Mathematics • Year 7 • Unit 1 • Lesson 6
Fractions in the Real World
Use fractions to share pizza fairly, work out how much pocket money is left after spending, and read fractional amounts on packets and recipes.
1. Word problems
Each problem uses fractions from Lesson 6: finding a fraction of a quantity, comparing two fractions of the same whole, or converting between improper and mixed forms. Show your working — a single answer with no working only earns half marks.
1.1 — Pizza party. A large pizza is cut into 12 equal slices. You eat 3 slices; your friend eats 4 slices.
(a) Write the fraction you each ate.
(b) Who ate more, and what fraction of the pizza is left? 2 marks
1.2 — Pocket money. Maya gets $40 pocket money. She spends 3/8 of it at the canteen.
(a) How much did she spend?
(b) How much does she have left? 3 marks
1.3 — Recipe time. A pancake recipe uses 2 1/4 cups of flour. Liam wants to write this on his shopping list as an improper fraction so he can measure with quarter-cup scoops.
(a) Convert 2 1/4 to an improper fraction.
(b) How many quarter-cup scoops of flour will he need? 2 marks
1.4 — Lego set. A Lego set has 240 bricks. After an afternoon of building, Aisha has used 5/6 of the bricks.
(a) How many bricks has she used?
(b) How many bricks are left in the bag? 3 marks
1.5 — Class survey. In a class of 30 students, 2/5 chose soccer as their favourite sport, 1/3 chose basketball, and the rest chose other sports.
(a) How many students chose soccer?
(b) How many students chose basketball?
(c) How many chose other sports? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A Year 7 student says: "1/8 must be bigger than 1/4 because 8 is bigger than 4." Explain in your own words: (i) is the conclusion right or wrong, (ii) what mistake the student is making about denominators, (iii) what the correct rule is for comparing fractions with the same numerator. Use a real-life example (like pizza slices or chocolate bars) to support your explanation.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Pizza party
(a) You ate 3/12, friend ate 4/12.
(b) Friend ate more (4 > 3 with the same denominator). Left over: 12 − 3 − 4 = 5 slices, so 5/12.
1.2 — Pocket money
(a) 3/8 of $40: 40 ÷ 8 = 5, then 5 × 3 = $15 spent.
(b) Left: 40 − 15 = $25. (Quick check: $25 is 5/8 of $40, since 5/8 of 40 = 5 × 5 = 25.)
1.3 — Recipe
(a) 2 1/4 = (2 × 4 + 1)/4 = 9/4.
(b) He needs 9 quarter-cup scoops.
1.4 — Lego
(a) 5/6 of 240: 240 ÷ 6 = 40, then 40 × 5 = 200 bricks used.
(b) Left: 240 − 200 = 40 bricks. (Check: 1/6 of 240 = 40. ✓)
1.5 — Class survey
(a) Soccer: 2/5 of 30 = (30 ÷ 5) × 2 = 6 × 2 = 12.
(b) Basketball: 1/3 of 30 = (30 ÷ 3) × 1 = 10.
(c) Other: 30 − 12 − 10 = 8.
Check: 12 + 10 + 8 = 30 ✓.
2.1 — Explain your thinking (sample response)
The conclusion is wrong. The student is treating the denominator like a regular whole number, but the denominator tells you how many equal parts the whole is split into. The bigger the denominator, the smaller each part is. For example, a pizza cut into 8 equal slices gives much smaller slices than the same pizza cut into 4 equal slices. So 1/8 (one of 8 small slices) is smaller than 1/4 (one of 4 big slices). The correct rule for fractions with the same numerator: the fraction with the smaller denominator is larger.
Marking: 1 for saying conclusion is wrong; 1 for naming the misconception about denominators; 1 for the correct rule; 1 for a clear real-life example.