Building Cubic Volume

Overview

Students investigate volume as the amount of three-dimensional space inside a closed object. Working in pairs, they fill rectangular prisms with identical centicubes, record the number of cubes in one layer and calculate the total volume using cubic units.

Learning intentions

• WALT define volume as the amount of three-dimensional space an object occupies.
• WALT measure volume by packing a rectangular prism with identical cubic units.
• WALT find the volume of a rectangular prism by multiplying cubes in one layer by the number of layers.
• WALT choose and use appropriate measurement units, including cubic centimetres, millilitres and litres where relevant.

Success criteria

• I can explain that volume measures the space occupied by a three-dimensional object.
• I can fill a rectangular prism without gaps or overlaps using identical cubes.
• I can calculate volume by finding the number of cubes in one layer and multiplying by the number of layers.
• I can record an answer using an appropriate cubic unit, such as cm³.

Curriculum links

• Measurement — measuring volume using cubic units and measuring capacity using millilitres and litres.
• Mathematics and Statistics — Mathsteasers: higher-order thinking and problem-solving challenges for advanced learners.
• Mathematics and Statistics — Mathsteasers / Alignment: connecting practical measurement with number and multiplication knowledge.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: reasoning, explaining strategies and justifying solutions.

Lesson structure (80 minutes)

1. 0–8 min · Hook and prior knowledge. Teacher shows a small empty box and asks, “How could we work out exactly how much space is inside it?” using the hook and prediction slide. Students make a quick individual prediction, then share ideas with a partner, including possible tools and units.

2. 8–20 min · Build the concept. Teacher uses the volume teaching slides to distinguish length, area, capacity and volume, defining volume as the amount of three-dimensional space enclosed by a closed surface. Demonstrate that one small cube represents one cubic unit and model the difference between cubes packed with gaps and cubes packed tightly. Students handle one cube, identify its three dimensions and explain why a flat square measures area rather than volume.

3. 20–35 min · Teacher modelling. Teacher displays a rectangular prism made from centicubes and models: count the cubes across and along in one layer, multiply to find the cubes in that layer, then multiply by the number of layers. Record: volume = cubes in one layer × number of layers; for example, 4 × 3 × 2 = 24 cm³. Use the worked-example slides to model accurate counting, efficient multiplication and correct notation. Students copy one worked example and explain the steps to a partner using the sentence frame, “First I…, then I…, so the volume is…”.

4. 35–57 min · Pair investigation. Teacher places students in eight pairs and gives each pair centicubes, two or three small rectangular containers or prism outlines, and the cubic volume investigation worksheet. Students build or fill each prism, ensuring there are no gaps or overlaps. They record the number of cubes in one layer, the number of layers, their multiplication equation and the volume in cm³. Partners take turns as Builder and Checker, swapping roles for each example. Teacher circulates, asking, “How do you know your layer is complete?” and “Could you calculate the total without counting every cube?”

5. 57–70 min · Reasoning challenge and discussion. Teacher presents the challenge on the investigation and discussion slides: “Two prisms have the same volume. Must they have the same dimensions? Prove your answer with cubes or a drawing.” Students work in pairs to find at least two different rectangular prisms with the same volume, then prepare a short explanation. Invite pairs to share examples such as 2 × 3 × 4 and 1 × 4 × 6, discussing why both contain 24 cubic units. Year 4 students may build and count; Year 5 students should use multiplication and justify equivalence.

6. 70–80 min · Plenary and exit check. Teacher revisits the learning intentions using the plenary and exit-ticket slides. Students complete the final questions on the worksheet: “What does volume measure?” and “Find the volume of a prism with 5 cubes in each layer and 3 layers.” Students share one strategy and one common mistake to avoid, such as confusing cm² with cm³.

Resources

• the complete volume slide deck
• the cubic volume investigation worksheet
• Centicubes or other identical linking cubes
• Small rectangular containers, boxes or prism outlines
• Whiteboard and markers
• Rulers marked in centimetres
• Pencils and erasers
• Prepared prism examples for modelling
• Exit questions displayed on the final slide

Assessment

• Observe pair investigations for accurate packing, counting, multiplication and use of cubic units. Question students individually so both partners demonstrate understanding.
• Check worksheet records for a complete layer count, number of layers, correct equation and appropriate unit notation.
• Use the exit check to identify whether students can define volume and calculate a rectangular prism’s volume. Group students for a follow-up session based on whether they need concrete practice, array support or multiplication extension.

Differentiation

• Support students with pre-built prisms, a labelled diagram showing length, width and height, and the sentence frame: “There are ___ cubes in one layer. There are ___ layers. ___ × ___ = ___ cm³.”
• Allow students who need additional support to count physical cubes before recording an equation. Pair thoughtfully and use the Builder/Checker roles to support participation and language development.
• For EAL learners, explicitly model and display: volume, cube, layer, rectangular prism, cubic centimetre, length, width and height. Use gestures, diagrams and repeated oral rehearsal rather than relying on definitions alone.
• Extend confident Year 5 students by asking them to design two or more prisms with a volume of 36 cm³, explain which dimensions change the volume, and connect cubic centimetres with the capacity of 1 mL where appropriate.