Composite Classroom Shapes

Overview

Lesson 9 of 10 in the unit Area and Squared Numbers. Students use multiplication and addition to find the area of composite shapes made from two or more rectangles, explaining how and why they partition each shape.

Learning intentions

• WALT find the area of a shape made from more than one rectangle.
• WALT split a composite shape into smaller rectangles.
• WALT calculate and combine the areas of the parts.
• WALT explain and compare different partitioning methods.

Success criteria

• I can split a composite shape into rectangles.
• I can calculate the area of each section using length × width.
• I can combine areas accurately using square units.
• I can explain my partitioning and compare it with another method.

Curriculum links

• Measurement: use standard units and appropriate strategies to calculate and compare area.
• Number and algebra: use multiplication and addition to solve practical problems.
• Mathematical reasoning: explain, represent and check solutions in more than one way.
• Key competencies: thinking; using language, symbols and texts; managing self; participating and contributing.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and prior knowledge Open with the hook and learning intention slides. Display an irregular L-shaped classroom floor plan and ask: “Could we find its area without measuring every small square?” Students briefly discuss what they already know about rectangles, area and square units. Share the WALT and success criteria using student-friendly language.

2. 5–12 minutes – Teacher modelling Use the worked-example slides to model an L-shaped figure. Think aloud: “I can partition this into two rectangles. I find each area, then add them.” Colour each rectangle, label its dimensions, calculate each area, and write the total in square units. Emphasise that partition lines may be drawn in different places, but the complete shape must be covered once with no gaps or overlaps.

3. 12–18 minutes – Concrete guided practice In pairs, students build an L-shape using two physical rectangular pieces or classroom objects. They trace around the outside, add a coloured partition line and explain their plan to a partner before calculating. Use large, uncluttered diagrams and verbal think-alouds. Check that students identify the correct length and width for each rectangle.

4. 18–32 minutes – Paired application Distribute the composite area practice worksheet. Students solve the teacher-provided and practical classroom-shape problems in pairs, then complete one independently. For each problem they should draw or follow a partition, calculate the sections, add the areas and include square units. Circulate and ask: “Where is your partition?” “How do you know the rectangles cover the whole shape?” “Can you check your total another way?” Use a teacher-led support group for students needing additional modelling.

5. 32–39 minutes – Compare methods Select two solutions for the same shape, ideally using different partitions. Display them using the methods comparison slides. Students use think-pair-share to identify what is the same, what is different and why both totals should agree. Invite students to point, build or explain orally before writing.

6. 39–45 minutes – Reflection and assessment Students complete a quick oral or written reflection: “My partition works because…” and “One way I checked my answer was…”. Revisit the success criteria and plenary slides. Students self-assess by showing one, two or three fingers for their confidence, then hand in their independent worksheet problem for checking.

Resources

• the composite shapes teaching deck
• the composite area practice worksheet
• Physical rectangular pieces, square tiles or paper rectangles
• Grid paper and pencils
• Coloured pencils or highlighters
• Rulers
• Large copies of uncluttered L-shaped diagrams
• Whiteboard and markers
• Optional calculator for checking, not replacing, the calculation

Assessment

• Observe pair discussions and concrete models for correct partitioning, accurate use of dimensions and appropriate mathematical language.
• Check the independent worksheet problem for: rectangles covering the shape, correct multiplication, accurate addition and square units.
• Use student explanations and confidence responses to identify who needs further support in the final unit lesson.

Differentiation

• Support: begin with physical pieces and grid overlays; use colour coding for each rectangle; provide partially partitioned diagrams and dimensions; reduce the number of sections; work with a teacher-led support group.
• Dyslexia-friendly: use a clear sans-serif font, large uncluttered diagrams, short instructions, colour rather than dense text, verbal think-alouds and repeated vocabulary. Allow students to point, build, speak or record an explanation before writing.
• Down syndrome support: give one instruction at a time, model each step visually, provide a worked example to refer to, use a peer buddy and check understanding through demonstration rather than extended written responses.
• Extension: solve the same composite area problem using a different partition, compare both methods and explain why the totals are equal. Challenge students to design an L-shaped classroom space with a given total area.