Mathematics • Year 7 • Unit 2 • Lesson 2
Writing Expressions — Mixed Challenge
Pull everything from Lesson 2 together: translate phrases using all four operations, handle multi-step phrases with brackets, spot a classic Year 7 translation mistake, and finish with an open-ended challenge.
1. Mixed problems — choose the right keyword
Each question uses a different part of Lesson 2. Show your working. 2 marks each
1.1 Translate each: (a) "the sum of a number and 12" (b) "the difference between a number and 8" (c) "the quotient of a number and 5".
1.2 Translate each "trap" phrase carefully: (a) "9 less than a number" (b) "a number subtracted from 9" (c) "9 more than a number".
1.3 Translate "4 more than triple a number". Show your two steps clearly.
1.4 Translate "the product of 7 and (a number plus 2)". Why are the brackets necessary?
1.5 A song lasts m minutes. Write expressions for: (a) the length of 5 of these songs, (b) how long is left if you've already listened to 4 minutes of one song.
1.6 A bottle holds L litres of water. Write expressions for: (a) the volume after 3 bottles are poured into one tank, (b) the volume in HALF a bottle, (c) the volume after 1 bottle is poured into a tank that already had 2 litres.
2. Find the mistake
Another Year 7 student has tried to translate "3 times the sum of a number and 4, then subtract 6". Their working is shown below. Exactly one line contains the key mistake. Spot it, explain why it's wrong, then redo the working correctly. 3 marks
Student's working:
Line 1: Let n = a number.
Line 2: "the sum of a number and 4" → n + 4
Line 3: "3 times the sum" → 3n + 4
Line 4: "then subtract 6" → 3n + 4 − 6
Line 5: Final answer: 3n − 2
(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? "3 times the SUM" means 3 multiplies the whole sum (n + 4) — not just the n. You need brackets.3. Open-ended challenge — write your own phrase
This question has many correct answers. 4 marks
3.1 Write THREE different English phrases that all translate to the same expression: 2n + 3.
After listing your three phrases, briefly explain (one sentence) why having different English phrasings for the same algebra is useful.
Bonus: Now do the same for the expression (n − 1) ⁄ 2. Write TWO English phrases that translate to it.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Sum / difference / quotient
(a) n + 12. (b) n − 8. (c) n ⁄ 5 (or n ÷ 5).
1.2 — Trap phrases
(a) "9 less than a number" → n − 9 (less than reverses; n first).
(b) "a number subtracted from 9" → 9 − n (subtracted from 9 means 9 is the starting point).
(c) "9 more than a number" → n + 9 (more than reverses too; n first).
1.3 — "4 more than triple a number"
Step 1: triple a number = 3n. Step 2: 4 more than 3n = 3n + 4. Answer: 3n + 4.
1.4 — "Product of 7 and (a number plus 2)"
Answer: 7(n + 2). The brackets are necessary because the 7 must multiply the WHOLE sum (n + 2), not just the n. Without brackets, 7n + 2 only multiplies the n — a different expression.
1.5 — Songs
(a) Length of 5 songs = 5m minutes.
(b) Time left in one song = m − 4 minutes.
1.6 — Bottles
(a) 3 bottles → 3L litres.
(b) Half a bottle → L ⁄ 2 (or ½L) litres.
(c) Tank already had 2 + one bottle → L + 2 litres.
2 — Find the mistake
(a) The mistake is on Line 3.
(b) "3 times the SUM" means 3 multiplies the whole sum (n + 4), so brackets are needed. The student wrote 3n + 4, which only multiplies n by 3 and leaves the 4 alone — a completely different expression.
(c) Corrected working:
Line 3 (fixed): "3 times the sum" → 3(n + 4).
Line 4: subtract 6 → 3(n + 4) − 6.
Final answer: 3(n + 4) − 6. Sanity check with n = 2: sum = 6, times 3 = 18, minus 6 = 12. Original answer 3n − 2 with n = 2 gives 4 — wrong!
3 — Open-ended (sample answers)
Three phrases for 2n + 3 (any sensible variations are fine):
• "3 more than double a number"
• "twice a number, plus 3"
• "the sum of two times a number and 3"
Why it's useful: different English phrasings often suit different real-life situations (e.g. "3 more than double" sounds natural for a price markup, while "twice the number plus 3" sounds natural for a points scoreboard). Being able to recognise them all keeps you flexible.
Bonus — two phrases for (n − 1) ⁄ 2:
• "half of (a number minus 1)"
• "1 less than a number, divided by 2"
Marking: 2 for three valid phrases (1 each, max 2); 1 for the explanation; 1 for the bonus.