Lesson Study on Proportional
Reasoning by OSO
George Mason University
Bell, Erhard, Perrow, & Smith
1
4/9/2015
Main Mathematical Task
Students with special needs and language
barriers will explore proportional reasoning
while solving two main math dilemmas.
Students are patiently encouraged to
construct their own individual or group
strategies for problem solving.
Bell, Erhard, Perrow, & Smith
2
4/9/2015
Virginia
Standards of Learning

Virginia SOL 6.6 The student will
a) multiply and divide fractions and mixed numbers; and
b) estimate solutions and then solve single-step and
multistep practical problems involving
addition, subtraction, multiplication, and division of fractions.

Virginia SOL 6.7 The student will solve single-step and
multistep practical problems involving addition, subtraction,
multiplication, and division of decimals.

Virginia SOL 6.18 The student will solve one-step linear
equations in one variable involving whole number
coefficients and positive rational solutions
Bell, Erhard, Perrow, & Smith
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4/9/2015
Warm-Up 1: Find the Lowest Price
The table shows the prices
for CDs at 3 different
stores.

Which store has the lowest
price per CD? How do you
know?
Use pictures, words, & numbers
to show how you got your
answer.
Store
# of
CDs
Total
Price
A
4
$30.00
B
2
$15.00
C
1
$8.99
Warm-Up 2: Quinn’s Lollipops
Quinn needed 15 bags of candy to
give to her friends. Quinn wanted
to put 3 lollipops in each bag.

How many lollipops did Quinn
need to buy?
Use pictures, words, & numbers to
show how you got your answer.
Bell, Erhard, Perrow, & Smith
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4/9/2015
Main Problem:
Caterpillars and Leaves
A sixth grade class needs 5 leaves each day to feed
its 2 caterpillars.
 How many leaves would the students need each
day for 12 caterpillars?
Show your answer in words, pictures, and numbers.
Relationship to the 6th grade
Math SOLs


Problems were selected to encourage
student’s abilities to develop their own
rational problem solving strategies.
Problems required the students to use
estimation and multiple steps with
addition, subtraction, multiplication, and
division.
Bell, Erhard, Perrow, & Smith
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4/9/2015
Why We Chose these Activities


Our team discussed the abilities of the
sixth grade inclusion math class. We
considered the high percentage of
students who failed the 5th grade math
SOL test.
To maintain consistency, we used the
same type of warm up activity the
students have been doing all year.
Bell, Erhard, Perrow, & Smith
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4/9/2015
Student Strategies



Students worked in groups of four to
solve the main dilemma.
They were encouraged to try a variety of
ways to solve the problem. All ideas
were considered.
Students described and illustrated their
strategies using posters.
Bell, Erhard, Perrow, & Smith
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4/9/2015
Three Strategies Observed

Wesley’s group used the unit rate to solve the
problem. 1 Caterpillar eats 2.5 leaves.

Kylie’s group used equivalent the ratio. 2
caterpillars eat 5 leaves, 12 caterpillars must eat 6
times that many leaves.

Jacob’s group used the co-variant method. The first
two caterpillars ate 5 leaves, and the next two ate
five leaves and the next two ate five leaves, adding
2 more caterpillars and 5 more leaves until 12
caterpillars are present.
Bell, Erhard, Perrow, & Smith
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4/9/2015
Revisions pg. 1

For the original presentation, four different problems
were prepared. Only two problems were used after
the warm-up: 1. Caterpillar & Leaves, 2. Trick or
Treating Dilemma.

One team member used Quinn’s Lollipop warm-up
that correlated with the caterpillar question.

One team member eliminated the warm up due to
time constraints.
Bell, Erhard, Perrow, & Smith
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4/9/2015
Revisions, pg. 2

Another member changed the number of leaves to
even numbers and used paper leaves instead of
counters. Paper leaves could be torn in half.

Two of the members eliminated the Halloween
question as their closure activity.

One member created a new closure question that
students had to work on independently.
Bell, Erhard, Perrow, & Smith
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4/9/2015
Manipulatives we used
Reflection




This PowerPoint is a composite of the most
effective strategies we discovered for presenting
this lesson.
We all felt that we grew in our understanding
and ability to encourage proportional reasoning
among our students.
We also develop a greater respect for allowing
students to construct their own strategies for
problems solving.
This occurred most readily in a atmosphere of
inquiry without judgment.
Bell, Erhard, Perrow, & Smith
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4/9/2015