Year 8

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## Lesson details

### Key learning points

- In this lesson, we will learn how to estimate and solve problems using estimation.

### Licence

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

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### 6 Questions

Q1.

A classroom is measured 5.4 x 3.4 metres, measured to 1 d.p. Calculate the lower bound of the area of the room.

17.889 𝑐𝑚^2

18.36 𝑐𝑚^2

18.8025 𝑐𝑚^2

Q2.

James ran a distance of 400m in a time of 25.2 seconds. The distance of 400m was measured to the nearest 10 metres. The time of 25.2 was measured to the nearest tenth of a second. Work out the upper bound James' average speed.

15.7 m/s

16.04 m/s

16.07 m/s

Q3.

James ran a distance of 400m in a time of 25.2 seconds. The distance of 400m was measured to the nearest 10 metres. The time of 25.2 was measured to the nearest tenth of a second. Work out the lower bound James' average speed.

15.67 m/s

15.69 m/s

15.71 m/s

Q4.

Carl measured the length and width of a rectangle. He measured the length to be 19cm correct to the nearest centimetre. He measured the width to be 20cm correct to the nearest 10cm. Calculate the lower bound for the area of this rectangle.

292.5 cm^2

370 cm^2

380 cm^2

Q5.

6 heights are listed, given to one decimal place: 4.6cm, 6.3cm, 9.8cm, 3.2cm, 5.7cm, 3.6cm. Work out the greatest possible mean.

5.48cm

5.53cm

5.98cm

Q6.

A circle has an area of 130cm^2 to the nearest 10cm^2. Work out the upper bound of the radius. Give your answer to 3 d.p.

39.789

6.308

6.433

### 6 Questions

Q1.

Estimate the total cost of 32 books at £178 each and 57 markers at £22.30 each.

£6700

£6715

£6967

Q2.

Student A estimated that 23.5 x 91 = 1800. Student B estimated that 23.5 x 91.4= 2160. What did student B do?

Nothing, they just multiplied the original values

Rounded both values down and then multiplied.

Rounded both values to to 1 s.f. and then multiplied

Q3.

Work out an estimate for 9.97% of 3967

300

392.7

396.7

Q4.

Estimate the value of: 6.2 + 7.9 x 3.2 - 9.8

18

21.68

32

Q5.

I estimated that 7.85 x 29 = 240. Why is my estimated answer more than my exact answer?

It shouldn't be. Estimation is incorrect

Only one value was rounded up and so answer is only a little greater than the exact value

Q6.

Find an estimate for √78

8

8.5

9