Volume of Cuboids

Overview

Lesson 3 of 5 in the unit 3D Shapes and Volume. Students connect arrays of unit cubes and layers to the formula (V = l \times w \times h), then measure, estimate, calculate and check the volume of cuboids.

Learning intentions

• WALT calculate the volume of cuboids using length × width × height.
• WALT explain how layers of equal-sized cubes make a cuboid.
• WALT use appropriate cubic units and check whether an answer is reasonable.
• WALT communicate our mathematical thinking clearly with a partner.

Success criteria

• I can identify the length, width and height of a cuboid.
• I can multiply the three dimensions accurately.
• I can write my answer using cubic units, such as cm³.
• I can check my answer by estimating or building/counting layers.

Curriculum links

• Measurement: measure, estimate and calculate the volume of rectangular prisms using standard units.
• Number and algebra: use multiplication, arrays and place-value strategies to solve problems.
• Geometry: describe and represent properties of three-dimensional shapes.
• Mathematical communication: explain strategies, record working clearly and justify whether an answer is reasonable.

Lesson structure (45 minutes)

1. 0–5 minutes – Engage and connect

Open with the hook and learning intention slides. Show a cuboid made from unit cubes and ask: “How could we find how many cubes fit inside without counting every cube?” Briefly revisit length, width and height, using a labelled model. Read the WALT and success criteria aloud; provide an audio version or teacher read-aloud for students who need it.

2. 5–13 minutes – Model cubes, layers and the formula

Use the cubes, layers and formula slides to model a cuboid measuring 4 cm × 3 cm × 2 cm. Establish that one layer has (4 \times 3 = 12) cubes and two layers have (12 \times 2 = 24) cubes. Record:

• Volume = number of cubes
• Volume = length × width × height
• (V = 4 \times 3 \times 2 = 24\text{ cm}^3)

Colour-code each dimension consistently. Emphasise that volume measures space inside a solid and is recorded in cubic units, not square units.

3. 13–18 minutes – Guided example and checking

Complete a second example together, such as 5 cm × 2 cm × 3 cm. Ask students to estimate first, then calculate using a structured checklist: identify dimensions, multiply, write the cubic unit, check reasonableness. Invite students to explain why changing one dimension changes the number of layers or cubes.

4. 18–33 minutes – Partner investigation

Place students in 14 pairs, with one group of three. Distribute the volume investigation worksheet and provide each pair with a prepared cuboid or suitable classroom object, a ruler and unit cubes where available. Students should:

• identify and colour-code length, width and height;
• estimate the volume;
• measure each dimension in centimetres;
• calculate (l \times w \times h);
• check by building one layer, stacking layers or counting a model where practical;
• record the answer in cm³ and explain whether it is reasonable.

Circulate and question: “What does one layer contain?” “How many layers are there?” “Which measurement is the height?” Encourage partners to take turns measuring, recording and explaining.

5. 33–40 minutes – Compare and discuss

Open the investigation discussion slides. Select two pairs to share different-sized cuboids or different checking strategies. Compare estimates with calculated answers. Discuss common errors, including confusing area with volume, omitting cubic units, or multiplying only two dimensions. Ask: “If the height doubled, what would happen to the volume?”

6. 40–45 minutes – Individual exit check

Display the final questions on the plenary and exit-check slides. Students independently solve: “A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its volume? Show your working and explain one way to check it.” Students may write, give an oral explanation, or photograph a completed model. Collect responses to plan the next lesson.

Resources

• the complete volume of cuboids slide deck
• the volume investigation worksheet
• Prepared cuboid models or classroom cuboid-shaped objects
• Rulers or tape measures marked in centimetres
• Linking cubes or multilink cubes
• Large labelled cuboid model
• Calculators and multiplication grids, as appropriate
• Coloured pencils or highlighters
• Whiteboards and pens

Assessment

• Observe partner work for accurate identification of dimensions, measuring, multiplication and use of cubic units.
• Check the worksheet for an estimate, correct formula, clear working and a reasonable verification strategy.
• Use the individual exit check to identify students needing further support with dimensions, multiplication, units or explaining reasonableness.

Differentiation

• Support: use labelled models, dimension cards, colour-coded measurements, worked examples, a step-by-step checklist and practical measuring before symbolic calculation. Provide smaller numbers, multiplication grids and calculators when appropriate.
• For the student with Down syndrome: use smaller dimensions, repeated one-step examples, adult or peer prompting, concrete cubes and a match-the-model-to-answer activity. Accept pointing, matching, oral responses or a photographed model.
• Dyslexia-friendly options: use large, spaced calculations, uncluttered worksheet sections, short instructions, clear sans-serif text, colour-coded dimensions and audio/read-aloud instructions. Avoid dense text and accept oral explanations or photographs of models.
• Extension: investigate how doubling, halving or changing one dimension affects volume. Solve missing-dimension problems, such as finding the height when the volume and two dimensions are known.