Mathematics K–6 · Years 5–6
Slicing prisms: parallel cross-sections
Measurement and space
The idea
Every slice of a prism parallel to its base is the same shape and size as the base, and objects that are not prisms give slices that change.
Safety card
Hazards
- plastic knife or fishing-line cutter
- food allergies
Controls
- an adult cuts the fruit and vegetables with a kitchen knife; children use the clay cutter on clay only; no eating
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.
What you need
- modelling clay or playdough formed into a rectangular prism, a triangular prism, a cylinder, a square pyramid and a cone
- a plastic knife or a length of fishing line with handles (a clay cutter)
- a carrot
- grid paper to trace slices on
How to do it
- Slice the rectangular prism straight across, parallel to its base, in three places. Trace each cut face on the grid paper and compare them.
- Do the same with the triangular prism and the cylinder.
- Slice the pyramid and the cone parallel to their bases in three places and trace the cut faces.
- Slice the carrot straight across and then at a slant, and compare the two cut faces.
- Sort the objects into those whose parallel slices stay the same and those whose slices change, and name the first group.
What you should see
The rectangular prism gives three congruent rectangles, the triangular prism three congruent triangles and the cylinder three congruent circles. The pyramid gives squares that get smaller towards the apex and the cone gives circles that get smaller. A straight cut across the carrot is nearly a circle and a slanted cut is an oval that is longer than it is wide. The objects with unchanging parallel slices are the prisms and the cylinder.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Every slice through a cylinder is a circle, whatever the angle of the cut.
- A pyramid is a prism because it has a flat base.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA3-3DS-01MAO-WM-01
- Australian Curriculum v9AC9M6SP01
Sources
The pages the author read to write this activity.