Mathematics • Year 7 • Unit 2 • Lesson 5
Add/Subtract Algebraic Terms — Mixed Challenge
Pull everything from Lesson 5 together: expand brackets, subtract brackets (flip signs!), distribute multipliers, combine multi-step expressions, spot a Year 7 sign error, and finish with an open-ended construction puzzle.
1. Mixed problems — simplify each
Each question uses a different idea from Lesson 5. Show your working. 2 marks each
1.1 Simplify (x + 8) + (3x + 2).
1.2 Expand: 4(2x + 3).
1.3 Simplify (7a + 5) − (3a + 2).
1.4 Simplify (6x + 4) − (2x − 5). (Watch the double subtraction!)
1.5 Simplify 2(x + 3) + 5(x − 1).
1.6 Simplify 4(2x − 1) − (3x + 2). Then substitute x = 3 to check.
2. Find the mistake
Another Year 7 student has tried to simplify 3(x + 4) − (2x − 3). 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 3(x + 4) − (2x − 3):
Line 1: Distribute the 3: 3(x + 4) = 3x + 12.
Line 2: Remove the second bracket: −(2x − 3) = −2x − 3.
Line 3: Full expression: 3x + 12 − 2x − 3.
Line 4: x-terms: 3x − 2x = x. Constants: 12 − 3 = 9.
Line 5: Final answer: x + 9.
(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? When you remove −(2x − 3), the −3 should become +3 (two negatives = positive). The student only flipped one of the two signs.3. Open-ended challenge — design two expressions that match
Many answers work. 4 marks
3.1 Design TWO bracketed expressions (call them A and B) so that when you compute A − B, the answer simplifies to exactly 2x + 3.
Write down your choice of A and B, then show your working step-by-step to prove A − B = 2x + 3.
Bonus: Now design DIFFERENT A and B (where B contains a negative term inside) that still give A − B = 2x + 3. Show your working.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — (x + 8) + (3x + 2)
= x + 8 + 3x + 2 = 4x + 10.
1.2 — 4(2x + 3)
= 4(2x) + 4(3) = 8x + 12.
1.3 — (7a + 5) − (3a + 2)
= 7a + 5 − 3a − 2 = 4a + 3.
1.4 — (6x + 4) − (2x − 5)
Drop first: 6x + 4. Flip second: −2x + 5 (the −5 becomes +5). Together: 6x + 4 − 2x + 5 = 4x + 9.
1.5 — 2(x + 3) + 5(x − 1)
Distribute: 2(x + 3) = 2x + 6. 5(x − 1) = 5x − 5. Together: 2x + 6 + 5x − 5 = 7x + 1.
1.6 — 4(2x − 1) − (3x + 2)
Distribute: 4(2x − 1) = 8x − 4. Flip second: −(3x + 2) = −3x − 2. Together: 8x − 4 − 3x − 2 = 5x − 6.
Check with x = 3: original = 4(6 − 1) − (9 + 2) = 4(5) − 11 = 20 − 11 = 9. Answer: 5(3) − 6 = 15 − 6 = 9 ✓.
2 — Find the mistake
(a) The mistake is on Line 2 (it then makes Line 3 and Line 5 wrong too).
(b) When you remove a subtracted bracket, EVERY sign inside flips. So −(2x − 3) = −2x + 3, not −2x − 3. The student only flipped one of the two signs.
(c) Corrected working:
Line 1: 3(x + 4) = 3x + 12. ✓
Line 2 (fixed): −(2x − 3) = −2x + 3.
Line 3 (fixed): 3x + 12 − 2x + 3.
Line 4 (fixed): x-terms 3x − 2x = x. Constants 12 + 3 = 15.
Line 5 (fixed): Final answer = x + 15.
3 — Open-ended (sample solutions)
Example: A = (5x + 4), B = (3x + 1). Working: (5x + 4) − (3x + 1) = 5x + 4 − 3x − 1 = 2x + 3 ✓.
Other valid pairs: A = (4x + 5), B = (2x + 2); A = (7x + 6), B = (5x + 3); A = (10x + 10), B = (8x + 7).
Bonus (B has a negative term): A = (4x + 1), B = (2x − 2). Working: (4x + 1) − (2x − 2) = 4x + 1 − 2x + 2 = 2x + 3 ✓. (Notice: the −2 inside B becomes +2 when the bracket is removed.)
Marking: 2 for valid A and B with full check; 1 for clear bracket-removal working; 1 for the bonus with a negative inside B.