Units and accuracy.pptx

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Units and accuracy

Area and volume

Lesson 2 of 7

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Last Lesson and Before

Area and volume

Lesson 2 of 7

Answer each one, then check.

1

How many cm are in 1 m?

2

How many mm are in 1 cm?

3

Round 8.347 to 1 decimal place.

4

Last lesson: area of a 3 m by 2 m rectangle?

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Last Lesson and Before - Answers

Area and volume

Lesson 2 of 7

1

How many cm are in 1 m?

100

2

How many mm are in 1 cm?

10

3

Round 8.347 to 1 decimal place.

8.3

4

Last lesson: area of a 3 m by 2 m rectangle?

6 m²

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Learning Objectives

Area and volume

Lesson 2 of 7

1

Convert between units of area.

2

Convert between units of volume and capacity.

3

Write the error interval for a rounded or truncated number.

4

(Higher) Find upper and lower bounds of a calculation.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Why 1 m² Is 10 000 cm²

Area and volume

Lesson 2 of 7

Square the length factor for area; cube it for volume.

A square metre is 100 cm by 100 cm, so it holds 100 × 100 = 10 000 square centimetres. A cubic metre is 100 × 100 × 100 = 1 000 000 cubic centimetres.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Conversion Factors

Area and volume

Lesson 2 of 7

Units

Length

Area

Volume or capacity

mm and cm

1 cm = 10 mm

1 cm² = 100 mm²

1 cm³ = 1000 mm³

cm and m

1 m = 100 cm

1 m² = 10 000 cm²

1 m³ = 1 000 000 cm³

m and km

1 km = 1000 m

1 km² = 1 000 000 m²

Rarely needed

Capacity

-

-

1 cm³ = 1 ml; 1000 cm³ = 1 litre; 1 m³ = 1000 litres

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Converting Area

Area and volume

Lesson 2 of 7

Convert 3.5 m² into cm².

1

1 m² = 10 000 cm²

Multiply by 10 000 (a smaller unit means more of them)

2

Calculate

3.5 × 10 000 = 35 000

ANSWER

35 000 cm²

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Converting Volume to Capacity

Area and volume

Lesson 2 of 7

A tank holds 2 400 000 cm³ of water. Write this in m³ and in litres.

1

1 m³ = 1 000 000 cm³

2 400 000 ÷ 1 000 000 = 2.4 m³

2

1 litre = 1000 cm³

2 400 000 ÷ 1000 = 2400 litres

3

Check: 1 m³ = 1000 litres

2.4 × 1000 = 2400

ANSWER

2.4 m³, which is 2400 litres

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

PART TWO

Accuracy

A rounded measurement could be anywhere in a range.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Error Intervals

Area and volume

Lesson 2 of 7

If a length is 8.3 cm to 1 decimal place, it could be anything that rounds to 8.3.

The bounds

Half a unit either side: the lower bound is 8.25 and the upper bound is 8.35.

Error interval

8.25 ≤ l < 8.35. The upper bound itself would round up to 8.4, so use <.

To the nearest 10

70 to the nearest 10: 65 ≤ x < 75.

Truncation

4.7 truncated to 1 d.p. (digits chopped off): 4.7 ≤ x < 4.8.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

An Error Interval

Area and volume

Lesson 2 of 7

The mass of a parcel is 2.6 kg, correct to 1 decimal place. Write down the error interval for the mass m.

1

The degree of accuracy

0.1 kg

2

Half of it

0.05 kg

3

Lower and upper bounds

2.6 − 0.05 = 2.55 and 2.6 + 0.05 = 2.65

ANSWER

2.55 ≤ m < 2.65

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PART THREE · HIGHER

Bounds in Calculations

Choose the bounds that push the answer as far as it can go.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Which Bounds to Use

Area and volume

Lesson 2 of 7

Calculation

For the upper bound

For the lower bound

a + b

upper + upper

lower + lower

a − b

upper − lower

lower − upper

a × b

upper × upper

lower × lower

a ÷ b

upper ÷ lower

lower ÷ upper

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

The Upper Bound of a Speed

Area and volume

Lesson 2 of 7

A runner covers 100 m, measured to the nearest metre, in 12.5 s, measured to 1 decimal place. Work out the upper bound of the runner's average speed.

1

Bounds of the distance

99.5 m and 100.5 m

2

Bounds of the time

12.45 s and 12.55 s

3

Biggest speed: biggest distance ÷ smallest time

100.5/12.45 = 8.0722…

ANSWER

8.07 m/s (to 3 s.f.)

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Key Terms

Area and volume

Lesson 2 of 7

Capacity

How much a container holds, in ml or litres.

Lower bound

The smallest value that rounds to the given number.

Upper bound

The value where rounding switches up to the next number; the interval stops just below it.

Error interval

The range of possible values, e.g. 8.25 ≤ l < 8.35.

Truncate

Cut off digits without rounding.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Area and volume

Lesson 2 of 7

YOUR TASK

Fill the Room

12 minutes

Measure (or estimate) your classroom's length, width and height in metres. Work out its volume in m³ and in litres. Then work out its floor area in cm². Which of your answers are sensible to give exactly, and which should be rounded?

1

Measure in metres.

2

Convert with the right factor.

3

Decide how accurate your answer really is.

WHAT A GOOD ANSWER SHOWS

For a 9 m by 7 m by 3 m room: volume 189 m³ = 189 000 litres; floor area 63 m² = 630 000 cm². With measurements to the nearest metre, the answers are only good to 2 significant figures at most.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Can I...?

Area and volume

Lesson 2 of 7

Convert between units of area.

Convert between units of volume.

Convert between volume and capacity.

Write an error interval for a rounded number.

Write an error interval for a truncated number.

(Higher) Find the bounds of a calculation.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Summary & Exam Focus

Area: square the length factor. Volume: cube it.

1 cm³ = 1 ml; 1000 cm³ = 1 litre; 1 m³ = 1000 litres.

Error interval: half a unit either side, ≤ then <.

(Higher) Maximise or minimise each part of the calculation.

EXAM FOCUS

The length of a pencil is 14 cm, correct to the nearest centimetre. Write down the error interval for the length l. (2 marks)

In an error interval the lower bound gets ≤ and the upper bound gets <. Writing ≤ at both ends loses a mark.

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