3(x + 4) is not 3x + 4, and the child who writes it has not been careless — they multiplied the first term and stopped. These free printable worksheets put somebody else's line of working on the page and ask which answer is the right one.
Reading a wrong line is a different skill from writing a right one, and it is the one an exam rewards. A child who can expand a bracket may still not notice that a friend forgot the second term, because checking someone else's work means holding their reasoning and your own at the same time. That is worth practising on its own.
Why this sheet works
The four answers offered are not near-misses. Each one is a real mistake with a name: only the first term multiplied, only the second, the number added instead of multiplied, the whole bracket treated as a single product. Choosing between them means saying what went wrong, not just what looks odd.
How this one works
One question from this sheet, worked through a step at a time.
Ana says 5(x + 6) + 5(x + 5) comes to 10x + 55. Which is correct?
5(x + 6) + 5(x + 5)
5(x + 6) + 5(x + 5)=5x + 30 + 5x + 25
5(x + 6) + 5(x + 5)=5x + 30 + 5x + 25
5(x + 6) + 5(x + 5)=10x + 55
5(x + 6) + 5(x + 5)=10x + 55
they wrote:10x + 55
Do not check by reading their line. Somebody else's working is the most persuasive thing on the page, and rereading it is how you end up agreeing with it — do the step yourself first, then compare.
On your own, and writing the step nobody writes down: 5(x + 6) + 5(x + 5) becomes 5x + 30 + 5x + 25.
Tidy that up and it is 10x + 55.
Now compare — and this time the two agree. The line on the page was already right, which is a finding, not a missing mistake. Some of them are.
Read each line of working and choose the answer that is correct.
1Ana says 5(x + 6) + 5(x + 5) comes to 10x + 55. Which is correct?6x + 3510x + 3110x + 75010x + 55Why?
2Check this line: 6(x + 6) + 3(x + 6) = 9x + 54. Which is correct?9x + 547x + 429x + 6489x + 24Why?
3Sam wrote 5(x + 5) + 5(x + 4) = 10x + 25. Which is correct?10x + 50010x + 4510x + 256x + 29Why?
4Spot the mistake: 6(x + 4) + 3(x + 6) = 9x + 432. Which answer is right?9x + 4327x + 309x + 429x + 22Why?
Algebra reasoning · DistributingAnswer key
1. 5(x + 6) + 5(x + 5) = 10x + 55, which is what was written — this line is correct2. 6(x + 6) + 3(x + 6) = 9x + 54, which is what was written — this line is correct3. 5(x + 5) + 5(x + 4) = 10x + 45, not 10x + 25 (the first bracket reached its x but not its number)4. 6(x + 4) + 3(x + 6) = 9x + 42, not 9x + 432 (the two numbers were multiplied together where they should be added)
