Perimeter with Reasoning

Overview

Year Group: Year 4
Subject: Mathematics
Duration: 45 minutes
Class size: 30 pupils
Curriculum Reference:

• National Curriculum for England, KS2 Mathematics:
  • Measurement - Geometry:
    • "Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres."
    • Develop reasoning about missing lengths in rectilinear shapes.
• White Rose Maths Scheme:
  • Summer Term, Week 3: Perimeter and Area (focus on missing lengths and reasoning).

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Learning Objectives

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

• Calculate the perimeter of rectilinear shapes with one missing side.
• Use reasoning skills to deduce missing lengths of a rectilinear shape.
• Justify their methods and explain their thinking when finding perimeters involving missing sides.

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Success Criteria

• I can add all known sides correctly to find a partial perimeter.
• I can work out the missing side by understanding opposite sides are equal in rectilinear shapes.
• I can explain and justify how I found the missing side.
• I can calculate the total perimeter by adding all sides, including the one I have found.

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Resources

• Whiteboard and markers
• Rectilinear shape diagrams (printed and enlarged for modelling)
• Pencils and rulers
• Individual whiteboards or mini whiteboards for AfL
• Worksheets with progressively complex rectilinear shapes

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Lesson Structure

1. Introduction (10 minutes)

Engage with Contextual Problem:
Begin with a visually attractive animation or slide of a garden fence shaped like a rectilinear shape missing one side length. Ask the pupils:

• "If I want to put a fence around this garden, how much fencing do I need? What happens if one side length is missing?"

Targeted Questioning Using Bloom’s Taxonomy:

• Remembering: What does perimeter mean?
• Understanding: How do you calculate the perimeter of a shape?
• Applying: How can we find the missing side if the shape is rectilinear?
• Analysing: Why do opposite sides in this shape have the same lengths?
• Evaluating: Which method would you use to work out the missing length, and why?
• Creating: Can you create your own rectilinear shape with a missing side and explain how to calculate its perimeter?

Whole Class Discussion:
Encourage children to explain their ideas with sentence starters such as:

• "I think the missing side is... because..."
• "The opposite sides are equal, so..."

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2. Modelling and Teaching Input (10 minutes)

Step 1: Display an example rectilinear shape on the board (with three sides labelled and one missing side).

Example:
A shape with sides labelled 5 cm, 8 cm, 3 cm, and one missing side (x). Show the outline:

 ┌────5cm────┐  
│                 │ 8cm  
│                 │  
│        x cm   │  
└────3cm────┘  

Modelling Steps:

• Explain how to add known sides first.
• Use logic: in a rectilinear shape, opposite sides are equal. If one vertical side is 8 cm, the other vertical side is also 8 cm. Identify pairs of equal sides.
• Calculate the missing side by subtracting or using equality of opposite sides:
  "If one side is 3 cm, its opposite must be the missing length x. The perimeter is the total of all sides, add all known sides and solve for x."

AfL Moment 1 (5 minutes in):
Use mini-whiteboards:
Give pupils the partially completed shape and ask: "What is the missing side?" Pupils hold up answers with explanations:

• Ask a few pupils to justify their reasoning aloud.
• Clarify any misconceptions seen here.

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3. Guided Practice (10 minutes)

Task: Pupils work on a set of rectilinear shapes with one or two missing sides, starting with simple cases and gradually increasing complexity.

• Task 1: Identify missing sides when only one side is missing.
• Task 2: When two sides are missing but related (opposite sides).
• Task 3: Problem-solving puzzle with perimeter given and one missing length to find.

Differentiation:

• Support scaffold for lower ability: use a checklist of steps or sentence frames.
• Challenge for higher ability: find perimeter when the shape is made of multiple rectangles combined, with 2 missing sides to reason about.

AfL Moment 2 (during task):
Move around classroom, listen to learners’ reasoning, ask them to articulate their thinking:

• "Why did you choose to find the missing side first?"
• "How did you decide the value of the missing length?"
• Record misconceptions and successes to adjust the pace.

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4. Common Misconceptions and Difficulties

• Pupils may add all given sides but forget to account for missing sides properly.
• Confusing perimeter with area, leading to incorrect calculations.
• Not recognising that opposite sides of rectilinear shapes are equal lengths.
• Miscalculating due to rushing or incorrect use of subtraction for missing sides.

Pre-emptive Strategy: Use explicit discussion during modelling to highlight these points and clear up misunderstandings as they arise during AfL.

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5. Plenary (5 minutes)

Class Discussion and Reasoning:
Use a new shape with a missing side displayed on the board. Ask the class:

• "Who can explain the steps you would take to find the missing side?"
• "What would happen if this side was not equal to the opposite? Would it still be a rectilinear shape?"
• "How do these strategies help you with perimeter in everyday life?"

Success Criteria Review:
Tick off completed criteria and self-assessment for pupils using a thumbs up/down or traffic light system.

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6. Extension & Homework Suggestion

• Pupils to draw their rectilinear shape with a missing side and write at least two reasoning sentences explaining how to find its perimeter.
• Encourage use of mathematical language such as "perimeter", "opposite sides", "addition", "length", and "missing side".

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Example Work for Pupils to Copy

Example 1:
Calculate the perimeter of this shape:

• Given sides are 4 cm, 7 cm, 5 cm. Missing side length is x.
• Opposite sides are equal, so if one side is 4 cm, the side opposite is also 4 cm.

Step 1: Add all known sides: 7 + 5 + 4 = 16 cm
Step 2: Missing side (x) must be equal to its opposite side, so x = 7 cm
Step 3: Total perimeter = 4 + 7 + 5 + 7 = 23 cm

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This lesson plan actively develops pupils’ reasoning and understanding about calculating perimeter with missing sides in rectilinear shapes while adhering strictly to the Year 4 National Curriculum in England and the White Rose Maths progression.