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Year 10
Higher

Problem solving with complex 2D shapes

I can use my understanding of 2D shapes to solve problems.

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New
New
Year 10
Higher

Problem solving with complex 2D shapes

I can use my understanding of 2D shapes to solve problems.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. When problem solving, consider whether any elements are familiar from other areas of maths.
  2. Keep the goal in mind, it is easy to get distracted by too much information.
  3. The size of a sector of a pie chart can be scaled to reflect the population size.

Keywords

  • 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 misconception

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.

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.

There is potential here to run a design project with pupils acting as interior designers. Create a brief and get students to design and cost the project. You can specify a room to be complicated (complex composite shapes forming the walls/floor) or relatively simple (rectilinear walls) to suit.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
A is a circular graph where sectors represent different groups proportionally.
Correct Answer: pie chart, pie graph
Q2.
Jacob wants to plot a pie chart to represent the data in the table. What angle for the sector representing 'museum' should Jacob use?
An image in a quiz
8°
18°
20°
45°
Correct answer: 144°
Q3.
A circle has diameter 10 cm. Its area is ____$$\pi$$ cm².
Correct Answer: 25, twenty five
Q4.
The diagram shows a sector of a circle with radius 10 cm. The angle at the centre of the sector is 70°. Which calculation would find the area of the sector?
An image in a quiz
$$\frac{70}{360} \times \pi \times 10$$
$$\frac{70}{360} \times 2 \times \pi \times 10$$
$$\frac{70}{360} \times \pi \times 5^2$$
Correct answer: $$\frac{70}{360} \times \pi \times 10^2$$
$$\frac{70}{360} \times \pi \times 20^2$$
Q5.
The diagram shows a sector of a circle with radius 12 cm. The angle at the centre of the sector is 60°. The area of the sector is $$\pi$$ cm².
An image in a quiz
Correct Answer: 24, tweny four
Q6.
The diagram shows a sector of a circle with radius 12 cm. The angle at the centre of the sector is 60°. The perimeter of the sector is cm (to one decimal place).
An image in a quiz
Correct Answer: 36.5, 36.5 cm

Exit quiz

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6 Questions

Q1.
The diagram shows a square inscribed inside a circle. The length of the square is 6 cm. What is the diameter of the circle?
An image in a quiz
$$3$$ cm
$$6$$ cm
$$3\sqrt{2}$$ cm
Correct answer: $$6\sqrt{2}$$ cm
$$12\sqrt{2}$$ cm
Q2.
The diagram shows a square inscribed inside a circle. The diameter of the circle is 6 cm. Work out the length of the square.
An image in a quiz
$$3$$ cm
$$6$$ cm
Correct answer: $$3\sqrt{2}$$ cm
$$6\sqrt{2}$$ cm
$$12\sqrt{2}$$ cm
Q3.
The diagram shows a square inscribed inside a circle. The length of the square is 8 cm. The area of the circle is $$\pi$$ cm².
An image in a quiz
Correct Answer: 32, thirty two
Q4.
The diagram shows a square inscribed inside a circle. The diameter of the circle is 8 cm. The area of the square is cm².
An image in a quiz
Correct Answer: 32, thirty two
Q5.
The diagram shows a square inscribed inside a circle. The diameter of the circle is 12 cm. Which calculation would find the area of the shaded region?
An image in a quiz
$$\pi \times 6^2 - (3\sqrt{2})^2$$
Correct answer: $$\pi \times 6^2 - (6\sqrt{2})^2$$
$$\pi \times 12^2 - (3\sqrt{2})^2$$
$$\pi \times 12^2 - (6\sqrt{2})^2$$
Q6.
The diagram shows a square inscribed inside a circle. The length of the square is 12 cm. The area of the shaded region is cm² (to one decimal place).
An image in a quiz
Correct Answer: 82.2