Proportional Reasoning Challenge

Name:

Date:

Students working with ratios and proportions

🎯 WALT & Success Criteria

We Are Learning To: Synthesise knowledge of proportions, ratios, and percentages to solve complex problems and explain our mathematical reasoning clearly.

Success Criteria - I can:

Apply ratios, proportions, and percentages accurately to solve real-life problems

Explain my reasoning clearly using mathematical language

Use visual representations to support my solutions

Reflect on my problem-solving strategies

🧮 Part 1: Warm-up Problems

1. A recipe calls for 3 cups of flour for every 5 cups of sugar. If you use 12 cups of flour, how much sugar do you need?

Answer: _______ cups of sugar

2. In a school, the ratio of Year 7 to Year 8 students is 4:3. If there are 168 Year 7 students, how many Year 8 students are there?

Answer: _______ Year 8 students

3. A jacket originally costs $80. It's on sale for 25% off. What is the sale price?

$55

$60

$65

$70

🏆 Part 2: Challenge Problem

4. School Fundraiser Challenge:
A school fundraiser sells three items: chocolate bars, bookmarks, and keychains. For every 4 chocolate bars sold, 3 bookmarks and 5 keychains are sold. The fundraiser made $450 in total.

Prices: Chocolate bar = $3, Bookmark = $2, Keychain = $4

How many of each item were sold?

Step 1: Set up the ratio and write what you know:

Step 2: Show your working (use diagrams, tables, or equations):

Step 3: Write your final answers:

Chocolate bars: _______ Bookmarks: _______ Keychains: _______

5. Explain your problem-solving strategy. What method did you use and why?

6. Extension Challenge: If the school wants to make $600 next time using the same ratio, how many of each item would they need to sell?

Chocolate bars: _______ Bookmarks: _______ Keychains: _______