Year 6 Mathematics · AC9M6SP01

Parallel Cross-sections of Three-dimensional Objects

Predict and recognise how slices relate to an object’s structure

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Learning goalsSay it simply

Learning goal

Students visualise and construct slices parallel to a base, identify when cross-sections remain congruent and compare prisms, cylinders, pyramids and cones.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: recognise and describe the parallel cross-sections of objects and recognise their relationships to the object’s base and shape
Key conceptTeach from the board

Slice a prism parallel to its base

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

parallel slice
Every parallel slice of a right rectangular prism is a congruent rectangle

For a prism or cylinder, cross-sections parallel to the base keep the base shape and size. For a pyramid or cone, parallel sections keep the shape but change size.

Compare constant and changing cross-sections

Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.

objectbaseparallel cross-sectionrectangular prismrectanglecongruent rectangletriangular prismtrianglecongruent trianglecylindercirclecongruent circlesquare pyramidsquaresmaller/larger similar squareconecirclesmaller/larger circle

A non-parallel cut can produce a different shape. The orientation of the cutting plane is part of the description.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6SP01 - Parallel Cross-sections of Three-dimensional Objects
Example 1

object base parallel cross-section rectangular prism rectangle congruent rectangle triangular prism triangle congruent triangle cylinder circle congruent circle square pyramid square smaller/larger similar square cone circle smaller/larger circle

Example 2

: using objects made of foam or polystyrene, slice along different cross-sections, and record the different shapes of faces that result; comparing cross-sections of different objects

Example 3

: using different pieces of fruit, slicing across different cross-sections, drawing the cross-section; reporting back to the class the results of the investigation

Example 4

: observing and drawing the shapes resulting from different ways of slicing through familiar objects; for example, slicing carrots at different angles or cutting through playdough models of objects; using playdough models, fruit or similar to establish which objects can be cut in such a way that the cross-section will always be the same shape

Curriculum examplesCopied content

AC9M6SP01: compare the parallel cross-sections of objects and recognise their relationships to right prisms

  • E1: using objects made of foam or polystyrene, slice along different cross-sections, and record the different shapes of faces that result; comparing cross-sections of different objects
  • E2: using different pieces of fruit, slicing across different cross-sections, drawing the cross-section; reporting back to the class the results of the investigation
  • E3: observing and drawing the shapes resulting from different ways of slicing through familiar objects; for example, slicing carrots at different angles or cutting through playdough models of objects; using playdough models, fruit or similar to establish which objects can be cut in such a way that the cross-section will always be the same shape
  • E4: understanding that right prisms are objects where parallel cross-sections to the base of the prism are the same shape and size
  • E5: connecting different right prisms to the shape of their parallel cross-sections, such as a triangular prism which can be described as a stack of the same sized triangles, and a cube or square prism, which can be described as a stack of the same sized squares
  • E6: investigating the design of First Nations Australians’ dwellings, exploring the relationship between the cross-sections and the dwellings’ construction

Use the central and application models above to connect each elaboration to the same underlying concept.

Questions and answersWith answers

Check understanding

  • Predict a prism slice.
  • Compare prism/pyramid.
  • Identify a cone section.
  • Explain parallel.
  • Describe a non-parallel cut.

Evidence of mastery

  • Represent or identify the concept
  • Explain the underlying relationship
  • Select an appropriate strategy or feature
  • Apply it in a new context
  • Justify and verify the response

Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.

Practice and reviewReady for practice
Every slice matches the baseOnly slices parallel to the base have the stated relationship.
Prism and pyramid treated alikePrism sections stay congruent; pyramid sections scale.
Cross-section called a face of the original objectIt is created by the cut.
Orientation omittedState the cutting plane’s direction.
Curriculum alignmentStart here

Learning goal

Students visualise and construct slices parallel to a base, identify when cross-sections remain congruent and compare prisms, cylinders, pyramids and cones.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: recognise and describe the parallel cross-sections of objects and recognise their relationships to the object’s base and shape
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