Infusing Math into Inquiry
Based Units 7-12
Joan Barrett
Madison County ROE
jbarrett@madison.k12.il.us
Objectives for Today
 To translate the IL Math Goals (and
Standards) into friendly language and to
review math content related to each
 To suggest some math activities you could
use in your IBL units related to the Math
Goals
 To allow you time today to integrate math
activities related to some of the Math Goals
into your IBL units
STATE GOAL 6: Demonstrate and apply a knowledge and sense of numbers, including
numeration and operations (addition, subtraction, multiplication, division), patterns, ratios
and proportions.
Number/Number Sense
Official Wording
In a Few Short Words
A. Demonstrate knowledge and use of numbers
and their representations in a broad range of
theoretical and practical settings.
Numbers by themselves
B. Investigate, represent and solve problems
using number facts, operations (addition,
subtraction, multiplication, division) and their
properties, algorithms and relationships
C. Compute and estimate using mental
mathematics, paper-and-pencil methods,
calculators and computers
D. Solve problems using comparison of
quantities, ratios, proportions and percents.
Computations
Ratios, Proportions
and Percents
A. Numbers by themselves
What students need to know and be able to do related to this standard
 Count- for older students that is combinations and permutations






(counting books display)
Read, write, order numbers and number words. Write a number
using scientific notation. Write a number as a decimal, percent,
fraction etc.
Know categories of numbers - Odd? Even? Prime or Composite?
Is it a square number? Triangular number?
Do operations on a number. Can I raise it to a power? Find the
square root?
Understand that you can break a number apart and put it back
together
Have a solid understanding of place value including decimals
Children should have a sense of how big a number is or how small
and what number makes sense in a scenarios.
•Individually read your
Bald Eagle Fact Sheet and
decide where each
number belongs.
•Compare the individual
decisions at your table
and be ready to explain
why each number makes
sense.
STATUS:
On July 12,______ , the bald eagle was
reclassified from endangered to threatened in the
lower ____ states. It remains unlisted in Alaska.
DESCRIPTION:
35
48
40
6
SIZE:
8
80,000
•Whole Group Discussion
•There is a copy of the
Bald Eagle Fact Sheet that
can be used as a template
for each teacher’s unit at
Joan’s handout website.
The majesty and strength represented by the bald
eagle are world renowned. The eagle is referred to
as 'bald' because of the white plumage on its head.
Its yellow eyes and beak stand in contrast to its
dark brown body. Eagles can reach flight speeds
between _____ and 44 miles per hour.
One of the largest raptors, the bald eagle is 32 to
_____ inches long with a wingspan of ____ to
____ feet. Males are smaller than females.
110,000
POPULATION:
30
_______ to _________ eagles exist in the wild;
4,500 breeding pairs in the lower 48 states.
1995
LIFESPAN:
Over ____ years in the wild; longer in captivity.
Can you figure out where the numbers from the box on the left fit into the fact sheet on
Bald eagles on the right? If you have good number sense you can fill in the numbers
even though you may not know a lot about eagles.
The answers can be found at http://www.kidsplanet.org/factsheets/bald_eagle.html
Make a number fact sheet about your favorite topic for your classmates to solve.
M2T2 Website for Numbersense


http://www.mste.uiuc.edu/m2t2/resources
.html#numbersense
M2T2 handouts of Sears Tower and
Gateway Arch
Some possible activities for 6A
 Do (or could) the students count anything in my unit? It could be people, birds in a
given area, supplies, seeds, days of rain, possibilities of routes, etc
 Could the students make “trading cards” for the subject of your unit? Birds, Foods,
Planets, Countries, Famous People, (Presidents). The cards would have pictures of the
subject on one side and their important stats on the other.
 Have students take part in the Classroom Feeder Watch sponsored by Cornell
University
 Create a counting book with facts and pictures similar to those displayed at this session.
Bibliography of these books are at Joan’s handout website.
 Have students create a number fact sheet on their topic. Fact Sheets could be used as a
“hook” at the beginning of a unit, an assessment during a unit, or a product to produce.
See Bald Eagle Fact Sheet, Sears Tower, and Gateway Arch samples
Websites related to 6A
 Hardcopy handout and electronic
copy at Joan’s website
Websites Related to Goal 6, Standard A
Gateway to Educational Materials
http://www.thegateway.org/
Website with Fact Sheets about animals
http://www.kidsplanet.org/factsheets/map.html
Animal Facts
http://www.zoo.org/educate/animalfacts1.htm
Animal Information
http://www.seaworld.org/animal-info/index.htm
Welcome to the Wonderful World of Insects
http://www.earthlife.net/insects/six.html
Classroom Bird Feeder Watch (Count)
http://birds.cornell.edu/cfw/home.html
World Fact Book
http://www.cia.gov/cia/publications/factbook/index.html
All Federal Agencies have Kids Pages with their Statistics at this central site
http://www.fedstats.gov/kids.html
Internet Public Library – section on Presidents of the United States
http://www.ipl.org/div/potus/
Websites Related to Goal 6, Standard A (cont.)
The Counting Game for PreK-1
http://home.earthlink.net/~cmalumphy/countinggame.html
A PreK-K site for counting
http://math.rice.edu/~lanius/counting/
Count – On (click on Numberland to get the numbers 1-100 and facts about each
http://www.counton.org/
Science Website for Children
http://www.kapili.com/topiclist.html
Weather for K-5 Students - National Oceanic and Atmospheric Administration site
http://www.education.noaa.gov/sweather.html
University of Michigan’s Weather and Animal web resources
http://groundhog.sprl.umich.edu/site/links/links.html
Iditarod- education
http://www.cabelasiditarod.com/2002/education.html
Enchanted Learning (multiple links for Science/animals and Soc Studies topics like States and
Presidents
http://www.enchantedlearning.com/Home.html
Early number concepts (delightful site for early primary)
http://www.abc.net.au/countusin/default.htm
B-C. Computation
Combining numbers (add, subtract, multiple, divide) in and
out of context. Students also need to decide the method
they’ll use (mental, calculator, or pencil) and whether the
answer needs to be exact or if an estimate will do.
Computation Strategies
Taken from Young Mathematicians at Work- Constructing Numbersense, Addition and Subtraction
By Catherine Fosnot and Maarten Dolk
A “String” is a series of problems that encourage the use of a given strategy. When
using strings, only write one problem at a time on the board or overhead and stop and talk
about each one before adding the next.
25 + 25
25 +26
25 + 24
24 + 26
Splitting
28
+
20 + 8
60
44
40 + 4
12
10 + 2
70 + 2 = 72
14 X 15
Individually think about what the
answer to this problem is.
Be ready to share your answer and
method of solving it.
We want to generate as many ways to
solve this problem as we can.
Graph paper and scissors
=
14
7
30
15
Then 14 x 15 = 7 x 30
Computation strategy handout
What computations do (or could) my
students do during my unit?
Do they total costs?
Divide materials among groups or people?
Do computations related to measurements?
Add distances covered each day of the
race?
Add and divide to find averages?
D. Ratios and Percents
In intermediate grades students
should have a good number
sense about fractions, decimals
and percents and realize that
they are interchangeable
names for the same quantity.
Some Possible Activities for 6D
(ratios and percents)
 Percentages: In my unit do the students figure percentages of
something happening or look at the ratio of one quantity to another?
 Fraction Sentences to Describe Data - Any graph that students look
at or create can generate fraction sentences. I.E. if there were 31
people that were surveyed and 3 said they are raising chickens on their
farm then the students could write that 3/31 (or about one tenth or
10%) of the farmers surveyed raise chickens.
 Great New Fractions-Percents-Decimals Interactive Website that
allows a student to change the numerator and denominator numbers
and automatically the corresponding decimal, percent and picture is
displayed. When you get to the site select “applet”
 http://my.nctm.org/eresources/view_article.asp?article_id=2071
 Scale Drawings: Any scale drawings (including maps) require ratios.
Some Possible Activities for 6D
ratios and percents - continued
Ratios/percents
Village of 100 - There are many websites related to Village of 100 but
this one gives the references to the agencies and sources of the data
http://www.populationconnection.org/Communications/ED2002WEB/
WorldOneHundredDataMaster.pdf
Indirect Measurement: Classic measurement problem with one
unknown. Height of a far away mountain or tree? The object to be
measured may be in an inaccessible area like across a river. Also
can find the height of tall objects using shadow measurements.
See “Shake and Peek” boxes in Probability section as simulation
for counting and determining ratio of Males to Females
Fraction Kit with Microsoft Word demo
STATE GOAL 7: Estimate, make and use measurements of
objects, quantities, and relationships and determine acceptable
levels of accuracy.
Official Wording
In a Few Short Words
A. Measure and compare quantities
using appropriate units, instruments
and methods.
Measuring Instruments and Units
B. Estimate measurements and
determine acceptable levels of
accuracy.
C. Select and use appropriate
technology, instruments and
formulas to solve problems,
interpret results and communicate
findings.
Estimation
Solving Measurement Problems
7A. Measuring Instruments and Units
 Students should be able to use



appropriate units for the task
measuring instruments (rulers, scales, clocks,
thermometers, calibers, probes that are attached to
calculators or handheld computers, etc.),
Demo Probes with handhelds
Some Possible Activities for 7A
 Find distances in the students environment (on their
bodies, on the playground or distances between familiar
landmarks in their town that would equal length or
distances related to your unit topic. I,e, the distance
covered in one day in the Iditarod is equal to the
distance between our school and the Dairy Queen.
Activities for 7A (continued)
 Measure objects related to your unit (i.e. seeds, plants)
over time using scales, rulers, etc
 Websites related to measurement
 Animated history of clocks
http://www.britannica.com/clockworks/main.html
 Metrics Matter
 http://tqjunior.thinkquest.org/3804/
 Metric History Timeline
 http://library.thinkquest.org/J002831/metrictimeline.ht
m
Demo IPAC probes
In my unit do (or could) my students
use any kind of measuring devices?
Paper clips? Rulers? Timers? Scales?
Thermometers? Protractors?
Probes attached to calculators?
Measuring devices attached to IPACs?
7B. & C. Estimating and Solving
Measurement Problems
 Students should be able to estimate
measurements
 Solve measurement problems (area,
perimeter, volume, etc.)
 Pe-rim-eter
Big Measurement Ideas
1.
2.
3.
Relationship between area and perimeter. If
one remains the same, does the other?
Relationship between surface area and volume
Relationship between diameter and
circumference
Area and Perimeter Task with graph paper and tiles
Class Chart on Circles
Websites related to 7B & C
A collection of applets for measurement for 4th-10th
grade students
 http://www.mste.uiuc.edu/java/default.php
 An Applet that allows students to investigate the
relationship between area and perimeter.
 http://www.mste.uiuc.edu/users/carvell/rectperim/R
ectPerim.html
Possible activities for 7B&C
 Could my students determine the length,
perimeter, area, volume or weight/mass of
anything in the unit? Especially consider
irregularly shaped objects.
 Is there an opportunity to introduce my
students to the relationship between area and
perimeter? I.e. if I keep the perimeter
constant, does the area stay constant?
Fencing for a garden – is there a “best way?”
 Brainstorm with your team on possible
measurement connections to your unit
STATE GOAL 8: Use algebraic and analytical methods to identify
and describe patterns and relationships in data, solve problems and
predict results.
Official Wording
A. Describe numerical
relationships using variables
and patterns.
B. Interpret and describe
numerical relationships using
tables, graphs and symbols.
C. Solve problems using
systems of numbers and their
properties.
D. Use algebraic concepts and
procedures to represent and solve
problems.
In a Few Easy Words
Patterns and Representing them
Tables, Graphs and Symbols
Numbers and their properties
Solve Problems using Algebra
Patterns and Representing them
 Repeating Patterns
 Growing patterns
 Power of patterns in all fields
 Do (or could) my students look at trends
or patterns of behavior or growth in my
unit?
8B. Tables Graphs and Symbols
 Write number sentences to describe scenarios,
stories or relationships. “Each yard of fencing
costs seventy five cents. So if I want to figure
the cost of any length fence I could write.
 F x .75 = C (cost)
 caterpillar exercise with pattern blocks
Activities and Websites Related to 8B.
 Translate sentences from the nonfiction materials students
are reading to number sentences.
 Educational Java Programs (Click on “Biology” to use a
mathematical model to look at the relationship of population
growth of oak trees, to squirrels to their predators – hawks.)
You can see side by side pictures of trees growing and the
corresponding graph. http://www.arcytech.org/java/
 Northwestern Mutual’s Longevity Game –
http://www.northwesternmutual.com/nmcom/NM/longevityga
meintro/toolbox--calculator--longevitygameintro-longevity_intro
8C&D. Solving Problems Using Algebra
 Using variables in number sentences (could
be boxes in the primary grades) is an
algebraic skill
 Understanding Equality
 Communitive, Associative, Additive identity,
etc.
 Generalizing from specifics is algebraic
thinking
 Sorting activity
STATE GOAL 9: Use geometric methods to analyze, categorize
and draw conclusions about points, lines, planes and space
Official Wording
In a Few Easy Words
A. Demonstrate and apply
geometric concepts involving Shapes by Themselves
points, lines, planes and space.
B. Identify, describe, classify
and compare relationships using Classify and Compare Shapes
points, lines, planes and solids.
C. Construct convincing
arguments and proofs to solve Construct convincing arguments
problems
D. Use trigonometric ratios and
circular functions to solve
Trigonometry, (Triangles)
problems.
9A. Shapes by themselves
 Think about 1 shape. Can the student draw or
construct a given shape? Is it 2 or 3 dimensional?
What is it’s geometrical name? How many sides
and/or faces and vertices does it have? What kind of
angles are in the shape? Is it symmetrical?
Concave? Convex, Open, closed? etc.
 Nickname
 Diamond
 Oval
Math Name
Rhombus
Ellipse
 2-D shape names end in “gon”
 3-D shape names end in “hedron”
 Demo Microsoft Draw for Irregular shaped polygons
9B. Classify and Compare Shapes
 Think about more than one shape.
Compare and contrast shapes. Are
they congruent? Similar? Which has
more sides? Categorize them
 Pattern and Geometry Power Point
STATE GOAL 10: Collect, organize and analyze data
using statistical methods; predict results; and interpret
uncertainty using concepts of probability.
Official Wording
In a Few Easy Words
A. Organize, describe and
make predictions from
existing data.
Organize and analyze given data
B. Formulate questions,
design data collection
methods, gather and analyze
data and communicate
findings.
C. Determine, describe and
apply the probabilities of
events.
Collect, organize, and analyze
your own data
Probability
10A. Organize, Describe, and analyze
GIVEN data
 We have been given data about the sugar
content of cereals on the top and middle and
bottom shelves of the grocery store.
 First, each of you have received a slip of paper
that has the name of a cereal from the top shelf
and the number of grams of sugar that cereal
has.
 Take the corresponding number of snap cubes
and bring them with you as we gather together
Let’s review “Measures of Central Tendencies”
from your data experiences
 Talk with a partner about the meaning of the
following words: Mode, Median, Mean, Range,
Outlier
 Can you create a set of numbers where the mean
median and mode are all the same, all different? Be
ready to share your sets of data. What other
questions could you pose to assess you students’
statistical understanding
 Mode, median, mean can all be found with physical
materials, paper and pencil calculations, and
software programs. Students should have
experience with all three.
Always have students write about
their data





fraction/decimal/percent
statements
write statements they
know for sure about the
data
What seems to be
implied from the data?
What questions does the
data raise?
Would you do anything
differently in collecting
the data if you repeated
the survey
10B. Collect, organize and analyze
your own data

Brainstorm all of the
errors that students
make when making a
graph. Be ready to
share them with the
group.
All graphs should have:








Overall relevant title for the graph
Each axis titled (horizontal and vertical)
Scale consistent on each axis
Numbers on the axis should be written on the line
not between lines (like on maps)
Zero marked or a place for zero on each axis
A Key if it is a Pic-to-graph
Independent variables go on the horizontal axis
and the dependent are graphed on the vertical axis.
The appropriate type of graph for the subject. No
line graphs unless looking at rate of change.
Activities and Websites related to 10B
 Students could design a survey related to issues
from the unit, display results in a graph, draw
conclusions, and make decisions/recommendations
based on the findings.
 Use Excel Spreadsheets to collect any numerical
data such as temperatures over time, plant growth
over time, weights and heights of animals, counts
of populations at a given place or time in history.
Etc.