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Proportional Reasoning Exploration

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Proportional Reasoning Exploration

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📚 Part 1: Multiple Choice & Learning Intentions

WALT: Explore ratios, find unit rates, and scale quantities using multiplicative thinking.

Success criteria: I can identify parts of a ratio, calculate unit rates, and scale amounts up or down.

1. If there are 6 red marbles for every 9 blue marbles, how many red marbles are there when there are 54 blue marbles?

24

36

18

48

2. A car travels 150 km in 3 hours. What is the speed in km per hour?

30 km/h

50 km/h

45 km/h

75 km/h

3. A recipe uses 4 cups of flour for every 3 cups of sugar. How much sugar is needed for 8 cups of flour?

4 cups

6 cups

12 cups

5 cups

4. A pack of 12 pencils costs $9. What is the cost per pencil?

$0.75

$1.50

$0.80

$0.25

✏️ Part 2: Short Answers & Practice

5. Find the unit rate and then scale up:

5 apples cost $10. What is the cost of 1 apple? How much do 12 apples cost?

6. Map scale problem:

On a map 1 cm represents 4 km. A route measures 3.5 cm on the map. How many kilometres is the real route? Show your working.

7. Matching — Draw a line to connect each ratio with its unit rate.
A. 8 apples : $12
B. 150 km : 3 h
C. 3 cups sugar : 4 cups flour
D. 5 pens : $7.50
1. $1.50 per apple
2. 50 km/h
3. 0.8 cups sugar per cup flour
4. $1.50 per pen
8. Explain your reasoning:

Choose one of the problems above and write one or two sentences explaining how you found the unit rate or how you scaled the ratio. _________

🌟 Part 3: Extension & Reflection

9. Extension (Advanced learners): Create your own proportional reasoning word problem using a real-life context (shopping, sport, cooking). Include the ratio and ask for a unit rate and a scaled amount.
10. Reflection and differentiation notes for teacher:

Self-check: Tick if you can do these:

Identify parts of a ratio  
Find a unit rate  
Scale amounts up/down

Differentiation ideas: Use counters or a calculator for computation support; provide ratio tables or challenge with open-ended scaling.

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