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Making a Difference

Age 11 to 14
Challenge Level

Why do this problem?

This problem offers students an opportunity to practise subtraction while challenging them to work systematically and think strategically.

Possible approach

This printable worksheet may be useful: Making a Difference.

Invite the students to draw a set of boxes like the ones below.


"Place the digits 2, 5, 7 and 8 into the four boxes, in whichever order you like, and then work out the answer to the subtraction."
Go round the room and invite students to share some of the differences they got.
"It seems like there's quite a few different ways to do it - I wonder how many different differences it's possible to make?"
You may wish to hand out this worksheet for students to record their working.

As the class are working, circulate and listen for useful observations from students, such as systematic ways of working to make sure they don't miss any possibilities.
Before students tackle the two questions at the bottom of the sheet, invite students to share any strategies that might be useful.

The final question about consecutive digits offers a nice opportunity for some discussion involving justification and proof. 


Key questions

How do you know you've found every possible difference?


Possible support

The subtraction task in Dicey Operations might be a good initial activity for students who find column subtraction difficult.


Possible extension

Another task requiring students to work systematically to find all solutions is Weights.