Mathematics • Year 7 • Unit 2 • Lesson 4
Collecting Like Terms — Mixed Challenge
Pull everything from Lesson 4 together: combine multi-variable expressions, handle negative coefficients, identify like vs unlike terms, spot a Year 7 sign mistake, and finish with an open-ended construction puzzle.
1. Mixed problems — simplify each
Each question uses a different idea from Lesson 4. Show your working. 2 marks each
1.1 Simplify 6n + 4n − 2n.
1.2 Simplify 3a + 7 + 2a + 1.
1.3 Simplify 5x + 4y − 2x + y.
1.4 Decide if each pair is "like" or "unlike": (a) 7m and 7n (b) 4ab and 9ab (c) 3x and 3 (d) −2y and 5y.
1.5 Simplify 8p − 5q + 2p − 3q − p.
1.6 Simplify 7c + 3 − 7c + 9. Then substitute c = 4 to check your answer makes sense.
2. Find the mistake
Another Year 7 student has tried to simplify 9x − 2y + 4 + 3x + 5y − 1. Their working is shown below. Exactly one line contains the key mistake. Spot it, explain why, and redo correctly. 3 marks
Student's working — simplify 9x − 2y + 4 + 3x + 5y − 1:
Line 1: Terms: 9x, 2y, 4, 3x, 5y, 1
Line 2: Group: (9x + 3x) + (2y + 5y) + (4 + 1)
Line 3: x-terms: 12x
Line 4: y-terms: 7y
Line 5: Constants: 5
Line 6: Final answer: 12x + 7y + 5
(a) Which line contains the key mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write out the corrected working in full, including the corrected final answer.
Stuck? The sign in front of each term belongs to the term. The student dropped negative signs when listing the terms.3. Open-ended challenge — design an expression
Many answers work. 4 marks
3.1 Write a starting expression with AT LEAST 6 terms (using variables x and y, plus constants) that simplifies down to exactly 2x + 3y + 5.
Then show your simplification step by step to prove it works.
Bonus: Can you design one where the original expression includes at least one NEGATIVE coefficient on x, and at least one NEGATIVE coefficient on y, but the answer is still 2x + 3y + 5?
How did this worksheet feel?
What I'll revisit before next class:
1.1 — 6n + 4n − 2n
= (6 + 4 − 2)n = 8n.
1.2 — 3a + 7 + 2a + 1
a-terms: 3a + 2a = 5a. Constants: 7 + 1 = 8. Answer: 5a + 8.
1.3 — 5x + 4y − 2x + y
x-terms: 5x − 2x = 3x. y-terms: 4y + y = 5y. Answer: 3x + 5y.
1.4 — Like or unlike?
(a) 7m and 7n: unlike (different variables).
(b) 4ab and 9ab: like (same variable part ab).
(c) 3x and 3: unlike (one has variable x, the other is a constant).
(d) −2y and 5y: like (same variable y; sign doesn't matter).
1.5 — 8p − 5q + 2p − 3q − p
p-terms: 8p + 2p − p = (8 + 2 − 1)p = 9p. q-terms: −5q − 3q = −8q. Answer: 9p − 8q.
1.6 — 7c + 3 − 7c + 9
c-terms: 7c − 7c = 0 (cancel). Constants: 3 + 9 = 12. Answer: 12. (No variable — the answer is just a number, no matter what c equals.)
Check with c = 4: original = 7(4) + 3 − 7(4) + 9 = 28 + 3 − 28 + 9 = 12 ✓.
2 — Find the mistake
(a) The mistake is on Line 1 (which then leads to wrong groupings in Lines 2, 4 and 5).
(b) The signs in front of each term belong to the term. The student dropped the minus signs when listing them: the second term is −2y, not 2y, and the last term is −1, not 1.
(c) Corrected working:
Line 1: Terms: 9x, −2y, +4, +3x, +5y, −1.
Line 2: (9x + 3x) + (−2y + 5y) + (4 − 1).
Line 3: x-terms: 12x.
Line 4: y-terms: 3y.
Line 5: Constants: 3.
Line 6: Final answer: 12x + 3y + 3.
3 — Open-ended (sample solutions)
Example: 5x − 3x + 4y − y + 2 + 3. Simplify: x-terms 5x − 3x = 2x ✓; y-terms 4y − y = 3y ✓; constants 2 + 3 = 5 ✓. So the expression simplifies to 2x + 3y + 5.
Bonus example (with negative coefficients): 4x − 2x + 6y − 3y + 8 − 3 + 0y — but this only has one negative. A better one: 5x − 3x + 8y − 5y + 5 − x + x still simplifies to 2x + 3y + 5. Even better: 7x + 4y − 5x + 6 − 1 − y + 0 works.
A guaranteed bonus answer with both negatives: 5x − 3x + 6y − 3y + 5 uses −3x and −3y as terms inside, and still gives 2x + 3y + 5. (Many valid answers exist.)
Marking: 2 for a valid 6+ term expression that simplifies correctly; 1 for clear step-by-step proof; 1 for the bonus with negative coefficients.