Slicing and cutting problems

Required materials

• a plastic knife, or "safe" kitchen knife
• spare paper or cardboard
• pencil, ruler, and eraser
• scissors
• cellotape or glue

See Materials that come with this resource to download:

• Slicing and cutting problems activity (.pdf)
• Play dough recipe (.pdf)

What to do

Get your child to use the dough to make and name a cube, a cylinder, a sphere, a cuboid (long cube or rectangular prism), a square based pyramid, a cone and a triangular prism.

Get your child to talk to you about the distinguishing features of each shape. For example,

• The square-based pyramid has 5 vertices (corners where 3 edges meet), 8 edges (where 2 "sides" or faces meet), and 5 faces, of which one is a square and 4 are triangles.
• Have your child choose some of the shapes with straight edges and, using paper or card, make and cut a pattern for this shape. They should include tabs on their pattern so the shape can be folded and glued to make a three dimensional model. For example:

Get your child to put their play dough shapes in the fridge while they cut out and glue/tape their paper/cardboard shapes together. Chilling the dough shapes will make them firmer and this will make the next task more successful.

Now say:

• I want you to slice at least twice through each play dough shape. But before you do, I want you to predict which shapes will have slices that are all the same size and shape, and which ones will have slices that are different sizes or shapes.
• Have them make their prediction and then have them slice through their play dough shapes to see if their predictions are correct.

Note that when a prism is sliced through, its slices are the same size shape, like this:

If you slice through a shape that is not a prism, e.g., a pyramid, the slices will change shape and size. So, a prism is a solid object that has two identical ends and all flat sides and the cross section is the same all along its length.

Talk together about what has happened and together agree which shapes are prisms.

What to expect your child to do

• Make and name common solid three-dimensional shapes.
• Make paper or cardboard patterns (nets) for common three-dimensional shapes.
• Identify features of prisms.

He kupu Māori:

He whakawhitinga kōrero

• Hangaia tētahi mataono rite ki te poikere. (Make a cube from the play dough.)
• He aha ngā ingoa pāngarau mō ēnei āhua? (What are the maths names for these shapes?)
• Whakamāramatia mai te āhua o te koeko tapawhā rite. (Explain to me the shape of the cone.)
• He tapawhā rite te pūtake o tēnei āhua. E whā atu anō ngā mata, he tapatoru te āhua. Ka tūtaki ēnei mata ki te tihi o te koeko. (The base of this shape is a square. There are four other faces which are triangular. They meet at the point or apex of the pyramid.)
• E hia ngā kokonga o te …? (How many corners has the … got?)
• He torotika, he kōpiko rānei ngā tapa? (Are the edges straight or curved?)
• He ōrite te āhua me te rahi o ngā mata katoa. (The shape and size of all the faces are the same.)
• E rua ngā mata porowhita. (There are two circular faces.)
• Ka whakamahi tāua i te kāri mārō hei hanga i tētahi poro tapawhā hāngai. He papatahi te kāri, engari ka whētuia hei hanga i te poro. He rite ki te pouaka. Ka kīia tēnei he raumata. Koia nei te raumata hei hanga poro tapawhā hāngai. (Together we’re going to use some cardboard to make a rectangular prism. The carboard is flat but we can fold it to make the prism. It’ll be like a box; this is called a net. This is a net for making a rectangular prism.)
• Me pēhea te hanga raumata hei mahi i tētahi poro tapatoru? (How can we make a net to build a triangular prism?)
• E rua ngā pito o te poro tapatoru, he tapatoru te āhua. He tapawhā hāngai ngā mata e toru e hono ana i ēnei pito. (There are two ends of the triangular prism which are triangular shaped. The three faces which join these ends are a rectangular shape.)
• Mēnā ka tapahia te [poro tapatoru] ki konei, ka pēhea te āhua o te mata tapahi ka hua mai? (If we cut the triangular prism here, what will be the shape of the sliced surface?)
• Mēnā ka tapahia ki konei, ka ōrite anō te āhua o te mata tapahi, ka rerekē rānei? (If it is sliced here, will the sliced surface be the same or different?)