Math PicnicEvery sheet is a promise

Why a strategy works worksheets

A child who works out 78 + 27 as 78 + 30 = 108, then 108 − 3 = 105 has done something clever, and being able to say WHAT is the difference between a trick and a method. These free printable worksheets show the working and ask for the reason.

Customize Practice Save as PDF New questions

If they get stuck

See it worked step by step →Answer it on screen →
Why a strategy works
Why a strategy works worksheet — Working to read, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Each question prints somebody else's working and four sentences underneath. One of them explains why that particular route arrives at the right answer; the other three explain a different strategy, so none can be crossed off as nonsense and the working has to be read.

Why this sheet works

Not one of the four options names a number. That is deliberate: an explanation that said "25 was split into 2 and 23" could be matched against the digits on the line without knowing what splitting is for, and a page answerable that way has asked nothing.

How this one works

Why does this working work?

87 + 29→87 + 30 = 117117 − 1 = 116
87 + 29→87 + 30 = 117
87 + 29→87 + 30 = 117117 − 1 = 116
  1. Read the WORKING first, not the sentences. All four sentences describe a real strategy — only one of them describes what happened here, so start where it happened.
  2. Put the first line beside the question: what did it DO to these numbers — move them, or break one apart? That one move is what the right sentence names.
  3. One number was rounded up, then the extra taken off. — 1 more than 29 was added, so 1 comes back off.

Pick another skill