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Additional Proportional Reasoning Problems

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Title: Additional Proportional Reasoning Problems


1
Additional Proportional Reasoning Problems
1
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Proportional Reasoning
  • Deliberate use of multiplicative relationships to
    compare and to predict

3
Mixing Colours
  • Jane
  • Lianne
  • same shade?
  • Explain.

2 cans
3 cans
2 cans
3 cans
4
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

5
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
16
- 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?
17
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?
18
Download Problem
Downloaded 3200 kB in 4 sec.
  • about how long for a 1200 kB file?
  • other useful equivalent rates?

19
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?

20
Student Samples
21
I noticed that you decided if there was an extra
person, it would take exactly one less hour. How
did you decide that?
22
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?
23
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?
24
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

35
Student Samples
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Remember
  • What makes a great answer?
  • Big ideas and lesson goals
  • Scaffolding and Challenging
  • Strategies used

40
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.
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