Mathematics • Year 7 • Unit 2 • Lesson 2
Expressions in the Real World
Turn real-life situations, buying snacks, sharing money, planning a party, into algebraic expressions. Pick a variable, find the operation, watch the order, and check by substituting a number.
1. Word problems
For each, (i) say what your variable stands for, (ii) write the expression, and (iii) test it with the suggested value. Show working.
1.1, Lollies in a bag. A bag contains n lollies. You eat 3 of them on the walk home.
(a) Write an expression for the number of lollies left.
(b) Check your expression with n = 12. 2 marks
1.2, Saving for a game. You start with $25 in your wallet. Each week you save w dollars more.
(a) Write an expression for the total amount in your wallet after 1 week of saving.
(b) Write an expression for the total after 4 weeks of saving w dollars each week.
(c) Check your expression in (b) when w = 10. 3 marks
1.3, Pocket money split. Mum gives you $p pocket money. You spend $4 on chips, then split what's left equally with your brother.
(a) Write an expression for the amount each of you ends up with.
(b) Why does this expression need brackets (or a fraction bar)? 3 marks
1.4, Class party. A pack of party cups holds 12 cups. You buy c packs. Each guest uses 2 cups during the party.
(a) Write an expression for the total number of cups bought.
(b) Write an expression for the total cups used by g guests.
(c) Write an expression for the number of cups LEFT OVER. 3 marks
1.5, Age in different years. Today, your sister is s years old.
(a) Write an expression for her age in 5 years' time.
(b) Write an expression for her age 2 years ago.
(c) Write an expression for HALF her current age.
(d) Test all three when s = 10. 3 marks
2. Explain your thinking
This question is about spotting the trap. Use full sentences. 4 marks
2.1 Pip writes: "I have n apples in my basket. My friend gives me 5 more. So I now have 5 − n apples." This is wrong in two different ways. (i) Identify both errors, (ii) write the correct expression, and (iii) explain (one sentence each) how a Year 7 student could avoid each error in future.
How did this worksheet feel?
What I'll revisit before next class:
1.1, Lollies left
(a) Expression: n − 3. (Start with n; eat 3 means subtract 3.)
(b) Check with n = 12: 12 − 3 = 9 lollies left ✓.
1.2, Saving for a game
(a) After 1 week: 25 + w dollars.
(b) After 4 weeks: 25 + 4w dollars (you saved w dollars each week for 4 weeks = 4w in total).
(c) With w = 10: 25 + 4(10) = 25 + 40 = $65 ✓.
1.3, Pocket money split
(a) Each person ends up with (p − 4) ⁄ 2 dollars.
(b) The brackets (or fraction bar) are essential because you split what's LEFT AFTER the chips. Without brackets, "p − 4 ÷ 2" would mean p − 2 by order of operations, which is wrong.
1.4, Party cups
(a) Cups bought = 12c.
(b) Cups used = 2g.
(c) Cups left over = 12c − 2g.
1.5, Age in different years
(a) In 5 years: s + 5.
(b) 2 years ago: s − 2.
(c) Half her age: s ⁄ 2 (or ½s).
(d) With s = 10: (a) 15 years, (b) 8 years, (c) 5 years, all sensible ✓.
2.1, Pip's apples (sample response)
(i) Two errors: Error 1 Pip used subtraction (−), but "gives me 5 more" means addition (+). Error 2 Pip swapped the order. Even if subtraction were correct, "n take away 5" would be n − 5, not 5 − n.
(ii) Correct expression: n + 5 apples.
(iii) Avoiding Error 1: use the keyword dictionary, "more" always means +, never −. Avoiding Error 2: test the expression with a real number. If n = 10, Pip should now have 15 apples. The expression 5 − n = 5 − 10 = −5, which doesn't make sense for a basket of apples.
Marking: 1 for spotting the wrong operation; 1 for spotting the wrong order; 1 for the correct expression n + 5; 1 for sensible avoidance strategies.