Why do this
problem?
This problem requires some visualisation and knowledge of
$3$D shapes. It gives children experience of identifying shapes
from pictures of them in different positions and
orientations.
Possible approach
Ideally, it would be good to have some modelling
clay/plasticene available for this activity (wooden or
plastic 3D shapes might also be useful).
You could start by showing the group a cube of clay and
asking them to describe the shape. Ask them to imagine how
they could cut the cube into four pieces which are exactly
the same size and shape. Give them time to think on their
own, then to share their ideas with a partner. You could then
give each pair their own cube of clay and invite them to test
out their cuts.
Gather all the cut cubes together to compare the different
cuts, encouraging the children to talk about what they
notice. You may find that some pairs have not got four
pieces, some may have differently-shaped or differently-sized
pieces and so this will promote much discussion.
From there, you can introduce the problem as it is written,
showing the group the pictures of the children's pieces. You
may find
this
sheet useful which has each picture as a separate card so
pupils can match the picture of the cut cubes to each child's
pieces. It may be helpful to have more cubes of clay
available in case it is necessary to re-create some of the
cuts in the problem.
Key questions
Which cube do you think that shape came from?
How would you cut a cube to make that shape?
Possible extension
Learners could try different ways of cutting cubes into more
than four pieces, and draw the results.
Possible support
Having modelling clay cubes available for the children to cut
in the ways drawn will help them access this problem.