Volume as additive
Recognise volume as additive; find volumes of composite solid figures made of two or more non-overlapping right rectangular prisms
Lesson
Set out your lesson
“Volume as additive means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Unit cubes or squared paper nets
- Pencil for recording
Extra for the adult
Worked example. A 2 by 3 by 4 cuboid has volume 24 unit cubes.
Optional challenge. For Volume as additive, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Volume as additive, not mastery.
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Teaching approaches
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1 approach
Volume as additive means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Unit cubes or squared paper nets; Pencil for recording. 1. Say the goal of Volume as additive in plain words once. 2. Adult builds a 2×3×4 cuboid and counts 24 unit cubes. 3. Child builds or sketches three cuboids/nets and records length×width×height. 4. Fresh check: one fresh L×W×H volume. Record and stop. Done: three correct volume or net records. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
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Practice this concept
Start practiceVolume as additive practice
Practice key ideas from Volume as additive.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Computing Volume Progression 3
Before you open · source notes
Volume progression 3 supports volume as additive when solids are joined. Not every surface-area total.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk the learner to find a combined volume by adding parts.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.
Illustrative Mathematics. “Computing Volume Progression 3.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.
CC BY-NC-SA 4.0 — link only
Check understanding
- Decompose an L-shaped solid into two cuboids and calculate total volume
- Solve a real-world problem requiring the volume of a composite figure (e.g. a step-shaped structure)
- Explain why splitting a composite solid into rectangular prisms allows calculation of total volume
“If an L-shaped swimming pool is made of two rectangular sections, can your child find the volume of each section separately and add them to get the total volume of the pool?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Measurement
- Age range
- Ages 10–11
Standards