Mathematics • Year 7 • Unit 2 • Lesson 1
Algebra in the Real World
Use the building blocks of algebra — variables, constants, coefficients, expressions and equations — to describe everyday situations like buying snacks, scoring a game, and packing lunchboxes.
1. Word problems
Each problem uses ideas from Lesson 1: pick a variable, write an expression, and decide whether the situation gives you an expression or an equation. Show your working — answers without working only get half marks.
1.1 — Apples in your lunchbox. One apple costs 80 cents. You buy n apples.
(a) Write an expression for the total cost (in cents).
(b) What is the variable? What is the coefficient? 2 marks
1.2 — Movie tickets. A movie ticket costs $15. Your group buys n tickets, plus pays $6 for popcorn to share.
(a) Write an expression for the total amount spent (in dollars).
(b) Identify the variable, the coefficient and the constant.
(c) If the group spends exactly $51, write the equation that lets us find n. 3 marks
1.3 — Game points. In a card game, each red card is worth 3 points and each blue card is worth 5 points. Sam has r red cards and b blue cards.
(a) Write an expression for Sam's total score.
(b) How many terms does the expression have, and what are the two coefficients? 2 marks
1.4 — Sticker mystery. Mia has a packet with x stickers in it, plus 4 loose stickers on the desk. Altogether she has 16 stickers.
(a) Write an EQUATION using x to describe this situation.
(b) Is "x + 4" by itself an expression or an equation? Why? 2 marks
1.5 — Pizza party. A large pizza is cut into 8 slices. You order p large pizzas for a party. Each guest eats 2 slices, and there are 5 leftover slices.
(a) Write an expression for the total number of slices ordered (use 8p).
(b) Write an expression for the total number of slices eaten, using g for the number of guests.
(c) If "slices ordered" = "slices eaten + 5", write that as an equation. 3 marks
2. Explain your thinking
This question is about communication, not just symbols. Use full sentences. 4 marks
2.1 A classmate says: "I don't get why we need letters in maths. Numbers are good enough." In your own words, explain (i) why algebra uses variables, (ii) give one real-life situation where a variable is more useful than a single number, and (iii) explain the difference between an expression and an equation using your own example.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Apples
(a) Total cost = 80n cents (80 cents per apple × n apples).
(b) Variable = n (number of apples). Coefficient = 80.
1.2 — Movie tickets
(a) Total cost = 15n + 6 dollars (n tickets at $15 each, plus $6 popcorn).
(b) Variable = n; coefficient of n = 15; constant term = 6.
(c) Equation: 15n + 6 = 51.
1.3 — Card game
(a) Total score = 3r + 5b.
(b) 2 terms. Coefficient of r = 3; coefficient of b = 5.
1.4 — Stickers
(a) Equation: x + 4 = 16.
(b) "x + 4" on its own is an expression because there is no equals sign. It just describes the total but doesn't tell us what the total IS.
1.5 — Pizza party
(a) Slices ordered = 8p (8 slices per pizza × p pizzas).
(b) Slices eaten = 2g (each guest eats 2 slices).
(c) Equation: 8p = 2g + 5.
2.1 — Explain your thinking (sample response)
(i) Algebra uses variables (letters like x or n) because the value of something isn't always known in advance, or it can change. A letter is a placeholder for "any number" — it lets us write one rule that works for every possible value, instead of writing a new sum for each one.
(ii) Real example: if I buy n cans of drink at $2 each, the total cost is 2n dollars. This single expression works whether I buy 1 can or 50 cans — n stands in for whichever number I end up choosing.
(iii) An expression is just a phrase (no equals sign), like 2n + 3. It describes how to calculate something. An equation is a sentence with an equals sign, like 2n + 3 = 11, which we can solve to find what n must be.
Marking: 1 for naming "placeholder/unknown"; 1 for a real example with a variable; 1 for the no-equals/has-equals distinction; 1 for a clear example of each.