Cubes and Cubic Units

Overview

Lesson 2 of 5 in the unit 3D Shapes and Volume. Students use linking cubes or unit cubes to build cuboids, count equal-sized cubes in layers, and connect physical models with the word cubed and the notation ³.

Learning intentions

• WALT understand that volume measures the space inside a 3D object.
• WALT use cubic units to measure volume.
• WALT find volume by counting equal-sized cubes in layers.
• WALT record volume using correct mathematical language and notation.

Success criteria

• I can explain what a cubic unit is.
• I can find volume by counting equal-sized cubes.
• I can describe how layers help me find volume.
• I can record an answer in cubic units, using units³ when appropriate.

Curriculum links

• Measurement: estimating, measuring and comparing the volume of objects using standard and informal cubic units.
• Geometry: visualising, constructing and describing three-dimensional shapes and their properties.
• Number: using multiplication to represent equal groups and arrays of cubes.
• Mathematical processes: communicating mathematical thinking, explaining strategies and checking reasonableness.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and connect

Open with the hook and learning intention slides. Show a small cube and ask: “How could we measure the space inside this box?” Students briefly discuss with a partner, then share ideas. Introduce the words volume, cubic unit, layer and cubed. Read each instruction aloud and allow oral rehearsal before students write.

2. 5–12 minutes – Explicit teaching

Use the cubic unit demonstration slides and model one unit cube as a cube measuring 1 unit by 1 unit by 1 unit. Explain that one cube represents 1 cubic unit, written as 1 unit³. Build a cuboid with 3 cubes in each layer and 2 layers. Count the cubes together: 3 + 3 = 6 cubic units, or 3 × 2 = 6 cubic units. Emphasise that volume is the space inside, not the outside surface.

3. 12–25 minutes – Build and count

Organise 29 students into mixed-ability pairs, with one group of three. Give each group linking cubes or unit cubes. Display the instructions on the build-and-count activity slides:

• Build a cuboid with 2–4 cubes in each layer.
• Add 2–3 equal layers.
• Count the cubes layer by layer.
• Record the volume in cubic units.

Encourage colour-coded layers. Circulate and ask: “How many cubes are in one layer?” and “How many layers are there?” Provide a demonstration for students who need it.

4. 25–35 minutes – Record and represent

Distribute the cubes and cubic units worksheet. Students draw or complete diagrams of their models, shade each layer a different colour, and record the volume. Model the sentence frame: “The volume is ___ cubic units because there are ___ cubes in each layer and ___ layers.” Students may dictate answers to an adult or peer, point to a completed diagram, or record verbally using a device if writing is a barrier.

5. 35–41 minutes – Compare and discuss

Return to the discussion and comparison slides. Invite pairs to show two models with different dimensions. Discuss whether models can have the same volume. For example, compare 2 × 3 × 2 and 1 × 3 × 4. Clarify that both contain 12 cubes, although their shapes are different. Reinforce that multiplying equal rows, columns and layers is a quicker way to count.

6. 41–45 minutes – Plenary and exit check

Use the plenary slides. Ask students to complete orally or on the worksheet:

• What is a cubic unit?
• How many cubic units are in a cuboid with 4 cubes in each layer and 2 layers?
• What does the ³ mean in unit³?

Select several students to explain their reasoning. Revisit the success criteria and note any students requiring further support in the next lesson.

Resources

• Linking cubes or unit cubes, with enough for 14 pairs and one group of three
• the cubes and cubic units teaching deck
• the cubes and cubic units worksheet
• Whiteboard and pens
• Prepared colour pencils or highlighters for layers
• Small 3D box or cube for the introduction
• Uploaded 3D shapes resource for visual reference
• Optional camera or visualiser for showing models

Assessment

• Observe whether students build complete cuboids with equal-sized layers and can identify cubes within a layer.
• Question students during construction and listen for correct use of volume, cubic unit, layer and cubed.
• Check worksheet diagrams and explanations for accurate counting and units. Use the plenary responses to identify misconceptions, particularly confusing volume with surface area or counting only visible cubes.

Differentiation

• Support: begin with small models, such as 2 × 2 × 2, and provide partially completed diagrams with colour-coded layers.
• Provide manipulatives, enlarged uncluttered diagrams, one instruction per line and the sentence frame: “The volume is ___ cubic units because…”
• For dyslexic students, use a clear sans-serif font, highlighted vocabulary, teacher read-aloud, oral rehearsal and reduced copying. Accept verbal explanations, labelled models or scribed responses.
• For the student with Down syndrome, provide a peer or adult demonstration, repeated modelling, a predictable partner role such as “layer counter”, visual step cards and extra processing time. Extension learners can build different cuboids with the same volume and compare their dimensions.