More compound measures.pptx

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

More compound measures

Multiplicative reasoning

Lesson 3 of 4

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Warm-up

Multiplicative reasoning

Lesson 3 of 4

Answer each one, then check.

1

Change 2.5 hours into hours and minutes.

2

What is density?

3

Work out 60 ÷ 1.5.

4

Work out 60 ÷ 60.

5

How many litres in 1 m³?

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Warm-up - Answers

Multiplicative reasoning

Lesson 3 of 4

1

Change 2.5 hours into hours and minutes.

2 h 30 min

2

What is density?

Mass divided by volume

3

Work out 60 ÷ 1.5.

40

4

Work out 60 ÷ 60.

1

5

How many litres in 1 m³?

1000

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Learning Objectives

Multiplicative reasoning

Lesson 3 of 4

1

Use rates such as population density and flow rate.

2

Work out average speed for a journey in stages.

3

Convert compound units, including density.

4

Solve multi-step problems with compound measures.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Everyday Compound Measures

Multiplicative reasoning

Lesson 3 of 4

Population density

population/area, for example people per km².

Rate of flow

volume/time, for example litres per minute.

Unit price

cost/quantity, for example £ per kg.

Average speed

(total distance)/(total time).

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Population Density

Multiplicative reasoning

Lesson 3 of 4

A town has 60 000 people and an area of 25 km². Find its population density.

1

Density = population/area

(60 000)/25

2

Work it out

2400

ANSWER

2400 people per km²

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Rate of Flow

Multiplicative reasoning

Lesson 3 of 4

A tank holds 1200 litres. Water runs into it at 15 litres per minute. How long does it take to fill, in hours and minutes?

1

Time = volume/rate

1200/15

2

Work it out

80 minutes

3

Convert

1 hour 20 minutes

ANSWER

1 hour 20 minutes

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A Two-Stage Journey

Multiplicative reasoning

Lesson 3 of 4

Average speed uses the whole distance and the whole time.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Average Speed in Two Stages

Multiplicative reasoning

Lesson 3 of 4

A car travels 60 km at 40 km/h and then 60 km at 60 km/h. Find its average speed for the whole journey.

1

Time for stage 1

60 ÷ 40 = 1.5 hours

2

Time for stage 2

60 ÷ 60 = 1 hour

3

Total distance and time

120 km in 2.5 hours

4

Average speed

120 ÷ 2.5 = 48

ANSWER

48 km/h (not 50 km/h)

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Converting Density

Multiplicative reasoning

Lesson 3 of 4

Steel has density 7.8 g/cm³. Write this in kg/m³.

1

1 g is 0.001 kg and 1 cm³ is 0.000 001 m³

1 g/cm³ = 0.001/(0.000 001) kg/m³

2

Simplify

1 g/cm³ = 1000 kg/m³

3

Multiply

7.8 × 1000

ANSWER

7800 kg/m³

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Converting Speed the Other Way

Multiplicative reasoning

Lesson 3 of 4

A cyclist rides at 15 m/s. Find her speed in km/h.

1

15 m per second in 1 hour

15 × 3600 = 54 000 m

2

Change to km

54 000 ÷ 1000

ANSWER

54 km/h

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Handy Conversions

Multiplicative reasoning

Lesson 3 of 4

Learn or work these out.

From

To

Rule

m/s

km/h

Multiply by 3.6

km/h

m/s

Divide by 3.6

g/cm³

kg/m³

Multiply by 1000

cm²

m²

Divide by 10 000

litres

cm³

Multiply by 1000

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Key Terms

Multiplicative reasoning

Lesson 3 of 4

Rate

A quantity compared with another, such as litres per minute.

Population density

The number of people per unit of area.

Average speed

Total distance divided by total time.

Flow rate

The volume passing a point per unit of time.

Unit price

The cost of one unit of a product.

Conversion

Changing from one unit to another.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Multiplicative reasoning

Lesson 3 of 4

YOUR TASK

Best Journey

12 minutes

Ali drives 90 km at 60 km/h and then 90 km at 90 km/h. Ben drives the whole 180 km at 72 km/h. Who has the higher average speed, and by how much?

1

Find each time.

2

Total distance over total time.

3

Compare.

WHAT A GOOD ANSWER SHOWS

Ali: times 1.5 h and 1 h, so 2.5 h for 180 km: 72 km/h. Ben: 72 km/h. They have the same average speed, even though Ali's speeds average to 75 km/h.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Can I...?

Multiplicative reasoning

Lesson 3 of 4

Work out population density.

Work out a rate of flow.

Find average speed for a whole journey.

Avoid averaging the speeds.

Convert m/s to km/h.

Convert g/cm³ to kg/m³.

Use unit prices.

Show clear working.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Summary & Exam Focus

Average speed = total distance ÷ total time.

Density, pressure and flow rate are all "one thing per another".

Convert units before dividing.

m/s to km/h: multiply by 3.6.

EXAM FOCUS

A car travels 60 km at 40 km/h and then 60 km at 60 km/h. Work out its average speed for the whole journey. (4 marks)

Find the time for each stage, then divide the total distance by the total time. The answer is not the average of the two speeds.

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