Year 10 - Maths
Problem solving with complex 2D shapes
2D and 3D shape: compound shapes
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Study Guides
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 use your understanding of 2D shapes to solve problems.
Key Notes
- When problem solving, consider whether any elements are familiar from other areas of maths.
- Keep the goal in mind, it is easy to get distracted by too much information.
- The size of a sector of a pie chart can be scaled to reflect the population size.
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.
- Compound shape: A compound shape is a shape created using two or more basic shapes.
- Composite shape: A composite shape is an alternative for a compound shape.
- Pie chart: A pie chart (pie graph) is a circular graph where sectors represent different groups proportionally.
Common Mistakes To Avoid
- For the problems with squares inscribed inside circles, pupils may think that the length of the square is equal to the diameter of the circle.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
When problem solving, consider whether any elements are familiar from other areas of maths. Keep the goal in mind, it is easy to get distracted by too much information.
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: For the problems with squares inscribed inside circles, pupils may think that the length of the square is equal to the diameter of the circle. Correction: This would be the case if the circle was inscribed inside a square. But when the square is inscribed inside a circle, the diagonal length of the square is equal to the diameter of the circle.
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
- Shapes on coordinate grids Study Guide
- Shapes within shapes Study Guide
Browse all guides in the Year 10 Maths guide library.