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Year 10
Higher

Shapes within shapes

I can express percentage shaded from shapes within shapes.

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New
New
Year 10
Higher

Shapes within shapes

I can express percentage shaded from shapes within shapes.

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Share activities with pupils
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Lesson details

Key learning points

  1. You can express a number as a fraction of another and therefore as a percentage.
  2. If you have two areas, you can express one as a percentage of another.
  3. This can involve calculating with a variety of shapes.
  4. A calculator can be very useful here.

Keywords

  • Area - The area is the size of the surface and states the number of unit squares needed to completely cover that surface.

Common misconception

Using the incorrect value for finding the percentage, for instance, the area of the unshaded when it asks for the shaded region.

Encourage pupils to underline/highlight whether they are finding the percentage of the shaded or unshaded region.

Have pupils compare the answers to Task B Q2 and the similar explanation slides using squares, then they could investigate a similar pattern with a triangles, hexagons etc. - would the result be the same? This will start them thinking about area scale factors for the future.
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.
25% of 2640 is .
Correct Answer: 660
Q2.
20 as a percentage of 50 is %
Correct Answer: 40, 40%
Q3.
The area of a square with edge lengths of 1.4 cm is cm².
Correct Answer: 1.96
Q4.
The area of a circle with a diameter of 30 m is $$\pi$$ m².
Correct Answer: 225
Q5.
Here are the first seven triangular numbers: 1, 3, 6, 10, 15, 21, 28. The next triangular number is .
Correct Answer: 36, thirty six
Q6.
The numbers 1, 4, 9, 16, 25, 36, 49, ... are called the numbers.
Correct Answer: square

Exit quiz

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6 Questions

Q1.
A shape has a total area of 50 cm². Part of the shape is shaded. An area of 24 cm² is left unshaded. % of the shape is shaded.
Correct Answer: 52, 52%
Q2.
A shape has a total area of 45 cm². Part of the shape is shaded. An area of 27 cm² is left unshaded. % of the shape is shaded.
Correct Answer: 40, 40%, forty
Q3.
Which descriptors of this shape are correct?
An image in a quiz
Correct answer: This is a compound shape.
This is a congruent shape.
Correct answer: This is a rectilinear shape.
75% is shaded
Correct answer: 80% is shaded
Q4.
The percentage of the shape which is shaded is %.
An image in a quiz
Correct Answer: 75, 75%
Q5.
Which calculation is correct to find the percentage of the rectilinear compound shape which is shaded?
An image in a quiz
$$\frac{10\times5}{9\times9+7\times12}\times100$$
Correct answer: $$\frac{9\times9+7\times12-10\times5}{9\times9+7\times12}\times100$$
$$\frac{10\times5}{9\times9+7\times12-10\times5}\times100$$
$$\frac{9\times9+7\times12-10\times5}{10\times5}\times100$$
Q6.
This shape is made from a circle and the removal of two congruent circles. The percentage shaded in this shape is %.
An image in a quiz
Correct Answer: 50, 50%, fifty