Happy Halving
Can you split each of the shapes below in half so that the two parts are exactly the same?
Can you split each of the shapes below in half so that the two parts are exactly the same?
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You could print off this sheet with the shapes drawn so you can try out your ideas. Or you could make the shapes on a pegboard.
You might like to cut out the shapes first. Then you could try cutting each shape and checking to see whether the two parts are the same  perhaps you'll need to turn one of them round!
Esin aged 7 from Mef School in Turkey sent these two solutions:
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Dost, also 7 from the same school, sent alternative answers:
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We also received this solution from Elizabeth, who goes to Warren Rd Primary School
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Aoibheann and Padraic from Cloghans Hill NS in Ireland sent in this very good explanation.
The first shape (like a rectangle) you split in two by drawing a line through the middle.
The second shape (like two squares overlapping) you can split two ways, diagonally through from left to right, top to bottom OR accross where they overlap diagonally.
The third shape which is irregular, you cannot halve as there are five points in length on one side and four on another with another one point in a different place therefore although you could use the two diagonal lines to match each other, you have one point hanging out over one edge and you have one point too few on the other.
The fourth shape (which looks like house designs) you can halve easily by drawing a horizontal line accross the middle of both making the same shape on the top and the bottom.
Thank you for those solutions, there are still others that may be found!
Why do this problem?
This problem consolidates children's understanding of halving in a spatial context and will help them to develop their powers of visualisation.
Possible approach
A precursor to this activity might be to show the group a square and ask them to split it in half in their "mind's eye". By discussing where they have imagined the "cutting line", the children will discover that there is more than one way to do this. From this point, you can talk about whether or not the two halves look the same each time. It is important pupils are clear that, in this
problem, the halves must look identical to each other.
It may be useful for the pupils to have this sheet of the shapes. Alternatively, they could use a pegboard or geoboard to try out their ideas.
In the plenary, you could focus on how they know the two parts they have created are definitely identical halves. This might involve children describing turning one part so that it fits on top of the other and some learners might want to practically do this by cutting out the two parts of each shape.
Key questions
Where could you try splitting the shape?
How do you know those two parts are identical halves?
What could we do to check?
Possible extension
Using the same size grid, children could create examples of shapes for a partner to split in half. This problem offers some more shapes which children could try.
Possible support
Pupils could try Halving before having a go at this problem.