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MathematicsGeometryAges 11–13

3-D shapes (age 11+)

Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections

Lesson

Set out your lesson

Practise the bounded task in 3-D shapes (age 11+); see exact limits before inferring broader coverage.

Before teaching

Use this short check, then start teaching.

Activity

Can distinguish flat faces, edges and vertices; all slicing is imagined, no knives or food containers.

Policy

Exact directed source edges retained; earlier authorship is not learner attainment.

Printer, credit, and teaching notes

Exact directed source edges retained; earlier authorship is not learner attainment.

Materials

  • These supplied stage cards

  • Scrap paper and pencil; oral/pointing response where appropriate

Sequence

  • Read readiness and decide on support without treating prerequisite authoring as learner readiness.

  • Open Show first and explain its model.

  • Use Guided Try with support and its separate adult key.

  • Close Show and guided keys before Try, unless this Try is explicitly supported.

  • Reflect on an actual attempt, including help used.

No Printer

Use the supplied screen cards; copying the exact task to paper is optional, not required.

Privacy

Use only invented scenarios and optional anonymous local notes. Do not request names, photos, family finances, medical data, accounts or uploads. Stop uncomfortable physical activity.

Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view.

Next: Show

Adult extras
Teaching limits and safe use

These are finite task opportunities, not proof of mastery. Record what was attempted and what support was used.

  • Verbal spatial models and a proposed net; no supplied perspective solid diagram or executed net folding. Net-fold determination clause remains blocked.

Use only invented scenarios and optional anonymous local notes. Do not request names, photos, family finances, medical data, accounts or uploads. Stop uncomfortable physical activity.

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Teaching approaches

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1 approach

Selected Default Gakuva

Practise the bounded task in 3-D shapes (age 11+); see exact limits before inferring broader coverage.

Practise the bounded task in 3-D shapes (age 11+); see exact limits before inferring broader coverage.

Family records and proof options

Keep a record of your learning

Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.

View learner plans ($12/mo per learner) See sample family archive

Learning resources

Extra practice links — they do not replace Gakuva’s teaching approach.

PhET Interactive Simulations · Practice link — not the full lesson

Area Builder

Open practice (new tab)
Before you open · source notes

Area Builder supports hands-on exploration for 3-D shapes (age 11+). Not every lab worksheet.

Free interactive page, no sign-in required for the tested path.

Before you open

Ask the learner what they changed in the sim or page and what they observed.

Opening this link does not save learning or assess mastery.

Source, access and review notes

Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.

PhET Interactive Simulations. “Area Builder.” External page; Gakuva does not copy, host, embed, or redistribute materials.

Unknown — link only

Check understanding

  • Count and describe the faces, edges, and vertices of a triangular prism and a square-based pyramid
  • Describe the 2-D cross-section produced by slicing a cylinder horizontally or a cone vertically
  • Use properties of 3-D shapes to determine whether a given net will fold into a specified solid
“If your child slices a cylinder straight across the middle like cutting a tin of beans in half, can they describe the shape of the cut surface? What about slicing at an angle?”

Curriculum record

Type
Conceptual
Subject
Mathematics
Domain
Geometry
Age range
Ages 11–13

Standards

acara-v9:AC9M6SP01ccss-math:7.G.3the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G7-E1.1the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G7-E2.6uk-nc-2013:KS3.Maths.Geo.15