Year 6 - Maths
When a 2D shape is decomposed and the parts rearranged, the areas remains the same
Draw, compose and decompose shapes
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils will use knowledge of shape properties to draw, sketch and identify shapes.
Lesson Summary
You will learn to decompose a 2D shape and create a different shape from the parts and explain why the area of the new compound shape is the same as the original 2D shape.
Key Notes
- The area of the compound shape is equal to the total areas of its parts
- 2D shapes can be decomposed and rearranged in different ways
- 2D shapes can be decomposed and rearranged in different ways but the total area stays the same
Vocabulary To Learn
- Compound shape: A compound shape is a shape created using two or more basic shapes.
- Area: Area is the measurement of a flat surface. It measures a 2D space.
Common Mistakes To Avoid
- Children may assume some shapes have a larger area than others by comparison of a certain dimension. In this lesson, pattern blocks can be arranged to create shapes with very different dimensions.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The area of the compound shape is equal to the total areas of its parts. 2D shapes can be decomposed and rearranged in different ways.
2. Use this key word in a maths sentence and explain it clearly. 'Compound shape'
A compound shape is a shape created using two or more basic shapes. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Children may assume some shapes have a larger area than others by comparison of a certain dimension. In this lesson, pattern blocks can be arranged to create shapes with very different dimensions. Correction: Encourage pupils to rearrange the composing shapes to prove that the compound shapes have the same area. This can be done effectively with tangrams or pattern blocks, both of which feature heavily in this lesson.
More Lessons In This Unit
- 3D shapes can be composed from 2D nets Study Guide
- Any parallelogram can be decomposed and the parts rearranged to form a rectangular parallelogram Study Guide
- Reason about compound shapes using the relationship between side lengths and area and perimeter Study Guide
- Reason about shapes using the relationship between side lengths and area and perimeter Study Guide
- Shapes with the same areas can have different perimeters and vice versa Study Guide
- The same 3D shapes can be composed from different 2D nets Study Guide
- Two congruent triangles can be arranged to compose a parallelogram Study Guide
- Use knowledge of shape properties to draw shapes accurately using rulers and protractors Study Guide
- Use knowledge of shape properties to sketch and identify shapes Study Guide
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