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Fractions and Probability Quest

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Fractions Meet Probability Adventures

Differentiated Worksheet (Year 7)

Fractions and probability illustration

📢 Teacher Read-Aloud Script

Tier 1: "You will work with simple fractions using denominators like 2, 3, 4, 5, and 10. For probability, you'll count outcomes and write them as fractions. Take your time and show your working."

Tier 2: "You'll work with fractions that need simplifying and some larger denominators. For probability, convert your answers to simplified fractions. Show all working clearly."

Tier 3: "You'll tackle mixed numbers and improper fractions, plus challenging probability questions. Some questions ask you to explain your reasoning using fractions."

📖 How to Read Your Answers

• Write fractions with a line: 3/4 or use the fraction boxes provided

• Show working in the small boxes

• For probability, write answers as fractions first, then simplify

🟢 TIER 1 (Questions 1-15)

Part A: Fractions (Questions 1-7)

1. Which fraction is larger? Circle your answer: 1/2 or 1/4
2. Write an equivalent fraction: 1/2 = ____/4
3. Add these fractions: 1/4 + 1/4 = ____
4. Subtract: 3/5 - 1/5 = ____
5. Multiply: 1/3 × 2 = ____
6. Which is equivalent to 2/4? Circle: 1/2 or 1/3
7. Add: 1/10 + 3/10 = ____

Part B: Probability (Questions 8-15)

8. A coin is flipped. List all possible outcomes: ____________
9. What is the probability of getting heads? Write as a fraction: ____
10. A dice has 6 sides. How many possible outcomes? ____
11. Probability of rolling a 3 on a dice = ____
12. Circle the word: Rolling a 7 on a 6-sided dice is: impossible / likely
13. A bag has 2 red balls and 3 blue balls. Total balls = ____
14. Probability of picking red = ____
15. Which is more likely: picking red (2/5) or blue (3/5)? ____________

🟡 TIER 2 (Questions 1-15)

Part A: Fractions (Questions 1-7)

1. Compare and write < or >: 3/8 ____ 5/12
2. Simplify: 6/9 = ____
3. Add: 1/6 + 1/3 = ____
4. Subtract: 5/8 - 1/4 = ____
5. Multiply: 2/7 × 3 = ____
6. Find equivalent fraction: 4/12 = ____/3
7. Add and simplify: 2/8 + 3/8 = ____

Part B: Probability (Questions 8-15)

8. A spinner has 8 equal sections: 3 red, 3 blue, 2 green. List outcomes.
9. Probability of spinning red = ____ (write as simplified fraction)
10. Probability of spinning blue = ____ (simplify if needed)
11. Which colour is most likely? ____________
12. A bag has 15 marbles: 6 red, 4 blue, 5 yellow. P(red) = ____
13. Simplify your answer from Q12: ____
14. P(not yellow) = ____
15. Is P(blue) greater than 1/4? Show working to explain.

🔴 TIER 3 (Questions 1-15)

Part A: Fractions (Questions 1-7)

1. Convert to improper fraction: 2 3/5 = ____
2. Compare: 7/4 ____ 13/8 (write < or >)
3. Add: 1 1/4 + 2/3 = ____
4. Subtract: 2 1/2 - 3/4 = ____
5. Multiply: 3/8 × 4 = ____ (write as mixed number)
6. Simplify: 18/24 = ____
7. Which is larger: 11/6 or 1 5/8? Show working.

Part B: Probability (Questions 8-15)

8. Two dice are rolled. How many total outcomes? ____
9. P(sum equals 7) = ____ (simplified)
10. P(sum greater than 10) = ____
11. A card is drawn from 20 cards: 8 red, 7 black, 5 blue. P(red) = ____
12. If you draw a card and it's red, what's P(black) on second draw?
13. Compare P(red) and P(black) from Q11. Which is greater?
14. A spinner has P(green) = 2/9. If there are 18 sections, how many are green?
15. Explain why P(impossible event) = 0/1 using fractions reasoning.

📋 Answer Key

Tier 1:

1. 1/2 2. 2 3. 1/2 4. 2/5 5. 2/3 6. 1/2 7. 4/10 or 2/5

8. heads, tails 9. 1/2 10. 6 11. 1/6 12. impossible 13. 5 14. 2/5 15. blue

Tier 2:

1. < 2. 2/3 3. 1/2 4. 3/8 5. 6/7 6. 1 7. 5/8

8. red, red, red, blue, blue, blue, green, green 9. 3/8 10. 3/8 11. red or blue 12. 6/15 13. 2/5 14. 10/15 or 2/3 15. Yes, 4/15 > 1/4

Tier 3:

1. 13/5 2. > 3. 1 11/12 4. 1 3/4 5. 1 1/2 6. 3/4 7. 11/6

8. 36 9. 1/6 10. 1/12 11. 2/5 12. 7/19 13. P(red) > P(black) 14. 4 sections 15. No outcomes possible means 0 favourable outcomes

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