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'Sizing Them Up' printed from http://nrich.maths.org/
Why do this problem?
is designed to help children begin to understand the meaning of area as a measurement of surface. It gives them a chance to choose and then justify a way of measuring. It can be solved in many different ways and the sample approaches offer a basis for discussion of possible different
This activity is deliberately open to encourage children to try to define "smallest" for themselves. At this level, the important point is to be able to explain and justify a particular order, rather than there being any right or wrong way to do it. Children might use criteria such as length, height or perimeter, for example. The activity could lead into the introduction of the concept of
area, (even if the word "area" itself is not used).
You could use the interactivity on an interactive whiteboard to introduce the shapes in the problem or simply show the class the shapes cut out from this sheet
. Try not to direct learners too much at this stage but make sure they understand that they can use any resources or equipment that they might find helpful.
Children could work in pairs with the shapes.
Once you feel that most learners have made progress and understand the problem well (this does not necessarily mean that they have found a 'final' solution), give out this Word document
or this pdf
. Suggest to the class that when they've finished or can't make any
further progress, they should look at the sheet showing three approaches used by children working on this task. Pose the question, "What might each do next? Can you take each of their starting ideas and develop them into a solution?". It might be appropriate to read through each method as a whole class before giving pairs time to work on each one. Alternatively, you may prefer
to allocate a particular starting point to each pair.
Allow at least fifteen minutes for a final discussion. Invite some pairs to explain how the three different methods might be continued. You may find that some members of the class used completely different approaches when they worked on the task to begin with, so ask them to share their methods too. You can then facilitate a discussion about the advantages and disadvantages of
each. Which way would they choose to use if they were presented with a similar task in the future? Why?
There is no reason why you should not make your own irregular shapes using the activity as an idea rather than a problem to be solved.
Why do you think this shape is bigger/smaller?
How are you going to decide which is smallest?
Children could be asked cut out shapes which they think are "the same size" but which are very different shapes from those given.
Some children might benefit from cutting out the shapes from this sheet
and putting them one on top of another to aid comparison.