Mathematics • Year 7 • Unit 2 • Lesson 4
Like Terms in the Real World
Use "collecting like terms" to tidy up real-world totals — adding scores, counting toys, calculating perimeters, working out shopping bills. The same idea every time: like things group with like things.
1. Word problems
For each, build the expression first (using like-term language) and then simplify by collecting like terms.
1.1 — Collecting cards. You have 5x cards in your album. Your friend gives you 3x more, and then you trade away 2x.
(a) Write an expression for the total you have now.
(b) Simplify your expression. 2 marks
1.2 — Bag of marbles. A bag has 4r red marbles and 6b blue marbles. You add another 3r red marbles and remove 2b blue marbles.
(a) Write an expression for the marbles in the bag now.
(b) Simplify your expression. Why can't the r terms and b terms be combined? 3 marks
1.3 — Shopping bill. A shopping list says: 3 apples at $a each, 2 oranges at $o each, and 5 more apples at $a each. The total cost (before tax) can be written as 3a + 2o + 5a.
(a) Simplify the expression.
(b) If a = $1.20 and o = $0.80, substitute to find the actual bill. 3 marks
1.4 — Lawn perimeter. A rectangular lawn has length x metres and width y metres. The perimeter is x + y + x + y.
(a) Simplify the perimeter expression by collecting like terms.
(b) Use your simplified expression to find the perimeter when x = 8 m and y = 5 m. 2 marks
1.5 — Pet shop count. A pet shop's stock report says: 6c cats and 4d dogs in the morning. By midday, 2c cats were sold, 3d more dogs arrived, and 4 fish were added (call fish f). By 3 pm, 1c was sold and 1f was sold.
(a) Write an expression for the total stock by 3 pm.
(b) Simplify it. 3 marks
2. Explain your thinking
This question is about why we can't combine unlike terms. Use full sentences. 4 marks
2.1 A classmate writes: "3x + 2y = 5xy because if you add 3 and 2 you get 5, and you should multiply the letters together when adding." (i) Explain why this is wrong, (ii) use a real-world example (apples and oranges, or anything similar) to show why x and y can't be combined, and (iii) write the correctly simplified version of 3x + 2y (if any).
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Collecting cards
(a) Expression: 5x + 3x − 2x.
(b) Simplified: 6x cards (5 + 3 − 2 = 6, variable stays).
1.2 — Bag of marbles
(a) Expression: 4r + 6b + 3r − 2b.
(b) Simplified: 7r + 4b. The r terms and b terms can't be combined because red marbles and blue marbles are different things — they have different variables.
1.3 — Shopping bill
(a) Simplified: 8a + 2o (combine the two apple terms: 3a + 5a = 8a).
(b) With a = 1.20 and o = 0.80: bill = 8(1.20) + 2(0.80) = 9.60 + 1.60 = $11.20.
1.4 — Lawn perimeter
(a) Simplified: 2x + 2y.
(b) With x = 8 and y = 5: perimeter = 2(8) + 2(5) = 16 + 10 = 26 m.
1.5 — Pet shop count
(a) Expression: 6c + 4d − 2c + 3d + 4f − 1c − 1f.
(b) Simplified: c-terms: 6c − 2c − c = 3c. d-terms: 4d + 3d = 7d. f-terms: 4f − f = 3f. Answer: 3c + 7d + 3f.
2.1 — Explain why 3x + 2y ≠ 5xy (sample response)
(i) The classmate is wrong because addition doesn't multiply the variables — adding two terms gives a sum, not a product. Also, 3x and 2y have DIFFERENT variables, which means they are unlike terms and cannot be combined at all.
(ii) Think of it as 3 apples + 2 oranges. You can't say that equals 5 "appleoranges" — that's not a real thing. Apples are apples, oranges are oranges. They have to be counted separately.
(iii) The correctly simplified version is just 3x + 2y — it's already as simple as it gets. There are no like terms to combine.
Marking: 1 for spotting addition ≠ multiplication; 1 for naming "unlike variables, can't combine"; 1 for a real-world example; 1 for the correct simplification (or recognising it can't be simplified).