Cubed Numbers in Action

Overview

Lesson 4 of 5 in the unit 3D Shapes and Volume. Students use unit cubes and practical stations to connect cubed numbers with volume, solve simple problems, and explain how they know their answers are correct.

Learning intentions

• WALT explain what a cubed number means.
• WALT connect (n³) with (n × n × n).
• WALT calculate simple perfect cubes from 1³ to 5³.
• WALT use cubed numbers to solve and explain volume problems.

Success criteria

• I can explain that (n³) means (n × n × n).
• I can calculate 1³, 2³, 3³, 4³ and 5³.
• I can solve a volume problem involving a cube.
• I can justify my answer using words, a diagram or a calculation.

Curriculum links

• Number and Algebra: use multiplication and powers to identify and calculate simple number patterns.
• Geometry and Measurement: recognise cubic units and calculate the volume of cubes and rectangular prisms.
• Mathematical processes: represent problems, choose appropriate strategies, explain thinking and check the reasonableness of answers.
• Key competencies: thinking; managing self; participating and contributing; using language, symbols and texts.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and prior knowledge Open with the cube-building hook slides. Show a 1-by-1-by-1 cube and ask: “How many unit cubes would make a 2-by-2-by-2 cube? What about a 3-by-3-by-3 cube?” Students discuss with a partner, then share estimates. Briefly revisit that volume is the number of cubic units filling a solid.

2. 5–12 minutes – Explicit teaching: powers of three Use the cubed-number teaching slides to introduce the vocabulary cube, cubed number, power, unit cube, length, width, height and volume. Build or display cubes as you model:

• 1³ = 1 × 1 × 1 = 1
• 2³ = 2 × 2 × 2 = 8
• 3³ = 3 × 3 × 3 = 27
• 4³ = 4 × 4 × 4 = 64
• 5³ = 5 × 5 × 5 = 125 Emphasise that the small 3 means the number is used as a factor three times, not multiplied by 3. Check understanding with thumbs up/down and “explain it to your partner”.

3. 12–15 minutes – Organise stations Divide the class into four mixed-ability groups of approximately seven or eight. Explain that each group will spend six minutes at each station, with one minute to rotate. Display the instructions in the station instructions slides. Assign roles such as reader, builder, recorder and checker so every student participates.

4. 15–43 minutes – Practical station rotation Use a visible timer and rotate groups after six minutes, allowing one minute to move. Provide cube manipulatives, the worksheet and prepared cards at each station.

• Station A: Match it. Match cards showing 1³–5³, multiplication expressions, answers and cube models. Students explain one match to another group member.
• Station B: Build and calculate. Build 1-by-1-by-1 through 5-by-5-by-5 cube models, where practical. Record the number of unit cubes and the matching cubed number.
• Station C: Solve it. Complete the illustrated volume problems on the cubed numbers and volume worksheet. Students may respond with a calculation, labelled diagram, oral explanation recorded by a partner, or short written explanation.
• Station D: Find and fix the error. Examine examples such as “3³ = 9” or “4³ = 16”. Students identify the error, correct it and explain why the answer is incorrect. Circulate, ask “How do you know?” and “What does each factor represent?”, and use quick individual checks before students rotate.

5. 43–45 minutes – Plenary and exit check Return to the discussion and plenary slides. Ask: “A cube has side length 4 units. What is its volume? How can you prove it?” Students give a calculation and explanation to a partner. Collect or scan the final worksheet response, noting who can calculate but cannot yet explain.

Resources

• the complete cubed numbers lesson deck
• the cubed numbers and volume worksheet
• Linking cubes or other unit cubes
• Prepared matching cards for cubed numbers, expressions, answers and models
• Four station instruction cards
• Mini-whiteboards, markers and erasers
• Visible timer
• Vocabulary bank with simple definitions and visual examples
• Pencils, coloured pens and paper for diagrams

Assessment

• Listen for accurate use of cubed number, unit cube, volume and cubic units during partner talk and stations.
• Check matching, model-building and error-correction tasks for understanding that (n³ = n × n × n).
• Use the worksheet and plenary response to assess calculation, problem-solving strategy and justification. Record students needing further support before the final lesson.

Differentiation

• Provide concrete cube towers, partially completed multiplication arrays, a 1³–5³ reference table and visual worked examples. Rehearse each instruction orally before students begin.
• Pair dyslexic students and the student with Down syndrome with supportive peers. Use short illustrated problems, bold key numbers, a clear sans-serif font, generous spacing, text-to-speech or adult read-aloud support, and no penalty for spelling in mathematical explanations.
• Offer choice of written, oral, diagrammatic or practical responses. Give the student with Down syndrome a reduced number of examples, matching tasks and immediate positive feedback while maintaining the same mathematical idea.
• Extend confident students by asking them to compare perfect cubes, create a challenge problem, or find a missing side length when the volume is 8, 27, 64 or 125 cubic units.