Exploring Perimeter

Overview

This 20-minute lesson is designed for a Year 4 class of 29 students, focusing on understanding and calculating the perimeter of rectangles and rectilinear shapes. It aligns precisely with the National Curriculum for England: Mathematics – Year 4 focus on measurement (specifically length and perimeter). The lesson includes differentiated activities and challenges to engage learners at various ability levels, ensuring accessibility and extension opportunities.

National Curriculum Links

• Measurement – Year 4:
  • Convert between different units of measure (e.g. cm to m)
  • Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
• Mathematical Fluency and Reasoning:
  • Use mathematical vocabulary accurately
  • Solve problems involving perimeters

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Learning Objectives

By the end of the lesson:

1. Pupils will be able to recall what perimeter means and identify it as the total distance around a 2D shape.
2. Pupils will calculate the perimeter of standard rectangles by adding the lengths of all sides.
3. Pupils will estimate and measure perimeter using rulers marked in centimetres.
4. Pupils will extend their learning by calculating perimeter of rectilinear (L-shaped) figures.
5. Pupils will solve perimeter word problems that involve reasoning.

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Success Criteria

• I can explain what perimeter means.
• I can measure sides of shapes carefully using centimetres.
• I can add side lengths to find the perimeter.
• I can work out perimeter for more complex shapes.
• I can explain my answers and how I worked them out.

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Resources Needed

• Individual whiteboards or paper for working
• Rulers marked in cm for each student
• Shape cut-outs (rectangles and rectilinear shapes)
• Perimeter word problem cards (differentiated)
• Challenge cards for higher-attaining pupils
• Visual perimeter vocabulary cards (e.g. “perimeter,” “length,” “distance around”)

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Lesson Structure

Starter (5 minutes)

Engage and Assess Prior Knowledge

• Begin with a quick question: “What do you think the perimeter of a shape means?”
• Gather a few responses, clarifying the term as the distance around the outside of a shape.
• Show a simple rectangle drawn on the board with dimensions labelled. Ask students to suggest how to find the perimeter.
• Review or introduce perimeter vocabulary visually and orally.

Main Teaching & Differentiated Group Work (12 minutes)

Split the class into three groups of 9-10 pupils (by mixed ability to scaffold support and challenge):

1. Group 1 – Emerging

   • Task: Measure all the sides of simple rectangles and calculate perimeter by adding the lengths.
   • Support: Provide rulers, scaffold with number sentences (e.g. 5 cm + 7 cm + 5 cm + 7 cm = perimeter).
   • Assessment: Check measurement accuracy and ability to add correctly.

2. Group 2 – Developing

   • Task: Measure and find the perimeter of both rectangles and simple rectilinear shapes (L-shaped).
   • Prompt pupils to partition rectilinear shapes into rectangles.
   • Use rulers and challenge support: ask “What happens if you add the two longer and two shorter sides?”
   • Assessment: Observe reasoning and application of addition skills.

3. Group 3 – Confident and Challenge

   • Task: Solve perimeter word problems involving multiple shapes or missing side lengths (e.g. “One side is missing; how do you find the missing length then perimeter?”).
   • Introduce converting cm to metres for longer perimeters where appropriate.
   • Provide challenge cards such as “Create your own rectilinear shape with a perimeter of 24 cm.”
   • Assessment: Evaluate reasoning, problem-solving approach, and creativity.

Plenary (3 minutes)

• Gather all groups and discuss:
  • What strategies did they use to find the perimeter?
  • What was the trickiest part about finding the perimeter of rectilinear shapes?
• Quick quiz (oral or on whiteboards): “What is the perimeter of this rectangle?” using a shape on the board.
• Reinforce vocabulary and key learning points.

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Assessment and Feedback

• Ongoing formative assessment through observation and questioning during group work.
• Mark written calculations informally and offer instant feedback on errors or misunderstandings.
• Use plenary quiz answers to evaluate retention and understanding.

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Cross-Curricular Links & Wider Learning

• Link to Design & Technology when creating and measuring cut-out shapes.
• Link to English by encouraging pupils to explain their reasoning orally or in writing.
• Vocabulary development supports language skills within maths.

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Extension Ideas for Future Lessons

• Introduce compound shapes with curved edges (circumference).
• Use perimeter to solve practical problems (e.g. fencing gardens).
• Explore area alongside perimeter for differentiation.

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Teacher Notes

• Prepare differentiated materials in advance to suit needs.
• Consider seating arrangements to facilitate group work despite a class of 29 (use small group tables or zones).
• Encourage use of estimation before measurement to enhance number sense.
• Use questioning techniques to prompt deeper thinking: “How can you check your answer?” “What happens to perimeter if all sides get longer?”

This plan ensures a tight focus on curriculum objectives with engaging activities tailored to all abilities, encouraging both skill development and mathematical reasoning.