Mult-e-Maths



Converting between miles and kilometres 6MEA3

National curriculum objective

Pupils should be taught to:

• convert between miles and kilometres.

Prior knowledge and skills

• Know how to use and interpret data using a line graph.

• Know how to multiply and divide whole numbers by decimal numbers.

Vocabulary

miles, kilometres, conversion factor

Resources

• small whiteboards and pens

• Resource sheet

• calculators

Oral and mental starter

Pupils can use small whiteboards and pens for working out during this lesson.

Whole class

Assess pupils’ understanding of scaling. Ask them to provide examples of scaling that they have seen in the classroom and at home. Discuss suggestions and ensure the whole class understands that scaling up a quantity can be achieved using multiplication, and scaling down a quantity can be achieved using division.

Main teaching activity

Whole class

Assess pupils’ understanding of the relative sizes of miles and kilometres. They might not have come across miles in the classroom before, but are likely to have heard adults at home talking in miles when discussing distances.

Q What units might you use to measure the distance between two cities? (kilometres and miles)

Which is longer, a mile or a kilometre? (A mile is longer than a kilometre.)

If necessary, explain that miles are an imperial unit of measure for distance and kilometres are metric units of measure. The imperial unit was replaced some years ago by the metric unit in the UK but distances tend to still be measured in miles. The imperial unit is still used in other countries.

Explain that 5 miles is approximately the same distance as 8 kilometres. Write on the board: ‘5 miles ≈ 8 kilometres’. If necessary, explain that the symbol ‘≈’ means ‘approximately equal to’.

Q If 5 miles are approximately equal to 8 kilometres, approximately how many kilometres do you think are equivalent to 10 miles? (16 km) and 50 miles? (80 km)

Discuss suggestions. If no one mentions it, suggest that since 5 miles × 2 = 10 miles, then 8 km × 2 = 16 km. Similarly, since 5 miles × 10 = 50 miles, 8 km × 10 = 80 km. Consolidate this on the board:

5 miles ≈ 8 kilometres

10 miles ≈ 8 kilometres

50 miles ≈ 80 kilometres

This is one way to convert between miles and kilometres: use a known equivalence (5 miles ≈ 8 kilometres) and scaling up or down as necessary.

(Screen 1: Activity 1, Question 1)

Explain that another way to convert between miles and kilometres is to use a line graph. Discuss the parts of the graph on the board with the pupils.

Q What is shown on the horizontal axis? (kilometres)

What is shown on the vertical axis? (miles)

Explain that on this graph, each point on the line is plotted to show the distance in miles and the equivalent distance in kilometres, and vice versa. It is known as a conversion graph. Explain that they can use it to confirm that their earlier calculations of the number of kilometres equivalent to 10 and 50 miles are correct. Ask pupils show how to read the required information from the graph.

Q According to the graph, how many kilometres are equivalent to 5 miles? and to 10 miles?

If necessary, demonstrate for 5 miles: move up the vertical axis until you reach 5, then from 5 move in a straight line across until you meet the plotted line. (To draw in straight lines, select the ‘Line drawing’ tool [pic] from the ‘Annotations’ menu [pic] on the vertical toolbar. Click and hold the mouse at the point you want the line to start, then drag to the end point and release.) From the point where you meet the line, move in a straight line down to the horizontal axis; read the number of kilometres on the axis (8 km). Explain that it can be useful to use a ruler when moving between the axes and the plotted line to make sure you stay in the correct straight line. If necessary, use the graph to demonstrate for 10 miles/16 km as well.

Q How can you use the graph to convert 12 kilometres to miles? (Move along the horizontal axis to 12 km, then move in a straight line up until you get to the plotted line. Then move in a straight line to the left to the vertical axis and read the number of miles; 7.5 miles.)

Groups or Pairs

Pupils work in pairs or groups to solve the problems on the Resource sheet. When pupils are finished, discuss the solutions and ask pupils to discuss their strategies.

Whole class

(Screens 2–3: Activity 2, Questions 1–2)

Another way to convert between miles and kilometres is to use multiplication or division. Remind pupils that they have converted between different units of measure using multiplication or division before, when converting from centimetres to metres for example. Work through the questions on screen 2 as a class. Drag each answer panel to the bin to reveal the correct answer and conversion factor.

Move to screen 3. Explain that you can do a similar thing to convert between metric and imperial units, such as between miles and kilometres. As they are not the same unit you can’t simply multiply or divide by a power of 10, instead you need a conversion factor. This is the amount by which you would multiply 1 mile to get 1 kilometre or divide 1 kilometre by to get 1 mile. In the case of miles and kilometres, the conversion factor is ‘1.6’. This is because 1 mile ≈ 1.6 km.

Q How could you convert from miles to kilometres? (Multiply the number of miles by 1.6.)

Drag the top yellow panel to the bin to reveal the required operation. Ask pupils to convert each of the miles given to kilometres. They can use their small whiteboards or calculators to help. You can also use the calculator feature on the screen. Talk through each conversion, you might want to write each calculation on the board:

Q Using the conversion factor, approximately how many kilometres is 8 miles? (12.8 km; 8 miles × 1.6 = 12.8 km)

Drag the answer panels to the bin to confirm the answer in each case.

Q How could you convert from kilometres to miles? (Divide the number of kilometres by 1.6.)

Drag the yellow panel to the bin to reveal the required operation. As before, ask pupils to convert each of the kilometres given to miles, talk through each answer, then drag the answer panels to the bin to confirm each answer.

You could give pupils additional distances in miles or kilometres and ask pupils to perform the conversions.

Other tasks

You could ask pupils to:

• convert between other metric and imperial measures, e.g. between inches and centimetres (1 inch ≈ 2.5 cm); ounces and grams (1 ounce ≈ 3 g); pints and litres (1 pint ≈ 540 ml).

Review

Pairs

(Screen 4: Activity 3, Question 1)

Explain that on the right-hand side of the board there are some distances; some are descriptions of walks, jogs or runs had by people. Pupils work with a partner to arrange the distances in order from shortest to longest. Elicit that they need to convert each distance to the same unit first, either all miles or all kilometres.

Q Which distance is shortest?

Which is distance longest?

Ask pupils to justify their order. Discuss solutions and strategies. (Correct order, shortest to longest: 3 mile walk + 1 mile jog; 7 km; half of 20 km; 7 miles; 6 runs of 2 miles each; 4 walks of 5 km each; a 22.4 km hike.

Key ideas and assessment

Miles are an imperial measure of length that are often used to measure large distances such as that between towns, cities and countries etc. 1 mile is equivalent to approximately 1.6 kilometres. You can use this relationship in a number of ways to convert from miles to kilometres, and from kilometres to miles.

Can pupils:

• use scaling to convert between miles and kilometres?

• use a line graph to convert between miles and kilometres?

• use a conversion factor to convert between miles and kilometres?

Solutions

Resource sheet

1. a. 26 km b. 9 km

2. a. 18.5 miles b. 4.5 miles

3. 16 km

4. 13 miles

5. 3 miles

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× 10

× 2

× 2

× 10

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