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Shapes in a Grid

Age 7 to 11 Challenge Level:

Shapes in a Grid

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

The shapes stand for four different numbers less than ten.

You might like to try using this interactivity.

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Why do this problem?

This problem is a good introduction to algebra with shapes used as unknowns instead of the more conventional letters. The problem requires the use of logical thinking and the application of simple arithmetical rules.

Possible approach

You could introduce the problem to the whole group using the interactivity and ideally, say as little as possible at this stage.

Ask learners to work in pairs on the problem either at  a computer or from this printed sheet, so that they are able to talk through their ideas with a partner. (The interactivity does not give feedback but it does give a limited number of shapes of each type which does help to solve the problem.)  It might be suitable for them to cut out paper shapes that can be moved around the grid. Alternatively, they could write the appropriate figures onto the grid.  If the sheets were laminated, children could use wipeable markers to annotate the grid.

You could bring the group together after a short time to discuss progress so far, but you may want to leave them to work independently for a sustained period.  When appropriate, the group could come together to talk about how they approached the problem and what difficulties they encountered. How did they start? What could be found out after that? How did they work out the value of the last two shapes? It might help to use the interactivity during the plenary to aid the discussion.  
This problem may be a good context in which to talk about being stuck. Was there a point at which they felt they were stuck?  What did they do about it?  Being stuck is part of being a mathematician and the important thing is to have strategies up your sleeve for helping yourself become 'unstuck'.  Once you have overcome the challenge of being stuck,  you feel much more satisfied at having solved the problem compared with a problem which you knew how to solve immediately.

Key questions

Where could we start this problem?
What  do we know about the red triangle?
How can we use  what we know about the red triangle to work out the value of other shapes?
How will you remember what you have worked out so far?
How do the totals at the ends of the rows and at the foot of the columns help?

Possible extension

Learners could try What's It Worth? as a next step.

Possible support

Having a copy of the problem  and jotting down numbers as they are worked out will help some children keep track of what they are doing.  Using a sheet and the interactivity together might also be useful.