
While the MAY activities are fun and easy to use, they are sophisticated in the skills and knowledge that young
people will gain from them. Each lesson has the following:
 Name of lesson
 Objective
 Content strand
 Materials
 Procedures
 Recommended grade level(s)
 Assessment
 Reference
The lessons are also based on cross-age teaching, which emphasizes the value of social interactions and
cooperative learning to enhance subject mastery. The MAY curriculum emphasizes how math relates to
everyone’s daily life and community. Each lesson includes a recommended grade level to indicate appropriate
age groups to do the lessons. However, Teacher Cadet instructors, classroom teachers, and Teacher Cadets
may exercise some flexibility in determining what is most suitable for the physical, social, and academic skills of
the students with whom they work.
Within Experiencing Education (Theme IV of the Teacher Cadet curriculum) are the following:
 SAY/MAY/FLAY Letter to Principals
 Forms to Schedule SAY, MAY, or FLAY Lessons
 SAY, MAY, FLAY Evaluations
 SAY, MAY, FLAY Certificate of Accomplishment
 Rubrics that can be used to evaluate lessons taught by the Teacher Cadets
(Note: SAY stands for Science and Youth; FLAY stands for Foreign Language and Youth. These supplementary
curricula all enhance skills and interest in teaching these three critical need subjects.)
Theme III, Unit 3, of Experiencing Education, 10th Edition, of the Teacher Cadet curriculum contains instructions
regarding numerous ways in which MAY lessons can be incorporated, presented, and assessed. Also listed are
the numerous standards addressed in the Teacher Cadet course.
CERRA – SOUTH CAROLINA © 2010
PAGE 2
These MAY lessons are designed with much of the educational philosophies presented throughout Experiencing
Education, 10th edition, including the following: Gardner’s Multiple Intelligences, analytical and global learning
preferences, Maslow’s Hierarchy of Needs, cognitive development (as presented by Piaget) and
language/cultural development (as presented by Vygotsky), brain-based learning research, Bloom’s Taxonomy,
and use of various instructional strategies.
Teacher Cadets are encouraged to use other valid sources for additional information in preparation to teach
these MAY lessons. They may want to become more familiar with math terms, develop processing questions,
prepare visuals and models beforehand to use in instruction, and read materials related to the standards and
content of the lessons selected to teach.
July 2010
www.cerra.org
www.teachercadets.com
CERRA MATH AND YOUTH CURRICULUM
PAGE 3
Table of Contents
Numeration
Lesson 1: Cracker Fractions ...........................................................................................5
Lesson 2: The Great Pizza Swap ...................................................................................9
Lesson 3: Three Bean Salads........................................................................................13
Lesson 4: What Is Oobleck Like?...................................................................................16
Estimation
Lesson 5: All Bottled Up .................................................................................................18
Lesson 6: Breakfast Cereal ............................................................................................21
Patterns
Lesson 7: Button Punch Factory....................................................................................23
Lesson 8: Fruit and Vegetable Symmetry .....................................................................26
Lesson 9: Lid Ratios .......................................................................................................29
Lesson 10: Sort and Classify..........................................................................................32
Geometry
Lesson 11: Dot Paper Geometry ...................................................................................35
Lesson 12: Hurkle ...........................................................................................................44
Lesson 13: Straw Structures ..........................................................................................46
Probability and Statistics
Lesson 14: Compiling Data with M&M’s® .....................................................................47
Lesson 15: Raisin Statistics............................................................................................49
Games and Puzzles
Lesson 16: Fraction Game .............................................................................................52
Lesson 17: I Have…Who Has? .....................................................................................55
Lesson 18: Toothpick Puzzles .......................................................................................57
Mathematics through Literature ................................................................................60
CERRA – SOUTH CAROLINA © 2010
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List of Basic Materials Suggested for MAY Lessons
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Beans (dried)
Bottles of different sizes and shapes
Brass fasteners
Bulletin board paper
Buttons (assortment)
Calculators
Construction paper
Foods (variety needed according to lessons)
Geoboards
Glue
Hole punch
Index cards
Markers (washable)
Measuring container
Newspaper
Number cubes or dice
Paper cups
Paper plates of different colors
Paper towels
Posterboard
Rubber bands
Ruler
Safety scissors
Straws
String
Tape
Toothpicks
Washable markers
Yarn
Ziploc® bags of various sizes
Suggestion: Whenever possible, laminate items for re-use.
CERRA MATH AND YOUTH CURRICULUM
PAGE 5
Cracker Fractions
OBJECTIVE:
To recognize equivalent fractions.
CONTENT STRANDS:
Number and Numeration Systems
MATERIALS:
• Construction paper “crackers” which are divided into eighths by lines. Ten “crackers” are needed for
every four students in the class.
• One pair of safety scissors for each student
• Cracker Fractions Chart response sheet (one per student)
PROCEDURE:
Arrange the students into teams of four, and give each person a copy of the Cracker Fractions Chart.
Experiment #1: Give each group one cracker to divide equally among the members of the group. Once
they cut the cracker into equal pieces, they should complete the column of the chart under “Experiment #1.”
Review results in a brief class discussion. Ask the students, “How did you determine how to divide the
cracker? How many eighths did each person receive? What can you say about eighths and fourths from
this activity? (2/8=1/4)”
Experiment #2: Repeat the procedure as above, giving each group three crackers. Record results under
“Experiment #2.” Review results in a brief class discussion. Ask the students, “How did you determine how
to divide the cracker? How many eighths were there in all? How many eighths did each person receive?
What can you say about eighths and fourths from this activity?”
Experiment #3: Repeat the procedure, giving each group two crackers. If some groups come up with “1/2”
and some groups come up with “2/4” on the chart, ask the class why there are two different answers and
discuss the concept of equivalency. (Suggestion: Make a comparison to coins, where one fifty-cent piece
and two quarters both represent the same amount of money.) If all groups come up with the same fraction,
ask them to see if they can find another way to divide the crackers fairly. Record results under “Experiment
#3.” Discuss results with the class. Ask the students, “How did you determine how to divide the cracker?
How many eighths were there in all? How many eighths did each person receive? What can you say about
eighths and fourths from this activity?”
Experiment #4: Combine groups so that each has eight members. Give three crackers to each group and
repeat procedure as with experiment #1. Record results under “Experiment #4.” Discuss results with the
class. Ask the students, “How did you determine how to divide the cracker? How many eighths were there
in all? How many eighths did each person receive?”
Experiment #5: Repeat procedure with four crackers and eight members in each group, but tell groups
they should find three different fractions. Record results under “Experiment #5.” Discuss results with the
class. Ask the students, “How did you determine how to divide the cracker? How many eighths did each
person receive?”
Wrap-up: Discuss what students discovered while doing the activity. Was it more difficult to divide the
cracker with eight people in a group? What strategies were developed for solving the problems?
CERRA – SOUTH CAROLINA © 2010
PAGE 6
Cracker Fractions Chart (Answer Key)
#1
#2
Number of crackers
Number of people
Into how many pieces is
each cracker broken?
What is the name of
one piece?
How many pieces does
each person get?
Name the fraction that
each person gets.
#3
#4
#5
1
4
4
3
4
4
2
4
2 or 4
3
8
8
4
8
2
4
8
4
fourth
fourth
eighth
half
fourth eighth
1
3
half or
fourth
1 or 2
3
1
2
4
¾
½ or 2/4
2/4
4/8
1/4
rd
3/8
1/2
4
8
8
th
RECOMMENDED GRADE LEVEL: 3 – 6
ASSESSMENT:
Cracker Fractions Chart response sheet
REFERENCE:
Adaptation of Kay Toliver activity
CERRA MATH AND YOUTH CURRICULUM
PAGE 7
CRACKER FRACTIONS CHART
Number of
crackers
Number of people
#1
1
#2
3
#3
2
#4
3
4
#5
4
4
4
4
4
8
8
8
8
Into how pieces is
each cracker
broken?
What is the name
of one piece?
How many pieces
does each person
get?
Name the fraction
that each person
gets.
CERRA – SOUTH CAROLINA © 2010
PAGE 8
CRACKERS
CERRA MATH AND YOUTH CURRICULUM
PAGE 9
The Great Pizza Swap
OBJECTIVE:
To visualize equivalent fractions
CONTENT STRANDS:
Number and Numeration Systems
MATERIALS:
 Cardboard (with the thickness of a manila folder) or construction paper
or different colored paper plates (five plates per color) to make the
“dough”
®
 Ziploc bags (one for each group of four students)
 Pizza “ingredients” made from different colored construction paper:
pepperoni, black olives, mushrooms, anchovies
 Scissors
 Glue
 Models of fractions
PROCEDURE:
This lesson is created ideally for four groups of children with each group consisting of five students. You may
need to make adaptations in the materials and grouping activity to suit your classroom situation.
Before teaching this lesson, make the paper pizzas. Create “dough” for four sets of five different colors of paper
plates or cardboard circles, all the same size. Draw lines on the bottom side to show how each circle or plate will
later be cut into fractions. For each color set, mark lines to eventually divide one circle into thirds, one into
fourths, one into sixths, one into eighths, and one into twelfths. “Dough” should not be too thick to cut easily with
scissors. Glue the “ingredients” on the other side of the circle with no lines, and let the glue dry. You may want
to laminate the circles. Then cut each circle according to how it is marked into fractions, and place all five samecolored pizzas in each of the four Ziplock bags.
Ask students what kind of food makes them think of fractions, and when someone says “pizza,” tell the class that
they are going to participate in a math lesson with paper pizzas.
Create four groups, each of five students.
Give each group a Ziplock bag containing the pieces of five same-color pizzas. (Each member of a group
should have the same color pizza, but the color for each group is different from other groups.)
Have each group sort out its five pizzas, each pizza made of the same-size fractions. For example, one pizza
will have six pieces, each piece being one-sixth of the pizza.
Then each group member will be given one of these whole pizzas to exchange with students in other groups,
changing not only colors but also fractions.
Place prepared pizza ingredients into the Ziploc bags. One bag of ingredients is needed for each group
CERRA – SOUTH CAROLINA © 2010
PAGE 10
of four students.
Introduce the idea of “fair trade” to the class. Guide the students into understanding a fair trade by using
the concept of money. What is a fair trade for $1.00? Would four quarters be a fair trade? Would two
half dollars be a fair trade? Would nine dimes and one nickel be a fair trade? What makes a trade fair?
Ask, “Can we make a fair trade with fractions?” Review the concept of fractions and the terms
“numerator” and “denominator.” If you have models of fractions, demonstrate a fair trade of fractions to
students. For example, two-fourths is a fair trade for one-half. If you do not have models, demonstrate
a fair trade for fractions on the board or overhead.
Ask students what kind of food makes them think of fractions, and when someone says “pizza,” tell the
class that they are going to make their own pizzas.
Place students in groups of four.
Give four cardboard circles, glue, scissors, and Ziploc bag of paper ingredients to go on the pizza to
each group. Each member of the group should have the same color, but the color for each group is
different from other groups.
Have students make their own pizzas (be sure to put the ingredients on the side of the cardboard
“dough” that does not have the lines on it). After they finish making their pizzas, tell the class they are
about to participate in “the great pizza swap,” in which they will be trading pieces of the pizzas with other
classmates.
In order to do that, they will have to cut their pizza into pieces. Have the students cut their pizzas into
the correct number of pieces for their table. (Note that the pizza “dough” is to be already marked on the
back with lines which show how to cut the pizza into pieces.)
Discuss what has been done so far. For example, ask students in the “fourths” group, into how many
pieces was your pizza cut? (4 pieces). And what can you tell me about those pieces? (They’re all the
same size.)” Continue until all groups have answered the same questions and the point is made that all
of the pieces at that table must always be the same size.
Explain the next step:
“In a minute, we’re going to have the ‘great pizza swap,’ and you will be trading some of your pizza for
other pieces of pizza, but you have to make sure you do fair trades. Remember what we learned about
‘fair trades’ at the beginning of the lesson.”
“To prepare for this swap, I want you each to work out what would be fair trades for your pieces of pizza.
To help you do that, I am giving each of you a chart to fill out.” Give each student a copy of the “Pizza
Swap” Table.
Demonstrate the activity of filling out the chart and determining equivalent fractions. Tell students to use
only denominators of 3, 4, 6, 8, or 12. In the process of this, be sure to discuss “equivalency.” Tell the
students that if there is no fraction using 3, 4, 6, 8, or 12 as a denominator, to write “none” in that
column. (For example, there is no equivalent fraction for 1/12.)
Have students complete the “Pizza Swap” Tables chart and then discuss the results with the class.
“What are the equivalent fractions for 1/4? (2/8, 3/12) What about 2/4? (3/6, 4/8, 6/12)” Continue this
process with the remainder of the chart.
Tell students the pizza swap is about to begin. (Allow students to use the chart as they participate in the
swap.) The swap will last two minutes. The object of the swap is for each student to end up with a
whole pizza with as many different colors of dough as he can get, so he will want to try to get pieces
from the other tables. They have to remember that when they are done, each needs to have exactly
CERRA MATH AND YOUTH CURRICULUM
PAGE 11
one pizza, just as when they started.
Demonstrate a few examples of a swap. Countdown and start.
During the swap, circulate and talk to any student who seems to be stuck. Countdown to the end of
swap.
Ask students to show their pizzas, and discuss the results.
Determine who has the most colors on his/her pizza. Ask the question, “Did anyone not end up with a
whole pizza?” If someone responds “yes,” ask if he/she received a fair trade. “Suppose one student
does not have a whole pizza. What else could you determine?” (Another student has more than a
whole pizza.)
In the final wrap-up discussion, review the term “equivalency.”
RECOMMENDED GRADE LEVEL: 3rd – 5th
ASSESSMENT:
“Pizza Swap” Tables chart; one whole pizza made with various colors of “dough”
REFERENCE:
Adaptation of Kay Toliver activity
CERRA – SOUTH CAROLINA © 2010
PAGE 12
Pizza Swap Tables
Fractions
Equivalent fractions
Fractions
1/4
1/3
2/4
2/3
3/4
3/3
Equivalent fractions
4/4
Fractions
Equivalent fractions
1/6
Fractions
Equivalent fractions
2/6
1/12
3/6
2/12
4/6
3/12
5/6
4/12
6/6
5/12
6/12
Fractions
7/12
1/8
8/12
2/8
9/12
3/8
10/12
4/8
11/12
5/8
12/12
6/8
Equivalent fractions
7/8
8/8
CERRA MATH AND YOUTH CURRICULUM
PAGE 13
Three Bean Salads
OBJECTIVE:
To practice working with ratios and proportions
CONTENT STRANDS:
Number and Numeration Systems
Numerical and Algebraic Concepts and Operations
Patterns, Relationships, and Functions
MATERIALS:
 Three types of dry beans
 Red beans
 Lima beans
 Black-eyed peas
 Paper plates or paper cups to hold small portions of beans
 Recipes for Three Bean Salads (Preferably laminated for reuse)
 Record sheet of solutions (one copy per student - there are two copies of each of these on
attached sheet.)
 Answer Key
PROCEDURE:
Introduce the activity by asking students if they have ever used a recipe to prepare food, and have
students share personal experiences with recipes. Discuss the importance of following directions and
using the proper amount of each ingredient.
Tell students that they will be preparing a “Three Bean Salad” by following a given procedure, like a
recipe.
Put the dry beans on paper plate or in paper cup, and give to each student.
Give students a sheet of Three Bean Salad “recipes.”
Tell students the following information:
“All three types of beans go into each salad.
Use guesses and adjust as you work. Use the beans to solve the problems.
For each salad, use the clues to determine how many of each of the three types of beans are needed.
When you solve the problem, record solutions on the record sheet.”
Have students do #1 and stop. Lead a class discussion by asking individual students to answer
questions. Ask students, “How did you determine how many lima beans to use? Red beans? Blackeyed peas? What would have happened if you multiplied incorrectly? Is accuracy important?”
Allow the students time to complete the remainder of the “recipes,” and record the solutions on the record
sheet. Conduct class discussions about each of the “recipes” using questions similar to the ones above.
Give individual students an opportunity to explain the process he/she used. Ask if anyone used a
different process to solve the problem.
CERRA – SOUTH CAROLINA © 2010
PAGE 14
EXTENSION:
Make up a different salad. Write instructions for someone else to make your salad.
th
th
RECOMMENDED GRADE LEVEL: 5 – 9
ASSESSMENT:
Record sheet
REFERENCE:
Family Math
THREE BEAN SALAD SOLUTIONS (Answer Key)
Red Beans
Lima Beans
Black-eyed
Peas
1
4
2
4
2
4
4
2
RECIPE NUMBER
3
4
2
5
4
5
2
8
CERRA MATH AND YOUTH CURRICULUM
5
6
3
3
6
4
5
3
7
3
4
1
8
5
10
5
PAGE 15
THREE BEAN SALADS
Each salad contains Red beans, Lima beans, and Black-eyed peas
1
This salad contains:
 2 Lima beans
 Twice as many Red beans as
Lima beans
 10 beans in all
2
This salad contains:
 4 Red beans
 ½ as many Black-eyed peas as
Red beans
 10 beans in all
3
Lima beans make up ½ of this salad.
 The salad has exactly 2 Red
beans
 The number of Lima beans is
double the number of Red
beans
4
This salad contains:
 The same number of Red beans
as Lima beans
 3 more Black-eyed peas than
Red beans
 A total of 18 beans
CERRA – SOUTH CAROLINA © 2010
5
This salad contains:
 12 beans
 ½ of the beans are Red
 Lima beans make up ¼ of the
salad
6
This salad contains:
 At least 12 beans
 It has one more Lima bean than
Red beans
 It has one more Red bean than
Black-eyed peas
7
This salad contains:
 3 times as many Red beans as
Black-eyed peas
 One more Lima bean than Red
beans
 8 beans in all
8
This salad contains
 An equal number of Red beans
and Black-eyed peas
 5 more Lima beans than Red
beans
 No more than 20 beans
PAGE 16
What Is Oobleck Like?
OBJECTIVES:
To use literature to study mathematics
To use tally marks to determine frequency
CONTENT STRANDS:
Numbers and Numeration Systems
MATERIALS:
 Notebook paper and pencil
 Response sheet
 Paper towels - wet and dry
 Oobleck (To make oobleck, combine 1 to 1 1/4 cups cornstarch, 1 cup water, and 1 drop of green food
coloring for every four participants.)
 Plastic containers, paper plates or pie plates to hold the oobleck
PROCEDURE:
Read the book Bartholomew and the Oobleck up to the point that the king says, "Why, I'll be the mightiest man
that ever lived. Just think of it, tomorrow I'm going to have oobleck."
Ask participants to list what they think oobleck will look like. Allow time for the students to share some of their
ideas with the class.
Arrange the students into groups of four. Tell them that you have arranged to have some oobleck flown in for this
class. Hand out the "oobleck" container to each group.
Ask students to examine this substance and tell you what they noticed about it. Tell them to put their fingers into
it, but they are not to taste or eat it.
Hand out wet and dry paper towels; allow time for students to clean their hands.
Have students write individually a list of ten to fifteen words describing "oobleck" on notebook paper. Then
distribute a response sheet to each group of four students. List the words and the frequency they occurred on
the chart.
Compile a class list of the words and their frequency. Point out that some groups used the same word to
describe oobleck. Record the frequency for the class on the chalkboard or overhead.
Use other children's literature to help teach mathematical concepts.
RECOMMENDED GRADE LEVELS: 2nd – 8th
ASSESSMENT:
Response sheet
REFERENCE:
Adaption of Kay Toliver activity
CERRA MATH AND YOUTH CURRICULUM
PAGE 17
What is Oobleck Like?
CHARACTERISTIC
CERRA – SOUTH CAROLINA © 2010
TALLY
FREQUENCY
PAGE 18
All Bottled Up
OBJECTIVE:
To predict and compare the volume of several containers
CONTENT STRANDS:
Measurement
Probability and Statistics
MATERIALS:
• Four bottles (different sizes and shapes)
• A container to measure water (in ml)
• Water
• Data collection sheets
PROCEDURE:
Prior to this activity, label the four bottles A, B, C, and D. Fill each of the bottles with water.
Put students into groups of four.
Place the bottles on a table in the room so that all students can see all four bottles. Have the students draw the
four bottles on the first page of their data collection sheets.
Have the students work with their groups to complete the “prediction” section of their sheets. After they have
determined the order from most to least, guide the students into a discussion about the processes the group used
to come to a conclusion. “How can you tell which bottle holds the most? The least?” Ask the students if they
know a way to find the exact amount each bottle holds. (They should say that you can fill the bottles with water
and measure the water.)
Tell the students that you have already filled the bottles with water. Beginning with bottle A, pour the water into
the measuring container, and read the ml of water the bottle holds. Have the students record the data on their
sheets (Actual Data). Empty the measuring container and repeat with B. Do the same for C and D. Students
can list from most to least based on the actual data. Guide the students in a discussion. “How does the data
compare with your predictions? If you had any letter out of order, why do you think that the actual data was
different?”
The students can now graph the actual data on the last page of the data collection sheet. “Look at the graph to
determine which bottle holds the most. How can you tell?”
“Graphs provide visual representation. Did the graph make it easier to read the data quickly?”
EXTENSION:
Show the students another bottle which is close to the same volume, and have them determine where it fits in
relationship to the other four bottles.
RECOMMENDED GRADE LEVEL: 4th – 6th
ASSESSMENT:
Data collection sheets
REFERENCE:
AIMS Education Foundation
CERRA MATH AND YOUTH CURRICULUM
PAGE 19
CERRA – SOUTH CAROLINA © 2010
PAGE 20
CERRA MATH AND YOUTH CURRICULUM
PAGE 21
Breakfast Cereal
OBJECTIVE:
To use estimation to solve problems
CONTENT STRANDS:
Probability and Statistics
MATERIALS:
 Two large containers (You may make one of these by using five 12 inch squares of poster board
or cardboard. Tape the sides to form a box without a top. The second container should be
made exactly like the first.)
 Eight smaller containers (You may make one of these by using five 6-inch squares of poster
board or cardboard. Tape the sides to form a box without a top. Continue until you have made
eight containers.)
 Tape
 Poster board
 Cereal - enough to fill one of the large containers and all 8 of the smaller containers. (Hint:
Purchase the generic brand of cereal.)
NOTE: If you do not wish to make your own containers, you may purchase them. However, make sure
that the smaller containers fit into the larger container exactly.
PROCEDURE:
Place students into eight groups.
Explain that the workers in the “royal cereal department” lost count of the number of pieces of cereal and
lost their jobs. You are looking to fill the positions, and, as a test, you want each group to tell you how
many pieces of cereal there are in the container.
Discuss how to solve this, and explain the concept of “estimation” as a guess based on some knowledge.
Let groups share their ideas with the class.
Have teams work out estimates, and discuss the results. If you wish, take this opportunity to review place
values with larger numbers.
Then tell the students you are going to give them something to help them estimate better. Take out an
empty box the size of the full one and place it next to the full box on the table. Then take out smaller
boxes full of cereal (one for each group), and give one of these smaller boxes to each group. Ask
students if they can figure out how to use that to guess better.
Start the teams, and circulate as they do the activity. When the teams finish, write each group’s estimate
on the board or overhead. Lead a class discussion about the strategies that they used. (They should
have realized that their containers would fit exactly into the large container.)
Ask the students how they could find the solution exactly. (Count the pieces of cereal.) Once
discussions have concluded, tell the students the correct answer.
EXTENSION:
Have students figure out how to use this information to determine the attendance at a football or baseball
game, etc.
RECOMMENDED GRADE LEVEL: 4th – 8th
CERRA – SOUTH CAROLINA © 2010
PAGE 22
ASSESSMENT:
Explanations of processes used to estimate
REFERENCE:
Adaptation of Kay Toliver activity
CERRA MATH AND YOUTH CURRICULUM
PAGE 23
Button Punch Factory
OBJECTIVE:
To visualize patterns
CONTENT STRANDS:
Patterns, Relationships, and Functions
MATERIALS:
 Fold and Punch activity sheet (one per student)
 Circle activity sheet (one per student)
PROCEDURE:
Give each student a copy of the Fold and Punch activity sheet and the circle activity sheet.
Tell the students the following story:
You are in charge of making unusual hole patterns at the button factory. The factory manager charges
you five cents every time you use the punch machine.
So you want to fold your paper patterns in order to punch all the holes with one punch.
First try the patterns on the Fold and Punch sheet.
Then make some of your own designs.
Allow students time to complete the activity and then have students share solutions with the class.
Guide a discussion of the activity. “Will it always be possible to make a pattern with one punch only?” Ask
students to design a button which requires more than one punch, and share it with a neighbor. How can
you be sure your button requires only one punch?
EXTENSION:
Have students give the button designs they created to other students, and let the other students try to fold
the new button designs.
RECOMMENDED GRADE LEVEL: Grades 3rd – 9th
ASSESSMENT:
Fold and Punch activity sheet
REFERENCE:
Button Fold and Punch ©1997 Sherron Pfeiffer
CERRA – SOUTH CAROLINA © 2010
PAGE 24
CERRA MATH AND YOUTH CURRICULUM
PAGE 25
Circle Activity Sheet
CERRA – SOUTH CAROLINA © 2010
PAGE 26
Fruit and Vegetable Symmetry
OBJECTIVE:
To use fruit and vegetables to visualize different types of patterns and symmetry
CONTENT STRANDS:
Patterns, Relationships, and Functions
Geometry and Spatial Sense
MATERIALS:
NOTE: To reduce expenses, teachers may want to give students portions of these itemized fruits and
vegetables, pre-cut at different angles.
 Apples (one per group)
 Bananas (one per group)
 Kiwi (one per group)
 Squash (one per group)
 Carrot (one per group)
 Plastic knife (one per group)
 Response sheet (one per student)
 Pencil
 Newspaper to cover each working area
 Paper towels to wipe hands
PROCEDURE:
Prior to this activity, prepare working areas for groups of four students by covering the areas with newspaper.
Put the students into groups of four or five. Tell them to be sure to have a pen or pencil to write information.
Discuss with students a trip to the grocery store through the fruits and vegetables section. “What would you
see?” Give students time to respond. There is more to fruits and vegetables than what you see at a glance.
“How does the inside look? How many sides does a banana have? Do all bananas have the same number of
sides?” Symmetry is common in some fruits and vegetables. Review the concept of symmetry. Today we will
have a chance to take a close look at some fruits and vegetables.
Give each group one apple, one banana, one squash, one kiwi, one carrot, and one plastic knife. Give each
student a copy of the response sheet. (NOTE: If the apple or carrot cannot be cut with a plastic knife, give
students a Ziploc® bag containing the pre-cut – at different angles – items.)
Work through the following steps with the first fruit, the apple. Tell groups to concentrate on patterns and
symmetry that they may find in the fruits and vegetables. Tell each group to work with the apple. On their
response sheet, students should draw a picture of the apple before it is cut. Have students discuss within their
groups how the inside of an apple looks. Before allowing the students to cut the apple, point out that there is
more than one way to cut the apple. Each group should decide how to cut the apple, and predict what the cut
will look like. Let them cut the apple to verify their predictions, and draw a picture of the cut on their response
sheets. Cut the apple another way and predict. Draw a picture. Experiment cutting at different angles.
Let the students continue the process with the remaining fruits and vegetables. The teacher can circulate
throughout the room, and observe the students.
When students are finished, guide them in a discussion. “Describe any patterns you see in your cuts.” (Give
students time to answer.) “Did you discover a different pattern when you cut at a different angle, or did every
cut show the same design? Was there any symmetry in your cuts? If so, describe your cut and the symmetry
you found. How accurate were your predictions?”
CERRA MATH AND YOUTH CURRICULUM
PAGE 27
Give students an opportunity to compare their cut fruits and vegetables with other groups. Did all of the groups
find the same patterns? (For example, did all bananas have the same number of sides? Did all apples have
the same pattern?)
Are there any characteristics that all of the fruits and vegetables have in common? If so, do you think that all
fruits and vegetables have that characteristic in common? If not, find a characteristic common to most of them.
EXTENSION:
You may make this activity shorter by using just an apple. Complete the process of predicting, cutting, and
finding symmetry (or patterns) and then use the cross-section of the apple to make apple prints.
th
th
RECOMMENDED GRADE LEVELS: 4 – 8
ASSESSMENT:
Response sheet; students’ responses to open-ended questions
REFERENCE:
I Hate Mathematics by Marilyn Burns
CERRA – SOUTH CAROLINA © 2010
PAGE 28
Fruit and Vegetable Symmetry
Drawing
BEFORE
cut
Drawing
after FIRST
cut
Drawing
after SECOND
cut
Describe
any observations
you made
APPLE
BANANA
KIWI
SQUASH
CARROT
CERRA MATH AND YOUTH CURRICULUM
PAGE 29
Lid Ratios
OBJECTIVE:
To apply the concept of π or the relationship between the circumference of a circle and its diameter
CONTENT STRANDS:
Patterns, Relationships, and Functions
Geometry and Spatial Sense
Measurement
MATERIALS:
 Various sizes of circular lids (one per student)
 String cut into lengths of 100 cm (one string per student)
 Scissors (at least one pair for each group of four students)
 Large sheet of paper for each group (poster board, bulletin board paper)
 Pen or pencil
 Calculator (one per group)
 Ruler (at least one per group)
 Response sheet (one per group)
 Tape
PROCEDURE:
Review circles. Ask the students, “What do you know about a circle?” Include terms such as circumference,
radius, and diameter in the discussion. Be sure that the students understand the terms “circumference” and
“diameter.” Tell the students that they will be using string to find the circumference and diameter of a circle.
Put the students into groups of four per group. Tell the students to take a pen or pencil to their group with
them. Distribute the following materials to the group: four strings, scissors, large sheet of paper, calculator,
rulers, tape, and a response sheet. Have each student choose a lid from the assortment of circular lids.
Have the students cut string that measures around their lid exactly (circumference). Then have the students
cut string that measures across the center of their lid (diameter).
Group member #1 should then tape and label his/her diameter and circumference strings parallel onto the
large sheet of paper. The group should study the two strings and estimate “How many times longer is the
circumference string than the diameter string?” (How many diameter strings would fit along the
circumference string?) The estimate should be recorded on the response sheet.
Continue the process of taping and estimating with the other group members. Be sure to record the
information on the response sheet.
Use the ruler to measure the exact length (to the nearest tenth of a centimeter) of the strings to find the
circumference and diameter for each lid. Record the information on the response sheet.
Use a calculator to find the ratio of circumference to diameter for each lid. Round the answer to the nearest
hundredth of a centimeter, and record this information on the response sheet.
Give the students an opportunity to compare and discuss results within their groups. Then, conduct a class
discussion of the results.
Ask the students how their estimates compared with the actual computation of the ratios. Ask the students
to share with the class the results found when finding the ratio of circumference to diameter. “Are most of
your answers close to each other?” If any are not close to the others, why do you think these are different?
If the students measured and computed correctly, this ratio should be approximately the same for each lid.
CERRA – SOUTH CAROLINA © 2010
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Tell students this value has a special name,” π.”
Ask the students, “What would happen if they followed the same procedure with a larger circle or even a
smaller circle? Would we get the same results?” Give the students an opportunity to test their conclusion by
choosing any circular object in the room (only one object per group). Repeat the process.
The students should get an answer close to π. Tell the students that π has an approximate value of 3.14,
and that the circumference of any circle is always π (3.14) times the diameter.
EXTENSION:
Have the class test to see if the ratio is the same for larger circles. For instance, this activity can be
extended outside the classroom. Have the students construct a circle on the pavement outside of the
school. This can be done using a student, as the center of the circle, holding a rope which acts as the
diameter of the circle. Another student should pull the rope out tight from the center, and, using a piece of
chalk at the end of the rope, sketch the outline of a circle on the pavement. The students can then measure
the circumference and the diameter using either string or a trundle wheel. The ratio of the circumference
and the diameter should again be approximately the value as the ones found in the main activity.
RECOMMENDED GRADE LEVEL: 5th – 9th
ASSESSMENT:
Finding a value close to π; response sheet
REFERENCE:
Family Math
CERRA MATH AND YOUTH CURRICULUM
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GROUP
MEMBERS
ESTIMATE OF
HOW MANY TIMES
LONGER THE
CIRCUMFERENCE
IS THAN THE
DIAMETER
EXACT
MEASUREMENT
OF
CIRCUMFERENCE
(nearest tenth of a
centimeter)
EXACT
MEASUREMENT
OF DIAMETER
(nearest tenth of
a centimeter)
RATIO
CIRCUMFERENCE
DIAMETER
(nearest hundredth of
a centimeter)
#1
#2
#3
#4
CERRA – SOUTH CAROLINA © 2010
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Sort and Classify
OBJECTIVE:
To observe similarities and differences and to practice language skills relating abstract ideas to the real
world
CONTENT STRANDS:
Patterns, Functions, and Relationships
MATERIALS:
 Peanuts
 Pretzels
 “M & M’s”®
 SKITTLES®
 Cheese Balls
 CHEEZ-IT® Crackers
 Another square cracker such as TRISCUITS®, WHEAT THINS®, etc.
 String
 Notebook paper and pencil
 Ziploc® bags (quart size) - one for each student
 Small paper cups (four for each student)
If you choose not to have food, you may use other items to sort. Buttons, lids, bottle caps, plastic bread ties,
and seeds are examples of some other options.
PROCEDURE:
Prior to this activity, the teacher will need to prepare Ziploc® bags with a few of each of the items to be
sorted.
To begin the activity, give each student one of the prepared Ziploc® bags and four small cups.
Have the students remove the objects from the Ziploc® bag, and place them into the cups according to
similar characteristics. Do not assist the students with determining how to sort the objects.
After the items have been sorted, have the students write their rule for sorting the objects.
When everyone is finished, have the students place the objects back into the Ziploc® bag and then sort the
objects according to a different rule. Once again, have the students write the rule.
Repeat this procedure two more times.
Ask the children to explain their rules for sorting the items, and write their rules on the board or overhead.
Students may choose a variety of rules to sort such as color, shape, size, etc.
Have students discuss whether there is another way to sort.
If students do not choose to sort using a concept of “not,” sort them yourself, saying, for example, “These are
green,” “What can I say about these?” and “These are not green.” Then ask the children to find another way
to sort the items using the ideas of “not.”
------------------------------------------------------------For upper elementary through high school grades, the following extension may be used to complete the
lesson:
Make circles of string. Make a circle for each group of objects which have been sorted. Place the objects
into the circles.
CERRA MATH AND YOUTH CURRICULUM
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Practice sorting the objects in various ways using the circles of string.
Introduce the vocabulary word, Venn Diagram.
Use the string to make circles (Venn Diagrams) to represent characteristics of students in the class. For
example: I am a female, I have a sister, I have brown eyes, and so on. Have students with those
characteristics stand in the circles.
EXTENSION:
Make Venn Diagrams on paper to represent students in the class.
RECOMMENDED GRADE LEVEL
rd
th
Grades 3 – 12
ASSESSMENT:
Student explanation of “rule” used to sort.
CERRA – SOUTH CAROLINA © 2010
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Venn Diagram
1
CERRA MATH AND YOUTH CURRICULUM
2
PAGE 35
Dot Paper Geometry
OBJECTIVE:
To use geoboard or geoboard dot paper to create shapes and determine area
CONTENT STRANDS:
Geometry and Spatial Sense
MATERIALS:
 Geoboard and rubber band or geoboard dot paper (laminated) and washable marker - one per
student
 Copies of attached worksheets - one per student (The teacher may choose to create only a few of
these.)
PROCEDURE:
Review the terms “right triangle,” “right angle,” and “area” with students.
Have students create a right triangle on the geoboard or dot paper such that the base is four units and the
height is two units. Demonstrate on the board or overhead the process of determining area. Use the process
of breaking the shape into smaller known areas.
Distribute the Area of Right Triangles sheet to the students. Give students an opportunity to complete the
sheet. Let them use the geoboard or laminated dot paper to help visualize the problem.
After sharing answers to #1, #2, and #3, ask a student to share a solution to #4. Ask if anyone has another
solution. Ask the students, “Why will both solutions work?” Repeat the process with #5 and #6. If no student
has a different solution, challenge the class to create another triangle which has the desired area.
Ask the class, “Can we find the area of other shapes the same way?” (You may now choose to do the other
sheets or some of the other sheets using the same process.) One suggestion would be to have the students
find the area of their first name. Whose name has the greatest area? The least?
EXTENSION:
Have students create their own design and find the area.
Use this activity to help find the formula for the area of a right triangle.
RECOMMENDED GRADE LEVEL: 3rd – 6th
ASSESSMENT:
Completed worksheets; teacher observation of student understanding
REFERENCE:
Dot Paper Geometry ©1990 Cuisenaire Company of America, Inc.
CERRA – SOUTH CAROLINA © 2010
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CERRA MATH AND YOUTH CURRICULUM
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CERRA – SOUTH CAROLINA © 2010
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Hurkle
OBJECTIVE:
To name points on a coordinate grid and use compass points to find the hidden “Hurkle”
CONTENT STRANDS:
Geometry and Spatial Sense
Patterns, Relationships, and Functions
MATERIALS:
 Laminated copies of the attached “Hurkle” paper (two copies per group – one for the leader and one for
the other players to share)
 Washable markers or overhead transparency pens (four different colors per group)
PROCEDURE:
Review with students the process used for naming coordinates.
Explain (or review) compass directions (i.e., North, South, East, West, Northeast, Southwest).
Divide the class into groups of four. Distribute two laminated copies of “Hurkle” paper and four markers (a
different color per student).
Choose a leader from each group for the first game. Other players should have a turn when leading consecutive
games.
The leader decides on a point where the Hurkle is hiding and marks Hurkle’s hiding place on a hidden sheet.
The leader announces, “A small, fuzzy creature is hiding behind some point on the grid.” The object of the
activity is for the other planers to discover the coordinates of that point.
Players take turns guessing coordinates, naming them in ordered pairs, such as (6,8).
The leader responds to each guess with a clue, telling the players what direction that need to go from their guess
to find the Hurkle. For example, if the Hurkle is hiding at (6,8) and guess is (2,4), the leader will say, “Go
Northeast.”
Players keep track of their guesses and clues by marking their guesses using a colored marker. The leader
should mark the guessed point on his hidden “Hurkle” paper and then give the direction players need to move to
find the Hurkle. This helps avoid a common mistake of giving opposite directions or the direction from the Hurkle
to the guess.
Have the students discuss various strategies for making guesses.
EXTENSION:
Play the game on a grid with four quadrants rather than just the first quadrant.
RECOMMENDED GRADE LEVEL: 6th – 8th
ASSESSMENT:
Student’s ability to locate the Hurkle with accuracy.
REFERENCE:
Family Math
CERRA MATH AND YOUTH CURRICULUM
PAGE 45
CERRA – SOUTH CAROLINA © 2010
PAGE 46
Straw Structures
OBJECTIVE:
To build a structure as tall as possible with straws and masking tape
CONTENT STRANDS:
Geometry and Spatial Sense
Measurement
MATERIALS:
 Plastic Straws (20 per student)
 Masking tape (one roll for every two students)
PROCEDURE:
Put students into groups of four. Each group should receive eighty straws and two rolls of tape.
Give students the following instructions: “You are to build a structure using only the straws and tape you
have been given. The structure must be free standing. Your goal is to build the tallest structure
possible.”
Groups are allowed five minutes to build their structure.
After five minutes, announce, “Time is up!” Students must step away from their structures. The teacher
measures the height of each structure to determine a winner. A group is disqualified if their structure collapses.
Ask various participants to explain their approach to the activity and how well their approach worked. Tell the
students to look at the bases of all the structures.
Ask, “Does the shape of the base have any effect on the height of the tower?” Lead a group discussion of
all the shapes that can be seen in their structures.
EXTENSIONS:
 Have each group test the strength of its structure by placing weights (or metal washers) on the structure
until it collapses.

Have each group verify the correctness of its approach by building another structure out of toothpicks
and glue.
RECOMMENDED GRADE LEVEL: 3rd – 8th
ASSESSMENT:
The height of the tower
REFERENCE:
Adaptation of a Kay Toliver activity
CERRA MATH AND YOUTH CURRICULUM
PAGE 47
Compiling Data with M&M’s®
OBJECTIVE:
To compile data and compare results
CONTENT STRANDS:
Number and Numeration Systems
Probability and Statistics
MATERIALS:
®
 Small packages of plain M&M’s (If small packages aren’t available, separate the contents of a larger
®
bag into small zipper bags of about 20 M&M’s .)
®
 Response sheet listing possible M&M’s colors
 Transparency of response sheet
®
NOTE: If students will be allowed to eat the M&M’s after the lesson, please ask them to wash their hands first
as well as work on clean surfaces. As with any classroom food-related project, make sure that students do not
have food allergies or restricted diets.
PROCEDURE:
Give students the response sheet for M&M’s® colors.
Have students predict how many M&M’s® of each color are in one small bag and then write their predictions on
their response sheet.
Give students packages of M&M’s®. Ask them to complete the table by counting the number of each color and
record the numbers.
Using the transparency of the response sheet, compile students’ data of the actual number of M&M’s® by color.
Ask a selection of students to complete the remaining three columns.
Compare the class results to predictions from the M&M’s® /Mars Company:
Brown
30%
Yellow
20%
Red
20%
Orange
10%
Green
10%
Blue
10%
Lead a class discussion about why differences may have occurred between class results and predictions from
M&M’s® /Mars Company.
EXTENSIONS:
Skittles® can also be used.
RECOMMENDED GRADE LEVEL: 3rd – 12th
ASSESSMENT:
Response sheet
REFERENCE:
M&M’s® /Mars
Response Sheet for M&M’s
CERRA – SOUTH CAROLINA © 2010
PAGE 48
CERRA MATH AND YOUTH CURRICULUM
PAGE 49
TOTAL
YELLOW
RED
ORANGE
GREEN
BROWN
BLUE
COLORS
NUMBER
ESTIMATED
ACTUAL
NUMBER
FRACTIONAL
PART
DECIMAL
PART
PERCENTAGE
Raisin Statistics
OBJECTIVE:
To apply the concept of estimation
To use statistical measures
CONTENT STRANDS:
Probability and Statistics
MATERIALS:
 One small box of raisins for each student
 One “Raisin Statistics Chart” handout for each group
 One calculator for each group
PROCEDURE:
Hand out one box of raisins to each student. Tell the students the boxes are to remain closed. If the students will
be allowed to eat the raisins at the end of the lesson, have everyone wash his or her hands before beginning
the lesson. Students should also be working on a clean surface.
Tell the students you would like them to estimate how many raisins are in their boxes. Discuss what it means to
estimate, and make sure they understand that they should have some reasoning behind the number they
chose.
Have several students give you their estimates and explain their reasoning.
Ask the question, “What information would you want to have to make a very good estimate of how many raisins
are in a box without opening it?” Lead a discussion to the idea that it would be good to have counted the raisins
in several boxes.
Arrange the students in groups of four. Give each group a “Raisin Statistics Chart.” Explain the top part of the
chart so that they know what data to include.
Have each group complete the estimate column of their chart.
Tell the students to open their boxes, count the actual number of raisins, and record this information on the
chart.
Find out which student made the best estimate, and congratulate the student.
Compile each group’s statistics on the board or overhead.
Ask students if there is any way to summarize all of this data about the raisins. Have the students list their
group’s data in numerical order from least to greatest. Lead a discussion to the idea of statistical measures.
Introduce or review the following concepts of range, mode, mean, and median;
 range: greatest # of raisins minus the least # of raisins (greatest # - least #)
 mode: the number of raisins that occurred the most often
 mean: average number of raisins
 median: the number in the middle (For a group of four, choose the two middle numbers, add
them together, and divide by two.)
Have each group fill in the bottom section of the chart based on their data.
Compile the statistical data for the class results that were on the board. Have students compare their group’s
data to the class data.
CERRA – SOUTH CAROLINA © 2010
PAGE 50
Ask which of these measures would be most useful to them in estimating the number of raisins in an unopened
box. (There is not necessarily a correct answer to this; it depends on why you want to know. The goal of this
discussion is not to have students agree on one answer, but to lead them to realize that different statistical
measures are most useful for different purposes.)
EXTENSIONS:
Make a graph of the data. (For example, box and whiskers plot.)
rd
th
RECOMMENDED GRADE LEVEL: 3 – 12
ASSESSMENT:
Response sheet
REFERENCE:
Adaptation of Kay Toliver activity
CERRA MATH AND YOUTH CURRICULUM
PAGE 51
Raisin Statistics Chart
Student’s Name
Estimate
Actual
Range: ______________
Mean: ______________
Mode: ______________
Median: ______________
CERRA – SOUTH CAROLINA © 2010
PAGE 52
Fraction Game
OBJECTIVES:
To recognize fractional areas of a circle
To recognize which fractional areas when combined are more than half the area of a circle
To use equivalent fractions
CONTENT STRANDS:
Number and Numeration Systems
MATERIALS:
 Fraction board (laminated so that it can be reused)
 Two number cubes (You may use dice.)
 Washable markers
PROCEDURE:
Begin the activity by reviewing fractions. Ask students, “What is the ‘numerator’ of a fraction? What is the
‘denominator’?” Review equivalent fractions. Ask, “What is another name for 2/4? For 3/6? For 4/6?”
Guide a discussion of fractions with the students.
Introduce the game. The goal of the Fraction Game is to claim as many circles as possible. Players roll dice
to determine a fraction, and shade that fraction on the game board. A circle is awarded to a player who has
colored more than half of it.
To begin play, each player rolls the number cubes. The largest number on the cubes is the denominator of
a fraction, and the smallest number is the numerator of a fraction. The player who can make the largest
fraction begins play.
The players think of the larger number on a cube as the number of parts into which the circle has been
divided (the denominator) and the smaller number as the number of those parts to be colored (the
numerator). For example, a player who rolls a 4 and a 6 may color four sections of a circle that is divided
into sixths. If the player prefers, the four-sixths may be chosen in 2, 3, or 4 different circles.
The players take turns rolling the cubes, each player using a marker to color his fraction on the Fraction
Game board.
A circle is awarded to a player who has colored more than half of it. The player puts his or her initials next to
the circle to denote a “win.”
If a circle is colored exactly half by one player (one-half or two-quarters) and half by the other player, neither
player wins it.
Play continues until all the circles have been awarded to the players or completely colored. The player
awarded more circles is the winner.
You can use equivalent fractions. For example, if you roll a 1 and a 2, you can color one-half, two-fourths, or
three-sixths.
Note: Since this is a game being played by groups of students, the teacher can circulate, and ask questions
to individual students such as “2/6 is equal to what other fraction?” The teacher checks for understanding
and guides students who need help while the game is played.
EXTENSION:
Change the game to make improper fractions.
CERRA MATH AND YOUTH CURRICULUM
PAGE 53
rd
th
RECOMMENDED GRADE LEVEL: Grades 3 – 6
ASSESSMENT:
Fraction Game Board Activity
CERRA – SOUTH CAROLINA © 2010
PAGE 54
Fraction Game Board Activity
CERRA MATH AND YOUTH CURRICULUM
PAGE 55
I Have…Who Has?
OBJECTIVE:
To apply math skills through the use of a game
CONTENT STRANDS:
All
MATERIALS:
 Enough index cards for all students in the class to receive at least one card
 Markers to write math problems on index cards
PROCEDURE:
Use the markers to prepare the index cards using the following procedure.
On the back of one index card, write a math problem beginning with the words “Who has.” For example,
“Who has 3/6?”
On the front of another card, write the answer to that problem and begin with the words “I have.” For
example, “I have 1/2.”
Write another problem on the back of the card that has the answer on it. Then, write the solution on a
third card. Continue this process until all the cards have been used. The solution to the last problem
should be written on the front of the first card.
Pass the prepared cards out to the students so that each student has at least one card.
Choose a student to stand and read the “Who has” side of the card to the class. The student holding the
card with the correct response on the “I have” side of the card stands and reads the solution (the “I have”
side of the card). The first student determines that the solution is correct and is seated. The second
student remains standing and then reads the “Who has” side of the card to the class. (As students stand
to read from their cards, they should always repeat the words “I have” and “Who has.”)
Play continues until all cards have been read. The first student to stand and read will be the last person
standing.
This game can be used to practice and reinforce any math concept. Some examples of questions are
included.
The teacher will need to verify answers. If a student gives an incorrect answer, guide the student to
discover the correct answer.
EXTENSION:
This game may be used with all grade levels and all subject areas.
RECOMMENDED GRADE LEVEL: A variation of this game can be used in all grades, 1st – 12th
ASSESSMENT:
Observation of student’s ability to determine the solution to the problem
CERRA – SOUTH CAROLINA © 2010
PAGE 56
I Have…Who Has?
(More, less, double, dozen, times)
I have 24.
I have 7.
I have 4.
I have 8.
I have 12.
I have 6.
I have 1.
I have 9.
I have 3.
I have 10.
I have 22.
I have 2.
I have 0.
I have 19.
I have 40.
I have 30.
I have 5.
I have 15.
I have 17.
I have 34.
I have 32.
I have 27.
I have 28.
I have 20.
I have 33.
I have 66.
I have 16.
I have 13.
I have 26.
I have 36.
Who has 17 less?
Who has 3 less?
Who has twice as many?
Who has 4 more?
Who has 6 less?
Who has this less 5?
Who has this multiplied by 9?
Who has this plus 1, minus 7?
Who has this doubled plus 4?
Who has a dozen more?
Who has minus 20?
Who has this minus 2, times 6?
Who has 19 more?
Who has this plus 21?
Who has this less 10?
Who has this minus 25?
Who has this times 3?
Who has this and 2 more?
Who has double this?
Who has two less?
Who has 5 less?
Who has one more?
Who has this minus 8?
Who has 13 more?
Who has double this?
Who has this less 50?
Who has three less?
Who has double this?
Who has this and 10 more?
Who has a dozen less?
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Toothpick Puzzles
OBJECTIVE:
To analyze and predict relationships
CONTENT STRANDS:
Patterns, Relationships, and Functions
Geometry and Spatial Sense
MATERIALS:
 Toothpick Puzzles activity sheets (one copy of each page per student)
 Twenty-four toothpicks for each student
 Notebook paper and pencil for each student
PROCEDURE:
Give each student twenty-four toothpicks and the Toothpick Puzzles activity sheet.
The teacher (or Teacher Cadet) may choose to have the class do only a few of these nineteen puzzles.
Allow the students to complete the assigned puzzles. As the students determine a solution to a problem, have them write the solutio
draw a picture of the solution on their notebook paper.
At the end of the activity period, have students share solutions with the class, and tell the class how they
determined the solutions.
EXTENSION:
More Toothpick Problems activity sheets
RECOMMENDED GRADE LEVEL: 3rd – 12th
ASSESSMENT:
Written description or drawings of solutions
REFERENCE:
Fun with Logic
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Toothpick Problems
1. Make three identical squares from the pattern of 15 toothpicks by:
 removing three and moving two;
 removing three and moving three;
 removing three and moving four.
2. Use 24 toothpicks to make the pleasing pattern based on a six-pointed star. Then move
six of the toothpicks to make a new pattern that includes twelve identical parallelograms in
a symmetrical arrangement.
3. The ten toothpicks make up a pattern of three squares. Remove one of the toothpicks and
change the positions of three others to form one square and two parallelograms.
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4. Move four toothpicks to make three equilateral triangles; (b) move four toothpicks, make
four identical diamonds.
5. Make the shape shown, and then add eight toothpicks to divide it into four parts of the
same shape and size.
6. Transform this pattern as follows:
 Remove four toothpicks, leave five identical squares;
 Remove six toothpicks, leave five identical squares;
 Remove six toothpicks, leave three squares;
 Remove eight toothpicks, leave four identical squares;
 Remove eight toothpicks, leave three squares.
Math through Children’s Literature
CERRA – SOUTH CAROLINA © 2010
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Algebra
Among the Odds and Evens: A Tale of Adventure by Pricilla Turner
Anno's Magic Seeds by Mitsumasa Anno
Bats on Parade by Kathi Appelt
How Many Snails? By Robert Wells
If You Hopped Like a Frog By David M. Schwartz
The Patchwork Quilt by Valerie Flournoy
The Rajah's Rice: A Mathematical Folktale from India adapted by David Barry
Data Analysis
The Foot Book by Dr. Seuss
The Great Turkey Walk by Kathleen Karr
One Day in the Prairie by Jean Craighead George
The Outsiders by S.E. Hinton
What's Faster Than a Speeding Cheetah? By Robert E. Wells
YIKES! Your Body Up Close by Mike Janulewicz
Geometry
Fun Ideas for Getting A-Round in Math CIRCLES by Catherine Sheldrick Ross
Grandfather Tang's Story, by Ann Tompert
The Greedy Triangle by Marilyn Burns
The Patchwork Quilt by Valerie Flournoy
Sir Cumference and the First Round Table, by Cindy Neuschwander
Sweet Clara and the Freedom Quilt by Deborah Hopkinson
Measurement
The Foot Book by Dr. Seuss
How Tall, How Short, How Faraway by David A. Adler
Is a Blue Whale the Biggest Thing There Is? by Robert Wells
Math Curse by Jon Scieszka & Lane Smith
One Inch Tall from Where the Sidewalk Ends by Shel Silverstein
Sir Cumference and the Dragon of Pi by Cindy Neuschwander
Number
Anno's Mysterious Multiplying Jar by Masaichiro and Mitsumasa Anno
Homecoming by Cynthia Voigt (travel expenses; distance travelled and rate of travel)
How Many, How Much by Shel Silverstein
Math Curse by Jon Scieszka & Lane Smith
One Inch Tall from Where the Sidewalk Ends by Shel Silverstein
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The Patchwork Quilt by Valerie Flournoy
Number & Operations
Anno's Mysterious Multiplying Jar by Masaichiro and Mitsumasa Anno
Fraction Fun by David A. Adler
Germs Make Me Sick by Melvin Berger
Math Curse by Jon Scieszka & Lane Smith
Number Systems & Numeration
Count Your Way Through Greece by Jim Haskins and Kathleen Benson
Patterns
Bats on Parade by Kathi Appelt
Probability
A Closet Full of Shoes by Shel Silverstein
Do You Wanna Bet? by Jean Cushman
The Giver by Lois Lowry
The Great Turkey Walk by Kathleen Karr
My Little Sister Ate One Hare by Bill Grossman
Picture Puzzle Piece by Shel Silverstein
Probably Pistachio by Stuart J. Murphy
What's Faster Than a Speeding Cheetah? By Robert E. Wells
YIKES! Your Body Up Close by Mike Janulewicz
Rates
Smart from Where the Sidewalk Ends by Shel Siverstein
Ratios
Smart from Where the Sidewalk Ends by Shel Siverstein
Source: http://www.ksu.edu/smartbooks/strandindex.html
CERRA – SOUTH CAROLINA © 2010
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Math Read-Aloud Books
Caple, Kathy. 1986. The Purse. Boston: Houghton Mifflin.
Carle, Eric. 1983. The Very Hungry Caterpillar. New York: Putnam Publishing Group.
Dr. Seuss. 1969. I Can Lick 30 Tigers Today, and Other Stories. New York: Random House.
Giganti, Paul, Jr. 1992. Each Orange Had 8 Slices: A Counting Book. New York: Scholastic.
Kellogg, Steven. 1976. Much Bigger Than Martin. New York: The Trumpet Club.
Pinczes, Elinor J. 1993. One Hundred Hungry Ants. New York: Scholastic.
Schwartz, David M. 1993. How Much Is a Million? New York: Mulberry Books.
Scieszka, Jon, and Lane Smith. 1995. Math Curse. New York: Viking Children’s Books.
Slobodkina, Esphyr. 1988. Caps for Sale: A Tale of a Peddler, Some Monkeys, and Their
Monkey Business. New York: HarperCollins Juvenile Books.
Viorst, Judith. 1978. Alexander, Who Used to Be Rich Last Sunday. New York: Scholastic.
Source: http://readwritethink.org/lesson_images/lesson144/ReadAloudBooksMath.pdf
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