1 Additional Proportional Reasoning Problems. Proportional Reasoning Deliberate use of...

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Additional Proportional Reasoning Problems

Proportional Reasoning• Deliberate use of multiplicative

relationships to compare and to predict

Mixing Colours

• Jane

• Lianne

• same shade?• Explain.

2 cans 3 cans

2 cans

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2

1

23 cans

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 Teagan’s hands

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Teagan and the Giant

a) 9b) 24c) 12d) 8

Possible Answers:

Student Samples

Four boxes of cookies cost $10.00.How much would 18 boxes cost?

A lion’s heart beats 40 beats in 60 seconds. How long would it take to beat 1 million times?

Student Sample Solutions

- I noticed you used the 1000 000 and you used the 60. You didn’t use the 40 - how come?

- Why did you choose to divide?

How long is 25 000 minutes anyway?

How long would it take to beat 1 million times if the lion’s heart beats 40 beats in 50 seconds?

Download Problem

• about how long for a 1200 kB file?

• other useful equivalent rates?

Downloaded 3200 kB in 4 sec.

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

I noticed that you decided if there was an extra person, it would take exactly one less hour. How did you decide that?

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?

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?

What if they weren’t lazier?!

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.

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Hint:

1 kilogram = 2.2 pounds

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

Good Consolidating Question

• 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.

A B