Transcript Proportional Reasoning Revisited

Proportional Reasoning
Revisited
Recognizing Multiplicative
Relationships
Scott Adamson
Chandler-Gilbert Community College
An Opening Problem
Sue and Julie are running equally fast
around a track. Sue started first. When
she had run 9 laps, Julie had run 3 laps.
When Julie complete 15 laps, how many
laps had Sue run? (Lamon, 1994)
A Common Response
Sue and Julie are running equally fast around a track. Sue started
first. When she had run 9 laps, Julie had run 3 laps. When Julie
complete 15 laps, how many laps had Sue run?
(Lamon, 1994)
Sue'
s Laps Now
Now
Sue'
s Laps
LaterLater
Sue'
s Laps
Sue'
s
Laps

Julie' s Laps Now Julie' s Laps Later
Julie' s Laps Now Julie' s Laps Later
9 x
 x
9
3 15
3 x3 9 15
15
 15
3xx9135
3
x  45
x  3  15  45
Proportional Reasoning
Simply put, “proportional
Proportional
reasoning is the
reasoning
capstone
tasks
of
the elementary
involve
comparing
school
quantities
curriculum
by using
and the
cornerstone ofand
multiplication
highdivision”
school mathematics
(Miller and
and science
Fey,
2000) (Post, Behr, and Lesh 1988).
Does It Make Sense?
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If one girl can walk to school in 10 minutes, two
girls can walk to school in 20 minutes.
If one box of cereal costs $2.80, two boxes of
cereal costs $5.60.
If one boy makes one model car in 2 hours, then
he can make three models in 6 hours.
If Huck can paint the fence in 2 days, then Huck,
Tom, and a third boy can paint the fence in 6
days.
If one girl has 2 cats, then four girls have 8 cats.
Proportional Reasoning
Describe the relationship between the areas
of the following circles:
r = 12 cm
r = 36 cm
Another Problem Situation
Bart is a publicity painter. In the last few days, he had to
paint Christmas decorations on several store windows.
Yesterday, he made a drawing of a 56 cm high Father
Christmas on the door of a bakery. He needed 6 ml of
paint. Now he is asked to make an enlarged version of the
same drawing on a supermarket window. This copy should
be 168 cm high. Approximately how much paint will Bart
need to do this?
Bakery’s door
Supermarket’s window
Interview with “Tommy”
Interview with “Tommy”
Interview with “Tommy”
Interview with “Tommy”
Interview with “Tommy”
If you were as strong as an ant…
Another strong ant…
Your Curriculum
Think – Brainstorm places in your
curriculum/teaching where proportional
thinking may be developed.
 Pair – Share your list with a partner.
 Share – Be prepared to share with the rest
of the room.
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Another Interesting Problem?
The arm of the Statue of Liberty is 42 feet
long. How long is her nose?
Resources
http://www.mmmproject.org/br/mainfram
e.htm
 http://seeingmath.concord.org/Interactive
_docs/PR_Warmup.htm
 http://www.learner.org/courses/learningm
ath/algebra/session4/part_c/index.html
 http://www.learnalberta.ca/content/mejh
m/html/video_interactives/rateRatioPropor
tions/rateRatioProportionsInteractive.html
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