Perimeter Recap & Problem Solving

Overview

This 30-minute lesson revisits calculating the perimeter of simple and rectilinear shapes, including squares, using centimetres and metres. It aligns with the UK National Curriculum for Year 5 (Mathematics) and emphasises reasoning and applying perimeter knowledge through real-life problems. The lesson includes clear success criteria, differentiation to meet diverse learners' needs, and extension activities for those ready to be challenged further.

Curriculum Links

Mathematics — Year 5

Measurement:
- Pupils should be taught to:
  - Solve problems involving the calculation and conversion of units of measure, using decimal notation to up to three decimal places where appropriate.
  - Convert between different units of metric measure (e.g., cm to m).
Geometry — Properties of Shapes:
- Pupils should be taught to:
  - Identify, describe and represent the position of shapes following translations or reflections.
  - Calculate the perimeter of composite rectilinear shapes in cm and m.

Learning Objectives

By the end of this lesson, pupils will be able to:

Calculate the perimeter of simple 2D shapes (rectangles, squares, triangles) accurately using centimetres and metres.
Calculate the perimeter of rectilinear composite shapes by applying known strategies.
Solve real-life perimeter problems using reasoning skills.
Demonstrate understanding of the relationship between perimeter, units of measurement, and shape properties.

Success Criteria

I can add the lengths of each side to find the perimeter.
I can convert units correctly between centimetres and metres when required.
I can use known strategies to find the perimeter of rectilinear composite shapes.
I can explain my reasoning clearly when solving perimeter problems.

Resources Needed

Whiteboard and pens
Printed worksheets with simple and composite shape diagrams (rectangles, squares, L-shaped figures)
Rulers (marked in cm and m scale)
Mini whiteboards and pens for pupils
Real-life perimeter challenge cards (e.g., garden fence, picture frame, running track perimeter)

Lesson Structure

1. Starter (5 mins): Quick Perimeter Recap

Show simple shapes on the board with side lengths labelled.
Ask: “What is perimeter?” and “How do we calculate it?”
Pupils respond with mini-whiteboards: they calculate perimeters of shapes shown (e.g., a square with sides of 7 cm, rectangle 8 cm by 4 cm).
Emphasise adding all sides and the shorthand formula for rectangles and squares.

Differentiation: Provide number bonds or addition scaffolds for pupils who need extra help.

2. Main Activity (15 mins): Perimeter of Rectilinear Composite Shapes

Explain what rectilinear shapes are (shapes made from only horizontal and vertical lines).
Demonstrate step-by-step how to break down an L-shaped figure into simpler lengths to calculate perimeter:
- Point out that some edges might be shared internally and not counted in the perimeter.
- Practise measuring and adding the external sides only.
Pupils work in pairs on printed worksheets with a variety of composite shapes labelled with mixed units (e.g., some sides in metres, others in centimetres).
Encourage pupils to convert all units consistently before adding (e.g., convert metres to centimetres or vice versa).
Circulate to prompt reasoning: “How do you know which sides to add?” and “Have you checked the units carefully?”

Differentiation: Provide partially completed examples or number lines for those struggling. Challenge advanced learners to find missing side lengths using perimeter information given.

3. Real-Life Problem Solving (7 mins)

Present 2-3 real-life perimeter scenarios using challenge cards (e.g., "You want to put a fence around your rectangular garden measuring 12 m by 9 m. How much fencing do you need?")
Pupils solve individually or in small groups, showing their working and explaining their reasoning aloud or in writing.
Select two or three to share solutions and thinking process with the class.

Differentiation: Provide visual aids and support vocabulary (perimeter, length, units) for EAL or SEND pupils.

4. Plenary (3 mins): Reflect and Assess Understanding

Ask pupils to self-assess against the success criteria with a traffic light system (Red = need more help, Amber = mostly confident, Green = fully confident).
Quick Q&A on common misconceptions or difficulties encountered.
Recap the importance of converting units and checking all sides are included.

Differentiation Strategies

Learner Type	Strategy
SEN	Use concrete manipulatives (rulers, measuring tapes), visual step guides, and peer support. Break tasks into smaller steps. Provide one-to-one verbal support where needed.
EAL	Pre-teach vocabulary (perimeter, rectilinear, composite), use diagrams, bilingual glossaries. Speak clearly and use gestures. Pair with proficient peers.
Average Learners	Scaffold questions progressively and provide worked examples preceding independent tasks.
Advanced Learners	Provide extension tasks involving missing side lengths, multiple units conversion, or creating their own perimeter problems with reasoning.

Extension Activities (for Advanced Learners)

Investigate perimeter vs area: Create shapes with the same perimeter but different areas and discuss findings.
Challenge: Design a rectilinear garden with a fixed perimeter and maximise the area — explain your reasoning and calculation methods.
Convert perimeters between mixed units including millimetres and kilometres for conceptual stretch.

Assessment

Informal formative assessment through mini-whiteboards and Q&A during activities.
Check for correct perimeter calculations and unit conversions on worksheet tasks.
Evaluate reasoning explanations verbally or in writing during real-life problem solving.
Use plenary self-assessment traffic lights to identify learners needing follow-up or extension.

Notes on Teaching Approach

Encourage mathematical talk: pupils explain how they calculated perimeter aloud or in pairs to embed understanding.
Use real-life contexts to increase engagement and relevance, fostering deeper reasoning skills.
Keep pace brisk but supportive to maintain focus over the 30-minute lesson slot.

This lesson plan ensures rigorous adherence to the UK National Curriculum Year 5 standards while actively engaging pupils in problem-solving and reasoning with perimeter.