Mathematics • Year 7 • Unit 2 • Lesson 1
What is Algebra? — Mixed Challenge
Pull everything from Lesson 1 together: name the parts of an expression, translate phrases into algebra, sort expressions vs equations, find a classic Year 7 mistake, and finish with an open-ended digit puzzle.
1. Mixed problems — choose the right idea
Each question uses a different part of Lesson 1. Decide which idea applies before you start. Show your working. 2 marks each
1.1 Classify each as an expression or an equation: (a) 4n − 3 (b) 4n − 3 = 17 (c) y = 5 (d) 2a + 3b.
1.2 For 6x − y + 11, state (a) the number of terms, (b) the coefficient of x, (c) the coefficient of y, (d) the constant term.
1.3 Translate each phrase into algebra. Use n for "a number". (a) "5 more than a number" (b) "triple a number, then subtract 2" (c) "half of a number, plus 1".
1.4 Rewrite using proper algebra shorthand (no × signs, coefficient in front): (a) x × 8 (b) 1 × y (c) −1 × m (d) 4 × a + 3.
1.5 A bus carries 50 passengers. After s stops, p people have got off the bus. Write an expression for how many passengers are still on board.
1.6 A pencil costs c cents. A rubber costs 30 cents more than a pencil. Write expressions for: (a) the cost of one rubber, (b) the cost of 4 pencils and 1 rubber.
2. Find the mistake
Another Year 7 student has tried to identify all the parts of the expression 5a − 2b + 9. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then redo the working correctly. 3 marks
Student's working — for 5a − 2b + 9:
Line 1: The expression has 3 terms: 5a, 2b and 9.
Line 2: The coefficient of a is 5.
Line 3: The coefficient of b is 2.
Line 4: The constant term is 9.
Line 5: This is an expression (no equals sign).
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write the corrected line in full.
Stuck? Remember: the sign in front of a term BELONGS to the term. The second term isn't 2b — it's something with a sign attached.3. Open-ended challenge — build your own expression
This question has more than one correct answer. Show one that works and explain. 4 marks
3.1 Write an algebraic expression that satisfies ALL of the following rules:
(i) it has exactly 3 terms
(ii) one term uses the variable x with coefficient 4
(iii) one term uses the variable y with a NEGATIVE coefficient
(iv) the third term is a constant term equal to 7.
Write down your expression, then briefly explain in one or two sentences how each rule is satisfied.
Bonus: Now write a real-world story (one sentence) that the expression could describe. For example, "x is the number of …, y is the number of …, and 7 is …".
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Expression or equation?
(a) 4n − 3 → expression. (b) 4n − 3 = 17 → equation. (c) y = 5 → equation (has =). (d) 2a + 3b → expression.
1.2 — Parts of 6x − y + 11
(a) 3 terms. (b) coefficient of x = 6. (c) coefficient of y = −1 (because −y means −1y). (d) constant term = 11.
1.3 — Phrases to algebra
(a) n + 5 (or 5 + n).
(b) 3n − 2.
(c) n⁄2 + 1 (or ½n + 1).
1.4 — Algebra shorthand
(a) x × 8 → 8x (number always first).
(b) 1 × y → y (don't write the 1).
(c) −1 × m → −m (don't write the 1).
(d) 4 × a + 3 → 4a + 3.
1.5 — Bus passengers
Passengers still on board = 50 − p. (The number of stops s doesn't appear in the expression — only the number who got off matters.)
1.6 — Pencil and rubber
(a) Cost of one rubber = c + 30 cents.
(b) Cost of 4 pencils + 1 rubber = 4c + (c + 30) = 5c + 30 cents.
2 — Find the mistake
(a) The mistake is on Line 1 (and you could also point at Line 3, since they share the same error).
(b) The sign in front of a term belongs to the term. So the second term isn't "2b" — it's −2b. The student dropped the minus sign when listing the terms.
(c) Corrected Line 1: The expression has 3 terms: 5a, −2b and +9. (And consequently the coefficient of b is −2, not 2.)
3 — Open-ended (sample solutions)
Example expression: 4x − 2y + 7. Rule check: (i) three terms 4x, −2y, +7 ✓; (ii) coefficient of x is 4 ✓; (iii) coefficient of y is −2, which is negative ✓; (iv) constant term is 7 ✓.
Other valid examples: 4x − 5y + 7, 4x − y + 7, 7 − 3y + 4x (same expression, reordered).
Story: "x is the number of books I bought at $4 each, y is the number of $2 vouchers I used (each one takes money OFF), and 7 is the postage fee."
Marking: 2 for a valid 3-term expression matching all rules; 1 for the explanation linking each rule to a part of the expression; 1 for a sensible real-world story.