Area Investigation Showcase

Overview

This is the final lesson in the ten-lesson unit Area and Squared Numbers. Students work in pairs to complete, explain and present a practical area investigation, using measurement, calculation, squared numbers and mathematical reasoning.

Learning intentions

• WALT apply area and squared-number strategies to solve a practical problem.
• WALT choose suitable tools, units and strategies.
• WALT check whether an answer is reasonable.
• WALT communicate and compare mathematical methods.

Success criteria

• I can choose suitable tools and strategies.
• I can calculate and label area correctly, including square units.
• I can check and explain my reasoning.
• I can listen and respond to another person’s method.

Curriculum links

• Measurement: solve practical problems involving area, length, units and appropriate measuring tools.
• Number: use multiplication, arrays and squared numbers to calculate and interpret results.
• Mathematical investigation: make decisions, record working, check reasonableness and communicate conclusions.
• Mathematics and statistics processes: explore and connect ideas, use representations, and participate in mathematical discussions.

Lesson structure (45 minutes)

1. 0–5 min – Revisit the learning

Display the learning intentions and success criteria using the opening and learning-goals slides. Ask: “Where might we need to know the area of something in real life?” Briefly revisit that area measures the surface covered, is recorded in square units, and that a square’s area can be found by multiplying its side length by itself.

2. 5–9 min – Model the investigation

Use the worked-example slides to model a small rectangular investigation, such as designing a reading mat. Think aloud: identify the shape, choose a measuring tool, record units, calculate length × width, label the answer, and estimate first to check reasonableness. Show how 6 × 6 can be written as 6² and explain that squared numbers describe equal groups in a square arrangement.

Introduce the pair task and success criteria. Explain that students may measure a suitable classroom object or use a teacher-prepared shape.

3. 9–12 min – Organise pairs and choices

Place students in 14 pairs and one group of three. Distribute the area investigation recording sheet and allow each pair to choose an object or prepared shape. Offer the Perimeter and Area Formula Mat as a reference for students who need a visual reminder.

Read all instructions aloud. Point out the visual checklist: identify the shape, measure, calculate, label, check, and prepare to explain. Allocate measuring tools and confirm that objects are handled safely.

4. 12–27 min – Complete the investigation

Pairs measure or design their shape and record a labelled diagram, measurements, calculation and answer on the worksheet. Encourage students to use squared numbers when working with a square or equal side lengths. They must include an estimate or reasonableness check, such as comparing the answer with a known object or using an approximate calculation.

Circulate and ask:

• “What does each measurement tell you?”
• “Why is this strategy suitable?”
• “What unit will your answer use?”
• “How do you know your answer makes sense?”

Provide teacher-prepared shapes, counters or a calculator for students who need reduced writing or practical support.

5. 27–34 min – Prepare and rehearse presentations

Pairs use the presentation-planning and rehearsal slides to prepare a one-minute explanation. Their presentation should include the problem or design, labelled shape, measurements, calculation, squared-number connection where appropriate, answer with units, and reasonableness check.

Give rehearsal time with a partner, teacher or support adult. Students may present verbally, draw and point, use the worksheet as a visual prompt, or submit recorded audio. Use the frame: “We investigated… We measured… We calculated… We checked… Our method was suitable because…”

6. 34–43 min – Mat showcase and mathematical discussion

Invite approximately eight pairs to present, selecting a range of shapes and strategies. Display or hold up each worksheet. After each presentation, allow one brief question or response from the class: “I noticed…” or “I wonder…”

Prompt students to compare methods, especially square multiplication and repeated addition. Remind the audience to listen for correct units, clear labelling and an explanation of how the answer was checked. If time permits, collect remaining presentations for a later display or audio sharing.

7. 43–45 min – Reflect and close

Return to the reflection and plenary slide. Students quietly complete the final reflection on their worksheet: one strategy they used, how they checked their answer, and one method they learnt from another pair. Invite two students to share. Revisit the success criteria and celebrate accurate reasoning, clear communication and constructive listening.

Resources

• the Area Investigation Showcase slide deck
• the area investigation recording sheet
• the Perimeter and Area Formula Mat
• Rulers, tape measures and metre rulers
• Prepared 2D shapes on card
• Safe classroom objects suitable for measuring
• Pencils, coloured pens and clipboards
• Optional calculators, counters and recording device
• Visual timer and board space for presentations

Assessment

• Observe whether students select suitable tools, measure accurately, calculate area and use square units correctly.
• Check worksheets for labelled diagrams, a valid strategy, squared-number use where appropriate, and a reasonableness check.
• Listen to presentations and responses for mathematical vocabulary, clear reasoning and respectful comparison of methods.

Differentiation

• Provide a choice of a practical object or teacher-prepared shape, with simpler rectangles and squares available. Use counters, large-print diagrams, highlighted measurements and adult or peer support as needed.
• For dyslexic students, read all task text aloud, use an accessible sans-serif font, generous spacing and a visual checklist. Accept diagrams, labelled working and oral or recorded presentations; assess mathematical reasoning separately from spelling.
• For the student with Down syndrome, give one instruction at a time, model each step, use concrete measuring experiences, pair with a supportive peer, provide extra processing time and accept pointing, drawing or oral responses.
• Offer presentation rehearsal and the frame “We measured… We calculated… We checked…”. Pair students thoughtfully and allow verbal, visual or recorded communication.

Extension

• Add a constraint such as designing a shape with a target area.
• Compare two different shapes or solutions with the same area.
• Explain an efficient alternative method, including why it works.