Year 10 - Maths
Shapes within shapes
2D and 3D shape: compound 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, knowledge of circles and polygons is drawn upon to find the arc length and area of a circle sector and areas of complex compound shapes.
Lesson Summary
You will learn to express percentage shaded from shapes within shapes.
Key Notes
- You can express a number as a fraction of another and therefore as a percentage.
- If you have two areas, you can express one as a percentage of another.
- This can involve calculating with a variety of shapes.
- A calculator can be very useful here.
Vocabulary To Learn
- Area: The area is the size of the surface and states the number of unit squares needed to completely cover that surface.
Common Mistakes To Avoid
- Using the incorrect value for finding the percentage, for instance, the area of the unshaded when it asks for the shaded region.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
You can express a number as a fraction of another and therefore as a percentage. If you have two areas, you can express one as a percentage of another.
2. Use this key word in a maths sentence and explain it clearly. 'Area'
The area is the size of the surface and states the number of unit squares needed to completely cover that surface. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Using the incorrect value for finding the percentage, for instance, the area of the unshaded when it asks for the shaded region. Correction: Encourage pupils to underline/highlight whether they are finding the percentage of the shaded or unshaded region.
More Lessons In This Unit
- Area of a sector Study Guide
- Area of compound shapes Study Guide
- Calculating arc length Study Guide
- Checking and securing understanding of area for compound shapes Study Guide
- Checking and securing understanding of area for standard shapes Study Guide
- Checking and securing understanding of circles Study Guide
- Checking and securing understanding of converting between metric and imperial measures Study Guide
- Checking and securing understanding of perimeter for compound shapes Study Guide
- Checking and securing understanding of perimeter for standard shapes Study Guide
- Checking and securing understanding of scales and conversion Study Guide
- Equations from complex shapes Study Guide
- Perimeter and area in a contextual setting Study Guide
- Problem solving with 2D shapes Study Guide
- Problem solving with complex 2D shapes Study Guide
- Shapes on coordinate grids Study Guide
Browse all guides in the Year 10 Maths guide library.