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Proportional Reasoning and Algebra

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Proportional Reasoning and Algebra

📊 Part 1: Patterns and Algebraic Rules

1. Look at this growing pattern: 5, 8, 11, 14, _____, _____

a) What are the next two terms? _______ and _______

b) Describe the pattern in words: _________________________________

2. Which algebraic rule represents the pattern above?

3n + 2

5n + 3

2n + 3

n + 4

3. Simplify these algebraic expressions:

a) 4x + 7 + 2x - 3 = _____________

b) 5y + 8 - 2y + 1 = _____________

4. Solve for the unknown:

a) 3s + 7 = 22 s = _______

b) 2t - 5 = 15 t = _______

⚖️ Part 2: Proportional Sharing and Ratios

5. Sarah and Tom share 60 lollies in the ratio 2:3. How many lollies does each person get?

Sarah gets: _______ lollies

Tom gets: _______ lollies

6. A recipe for 4 people uses 200g of flour. How much flour is needed for 10 people?

400g

500g

600g

800g

7. A jacket costs $120. It has a 25% discount. What is the sale price?

Discount amount: $________

Sale price: $________

🧠 Part 3: Problem Solving

8. Maya saves money following a pattern. In week 1 she saves $5, week 2 she saves $8, week 3 she saves $11.

a) How much will she save in week 6? $________

b) Write an algebraic rule for the amount saved in week n: ________________

c) In which week will she first save more than $30? Week ________

9. Explain your strategy for solving question 8. Use mathematical language in your explanation.

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