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Year 10
Foundation

Problem solving with 2D shapes

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

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New
New
Year 10
Foundation

Problem solving with 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. With diagrams, it can be beneficial to add information to them (such as extra lines).

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.

Common misconception

When finding the perimeter of a rectilinear compound shape, pupils might sum the perimeters of each rectangle.

Part of the perimeter for each rectangle is inside the compound shape. Therefore, not all of the perimeter of each rectangle contributes towards the perimeter of the compound shape in this problem.

Pupils could investigate creating compound rectilinear shapes by placing rectangles together in different way. Then they could observe which parts of each rectangle's perimeter make up the perimeter of the overall shape.
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 carpet costs £30 per m². 8.5 m² of carpet costs £ .
Correct Answer: 255, £255, 255 pounds, 255.00, £255.00
Q2.
A shape is a shape created using two or more basic shapes.
Correct Answer: compound, composite
Q3.
A rectangle has a base of 8 cm and an area of 40 cm². The height of the rectangle is cm.
Correct Answer: 5, five, 5 cm, five cm, five centimetres
Q4.
A circle has a diameter of 9 cm. What is its area (to 1 decimal place)?
14.1 cm$$^2$$
28.3 cm$$^2$$
56.5 cm$$^2$$
Correct answer: 63.6 cm$$^2$$
254.5 cm$$^2$$
Q5.
Which calculations would find the perimeter of the compound rectilinear shape?
An image in a quiz
35 + 12 + 27 + 16
Correct answer: 35 + 12 + 19 + 27 + 16 + 39
Correct answer: 2 × (35 + 39)
2 × (16 + 12)
2 × (35 + 12 + 27 + 16)
Q6.
The area of the compound rectilinear shape is cm².
An image in a quiz
Correct Answer: 852, eight hundred and fifty two

Exit quiz

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6 Questions

Q1.
The length of the square is 20 cm. Calculate the area of the shaded region, give your answer correct to 1 decimal place.
An image in a quiz
Correct answer: 85.8 cm²
314.2 cm²
343.4 cm²
400 cm²
Q2.
The radius of the circle is 20 cm. Which calculation can be used to find the area of the shaded region?
An image in a quiz
20² − $$\pi$$ × 20²
20² − $$\pi$$ × 40²
Correct answer: 40² − $$\pi$$ × 20²
40² − $$\pi$$ × 40²
Q3.
The compound rectilinear shape is constructed by joining two congruent rectangles. The total area is 90 m². The area of each congruent rectangle is m².
An image in a quiz
Correct Answer: 45, forty five
Q4.
The perimeter of the square is 40 cm. The area of the shaded region is cm² (to 1 decimal place).
An image in a quiz
Correct Answer: 21.5, twenty-one point 5, twenty one point 5
Q5.
The compound rectilinear shape is constructed by joining two congruent rectangles. The total area is 120 cm² and $$a$$ = 10. Calculate the length of the longest side.
An image in a quiz
6 cm
10 cm
Correct answer: 16 cm
52 cm
60 cm
Q6.
The compound rectilinear shape is constructed by joining two congruent rectangles. The total area is 80 cm² and $$a$$ = 8. The perimeter of the shape is cm.
An image in a quiz
Correct Answer: 42, forty two, 42 cm