Additional Proportional Reasoning Problems

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Additional Proportional Reasoning Problems
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Proportional Reasoning

• Deliberate use of multiplicative relationships to
  compare and to predict

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Mixing Colours

• Jane
• Lianne
• same shade?
• Explain.

2 cans
3 cans
2 cans
3 cans
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Teagan The Giant

• Teagan measures her height with 6 of her hands.
  The giant measures his height with 6 of his
  hands.
• If Teagan is 4 giant hands tall, how tall is the
  giant measured in Teagans hands

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Teagan and the Giant
Possible Answers
a) 9 b) 24 c) 12 d) 8
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Student Samples
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Four boxes of cookies cost 10.00. How much would
18 boxes cost?
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A lions heart beats 40 beats in 60 seconds. How
long would it take to beat 1 million times?
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Student Sample Solutions
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- I noticed you used the 1000 000 and you used
the 60. You didnt use the 40 - how come? -
Why did you choose to divide?
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How long is 25 000 minutes anyway? How long
would it take to beat 1 million times if the
lions heart beats 40 beats in 50 seconds?
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Download Problem
Downloaded 3200 kB in 4 sec.

• about how long for a 1200 kB file?
• other useful equivalent rates?

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Work Problem

• If it takes 4 workers 6 hours to repair a road,
  how long will it take 9 workers if they work at
  the same rate?

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Student Samples
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I noticed that you decided if there was an extra
person, it would take exactly one less hour. How
did you decide that?
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I noticed you have 4 different answers on the
page. Which of them do you think is correct?
Could there be more than one correct answer?
Which makes the most sense to you?
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Great approach to this problem. What would you
do to figure out how many people you would need
to finish in 2 hours or less?
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What if they werent lazier?!
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Keeping Tabs (EQAO Gr 9 Academic Spring 2009)

• A student council collects aluminum pop tabs to
  raise money to purchase a wheelchair. A company
  buys the pop tabs for 0.88 per kilogram.
• If 1267 pop tabs have a mass of one pound, how
  many pop tabs are needed to purchase a wheelchair
  worth 1500?
• Show your work.
•  

• Hint
• 1 kilogram 2.2 pounds

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Student Samples
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Student Samples
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Student Samples
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Student Samples
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Remember

• What makes a great answer?
• Big ideas and lesson goals
• Scaffolding and Challenging
• Strategies used

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Good Consolidating Question
A
B

• two places on diagram 12 cm apart 6 m
  apart for real.
• someone says enough info to know about any two
  locations on map
• Agree or disagree? Explain why.