📊 Part 1: Understanding Percentage Equivalence

1. Calculate both expressions using decimal multiplication:

a) 45% of 20 = 0.45 × 20 = _______

b) 20% of 45 = 0.20 × 45 = _______

c) What do you notice about your answers? ________________________________

2. Circle True or False for each statement:

30% of 40 = 40% of 30 True / False

25% of 60 = 60% of 25 True / False

15% of 80 = 80% of 15 True / False

3. Complete the equivalence pairs:

a) 12% of 50 = ____% of 12

b) 35% of 60 = 60% of ____

c) ____% of 25 = 25% of 16

4. Match the equivalent calculations by drawing lines:

18% of 50

24% of 75

36% of 25

75% of 24

25% of 36

50% of 18

📏 Part 2: Bar Models and Problem Solving

5. Draw a bar model to show that 30% of 40 equals 40% of 30:

6. A shop has 80 items. Sarah calculates that 15% of the items are on sale. Her friend Ben says this is the same as calculating 80% of 15. Is Ben correct? Show your working:

7. Complete this table using the percentage equivalence rule:

Calculation A	Calculation B (Equivalent)	Answer
28% of 25	25% of ____	____
____% of 45	45% of 16	____
42% of 30	____% of ____	____

🧠 Part 3: Justification and Real-World Application

8. Explain in your own words why 35% of 60 equals 60% of 35. Use the key vocabulary: decimal, multiplication, equivalent, proportion.

9. At a school fundraiser, 24% of the $75 raised came from cake sales. The organiser claims this equals 75% of $24. Calculate both amounts and explain whether the organiser is correct:

10. Create your own percentage equivalence problem using numbers between 10 and 50. Show that both calculations give the same answer:

Working: