📚 Learn and Warm Up

Proportional reasoning means comparing quantities and using a relationship to find an unknown amount. If one quantity is multiplied by a number, the related quantity is multiplied by the same number.

Warm-up: Complete the equivalent ratio model.

Red counters: ● ●

Blue counters: ● ● ●

Ratio red:blue = 2:3 = ____:6 = 6:____

Worked example 1: Scaling a ratio

The ratio of cats to dogs is 2:5. If there are 6 cats, multiply both parts by 3: 2 × 3 = 6 and 5 × 3 = 15. So there are 15 dogs.

Worked example 2: Finding a missing value

3 apples cost $6. At the same rate, 5 apples cost ______.

Cost per apple: $6 ÷ 3 = $2. Cost of 5 apples: 5 × $2 = $10.

✏️ Independent Practice

Show your thinking. Write units with your answers where possible.

1. Which ratio is equivalent to 4:7?

8:14

8:21

12:28

2. Complete the ratio table: 2 red beads match 5 blue beads.

Red beads: 2 4 8

Blue beads: 5 ____ ____

3. A recipe uses 3 cups of flour for 8 muffins. How many cups of flour are needed for 24 muffins?

4. Four bus tickets cost $18. How much will 10 tickets cost at the same price?

5. A cyclist travels 36 kilometres in 3 hours. What is the unit rate in kilometres per hour?

6. Match each value to an equivalent value: 1/2, 0.25, 75%.

____ 1/2 ____ 0.25 ____ 75%

A. 25% B. 0.5 C. 3/4

7. The ratio of adults to children at a sports event is 2:7. If there are 18 adults, how many children are there?

8. A map scale is 1 cm : 4 km. Two towns are 7.5 cm apart on the map. How far apart are they in real life?

9. Six notebooks cost $15. Which is the better value: 6 notebooks for $15 or 10 notebooks for $24? Explain using a unit rate.

10. Challenge: Sam says that the ratios 3:4 and 12:15 are equivalent because both numbers in 3:4 were multiplied by 4. Is Sam correct? Explain your thinking.