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Step-by-step practice: Maths · Level 5Chapter 8 · Metric length, mass and capacity
Level 5 · Chapter 8

Metric length, mass and capacity

By the end of this chapter you will be able to

  • Convert between metric units of length, mass and capacity
  • Add and subtract measures in mixed units
  • Read a scale in steps of 2, 5 or 10 units
  • Choose a sensible metric unit
  • Solve problems with totals of measures

You should already know

  • Length, mass and capacity to the nearest unit (Level 4, chapter 8)
  • Decimals to hundredths (chapter 7)

Where this leads

  • Perimeter of shapes and the time and money problems (chapter 9)

Step-by-step practice: maths (Level 5). Small steps, repeated until fluent. Content: Convert between km and m, m and cm, cm and mm, kg and g, and l and ml (Y5 paraphrase), Add and subtract lengths, masses and capacities in the same or mixed units (Y4 and Y5 paraphrase), Estimate, measure and read scales with a suitable interval of 2, 5 or 10 units (Y5 paraphrase), Solve a problem with a total length, mass or capacity (Y5 paraphrase).

Exercise P  Do you remember?

Non-calculator
1
FWhat is 6 × 9?
2
FWork out 1,250 + 750.
3
FWhat is 1/4 of 24?
4
FWrite 7/10 as a decimal.
5
FRound 2,385 to the nearest 10.
8.1

Converting length: km, m, cm and mm

Level 5
Convert between km and m, m and cm, and cm and mm
Video lesson: Converting length: km, m, cm and mmComing soon

1 km = 1,000 m, 1 m = 100 cm, and 1 cm = 10 mm. Going to a smaller unit makes the number bigger, so multiply.

To change a number of centimetres into metres and centimetres, divide by 100. 340 cm = 3 m 40 cm.

Key ideas

  • 1 km = 1,000 m; 1 m = 100 cm; 1 cm = 10 mm.
  • Smaller unit: multiply. Bigger unit: divide.
  • Write both parts with their units.
Worked example 8.1.1
Change 3 km to metres.

Method. Multiply by 1,000 to change kilometres into metres.

  1. Use the rule. 1 kilometre is 1,000 metres.
    1 km = 1,000 m
  2. Multiply the kilometres by 1,000. Each kilometre is 1,000 metres.
    3 × 1,000 = 3,000
  3. Write the answer with the unit. The unit is metres.
    3,000 m

Check. Check: 3,000 ÷ 1,000 = 3.

Watch out. Going to a smaller unit makes the number bigger. Multiply.

Worked example 8.1.2
Change 4 m to cm.

Method. Multiply by 100 to change m into cm.

  1. Use the rule. 1 m is 100 cm.
    1 m = 100 cm
  2. Multiply the m by 100. Each m has 100 cm.
    4 × 100 = 400
  3. Write the answer with the unit. The unit is cm.
    400 cm

Check. Check: 400 ÷ 100 = 4.

Watch out. A smaller unit gives a bigger number. Multiply by 100.

Worked example 8.1.3
Change 340 cm to m and cm.

Method. Divide by 100 to find the whole m; the remainder is the cm.

  1. Use the rule. 1 m is 100 cm.
    1 m = 100 cm
  2. Share 340 cm into groups of 100. Each group is one m.
    340 ÷ 100 = 3 r 40
  3. Write the answer. 3 whole m and the cm left over.
    3 m 40 cm

Check. Check: 3 × 100 + 40 = 340.

Watch out. Use a space between the two parts, and the unit after each: 3 m 40 cm.

Watch out

Watch out. 1 m is 100 cm, not 10 cm. Check the number of zeros for each unit.

Exam tip

Grown-up tip. Use a metre stick or a ruler. Ask: “How many centimetres in one metre? How many millimetres in one centimetre?”

Exercise 8A  Practice: converting length

Non-calculator
1
FChange 1,888 cm to m and cm.
2
FChange 32 mm to cm and mm.
3
FChange 1,253 cm to m and cm.
4
FChange 14 km to metres.
5
FChange 2 km to metres.
6
FChange 8 m to cm.
7
FChange 9 m to cm.
8
FChange 981 cm to m and cm.
9
FChange 5 cm to mm.
10
FChange 4 cm to mm.
11
FChange 1,127 cm to m and cm.
12
FChange 8 cm to mm.
13
FChange 1,086 cm to m and cm.
14
FChange 111 mm to cm and mm.
15
FChange 17 m to cm.
16
FChange 3 km to metres.
8.2

Converting mass and capacity: kg, g, litres and ml

Level 5
Convert between kg and g, and between litres and millilitres
Video lesson: Converting mass and capacity: kg, g, litres and mlComing soon

1 kg = 1,000 g and 1 litre = 1,000 ml. To change grams into kilograms and grams, divide by 1,000: 2,350 g = 2 kg 350 g.

Write the answer with both units, so that the reader sees the kilograms and the grams.

Key ideas

  • 1 kg = 1,000 g; 1 litre = 1,000 ml.
  • Smaller unit: multiply by 1,000.
  • Bigger unit: divide by 1,000; the remainder is the smaller unit.
Worked example 8.2.1
Change 3 kg to g.

Method. Multiply by 1,000 to change kg into g.

  1. Use the rule. 1 kg is 1,000 g.
    1 kg = 1,000 g
  2. Multiply the kg by 1,000. Each kg has 1,000 g.
    3 × 1,000 = 3,000
  3. Write the answer with the unit. The unit is g.
    3,000 g

Check. Check: 3,000 ÷ 1,000 = 3.

Watch out. A smaller unit gives a bigger number. Multiply by 1,000.

Worked example 8.2.2
Change 2,350 g to kg and g.

Method. Divide by 1,000 to find the whole kg; the remainder is the g.

  1. Use the rule. 1 kg is 1,000 g.
    1 kg = 1,000 g
  2. Share 2,350 g into groups of 1,000. Each group is one kg.
    2,350 ÷ 1,000 = 2 r 350
  3. Write the answer. 2 whole kg and the g left over.
    2 kg 350 g

Check. Check: 2 × 1,000 + 350 = 2,350.

Watch out. Use a space between the two parts, and the unit after each: 2 kg 350 g.

Worked example 8.2.3
Change 1,250 ml to l and ml.

Method. Divide by 1,000 to find the whole l; the remainder is the ml.

  1. Use the rule. 1 l is 1,000 ml.
    1 l = 1,000 ml
  2. Share 1,250 ml into groups of 1,000. Each group is one l.
    1,250 ÷ 1,000 = 1 r 250
  3. Write the answer. 1 whole l and the ml left over.
    1 l 250 ml

Check. Check: 1 × 1,000 + 250 = 1,250.

Watch out. Use a space between the two parts, and the unit after each: 1 l 250 ml.

Watch out

Watch out. 2,350 g is 2 kg 350 g, not 23 kg 50 g. Count the thousands first.

Exam tip

Grown-up tip. Use a kitchen scale and a measuring jug. Ask the child to read the scale and say the answer with both units.

Exercise 8B  Practice: converting mass and capacity

Non-calculator
1
FChange 11,122 ml to l and ml.
2
FChange 12,065 g to kg and g.
3
FChange 14 l to ml.
4
FChange 10 kg to g.
5
FChange 5,730 ml to l and ml.
6
FChange 19,242 g to kg and g.
7
FChange 11 kg to g.
8
FChange 12,128 g to kg and g.
9
FChange 19 l to ml.
10
FChange 18 l to ml.
11
FChange 6,395 ml to l and ml.
12
FChange 5 kg to g.
13
FChange 12 kg to g.
14
FChange 3,611 g to kg and g.
15
FChange 16,512 g to kg and g.
16
FChange 15 kg to g.
8.3

Adding and subtracting measures

Level 5
Add and subtract lengths, masses and capacities in the same or mixed units
Video lesson: Adding and subtracting measuresComing soon

To add or subtract mixed units, change both measures to the smaller unit first. Then calculate, and change the answer back.

For example, 2 m 35 cm + 1 m 80 cm = 235 cm + 180 cm = 415 cm = 4 m 15 cm.

Key ideas

  • Change both measures to the same unit first.
  • Add or subtract the smaller unit.
  • Change the answer back into mixed units.
Worked example 8.3.1
Work out 2 m 35 cm + 1 m 80 cm.

Method. Change both measures to the same unit, cm, then add, then change back.

  1. Change both to cm. 1 m = 100 cm.
    2 m 35 cm = 235 cm, and 1 m 80 cm = 180 cm
  2. Add the cm. Work with the same unit.
    235 + 180 = 415 cm
  3. Change back to m and cm. Share the cm into groups of 100.
    415 = 4 m and 15 cm
  4. Write the answer. Give the answer in mixed units, as the question was.
    4 m 15 cm

Check. Check: 4 m 15 cm - 1 m 80 cm gives 2 m 35 cm again.

Watch out. Keep the unit with each number. A total of 100 cm is 1 m.

Worked example 8.3.2
Work out 3 kg 250 g - 1 kg 600 g.

Method. Change both measures to the same unit, g, then subtract, then change back.

  1. Change both to g. 1 kg = 1,000 g.
    3 kg 250 g = 3,250 g, and 1 kg 600 g = 1,600 g
  2. Subtract the g. Work with the same unit.
    3,250 - 1,600 = 1,650 g
  3. Change back to kg and g. Share the g into groups of 1,000.
    1,650 = 1 kg and 650 g
  4. Write the answer. Give the answer in mixed units, as the question was.
    1 kg 650 g

Check. Check: 1 kg 650 g + 3 kg 250 g gives 1 kg 600 g again.

Watch out. Keep the unit with each number. A total of 1,000 g is 1 kg.

Worked example 8.3.3
Work out 1 l 500 ml + 750 ml.

Method. Change both measures to the same unit, ml, then add, then change back.

  1. Change both to ml. 1 l = 1,000 ml.
    1 l 500 ml = 1,500 ml, and 750 ml = 750 ml
  2. Add the ml. Work with the same unit.
    1,500 + 750 = 2,250 ml
  3. Change back to l and ml. Share the ml into groups of 1,000.
    2,250 = 2 l and 250 ml
  4. Write the answer. Give the answer in mixed units, as the question was.
    2 l 250 ml

Check. Check: 2 l 250 ml - 750 ml gives 1 l 500 ml again.

Watch out. Keep the unit with each number. A total of 1,000 ml is 1 l.

Watch out

Watch out. Do not add the metres and the centimetres separately as if they were the same unit. Change to one unit first.

Exam tip

Grown-up tip. Ask: “How many centimetres is that altogether? Now how many metres and centimetres?”

Exercise 8C  Practice: adding and subtracting measures

Non-calculator
1
PSWork out 3 m 20 cm - 2 m 66 cm.
2
PSWork out 2 kg 203 g + 1 kg 830 g.
3
PSWork out 4 kg 766 g + 2 kg 201 g.
4
PSWork out 4 cm 4 mm - 2 cm 6 mm.
5
PSWork out 4 m 37 cm - 2 m 18 cm.
6
PSWork out 2 kg 412 g + 298 g.
7
PSWork out 3 cm 8 mm + 1 cm 5 mm.
8
PSWork out 2 m 71 cm - 1 cm.
9
PSWork out 4 cm 2 mm - 2 cm 4 mm.
10
PSWork out 3 kg 93 g - 1 kg 363 g.
11
PSWork out 2 cm 8 mm + 5 mm.
12
PSWork out 3 cm 4 mm - 4 mm.
13
PSWork out 3 l 728 ml + 944 ml.
14
PSWork out 4 kg 245 g - 2 kg 783 g.
15
PSWork out 3 kg 834 g - 1 kg 781 g.
16
PSWork out 2 kg 351 g - 562 g.
8.4

Reading scales and choosing units

Level 5
Read a scale in steps of 2, 5 or 10 units, Choose a sensible metric unit for a measure
Video lesson: Reading scales and choosing unitsComing soon

Look at the labels first. Then count the small marks from the nearest label below the arrow. Each small mark is the step shown.

Choose a unit that gives a sensible number: a door is about 2 m tall, a pencil about 15 cm long.

Key ideas

  • Read the labels, then count the small steps.
  • Each small step is the step the question gives.
  • Choose the unit that fits the size of the thing.
Worked example 8.4.1
The kitchen scale: each small mark is 5 g. The arrow points to a value. What is it?
02550?g

Method. Start at the labelled number, count the small steps, then add.

  1. Find the labelled number below the arrow. Labels show the bigger steps.
    25 g
  2. Count the small steps of 5 from 25. Each small step adds 5.
    1 steps of 5 = 5 g more
  3. Add to find the reading. Add the steps to the labelled number.
    25 + 5 = 30
  4. Write the reading with the unit. Give the unit of the scale.
    30 g

Check. Check: 30 is 6 steps of 5 from zero.

Watch out. Count each small mark. Do not count the labels as steps.

Worked example 8.4.2
The shop scale: each small mark is 2 kg. The arrow points to a value. What is it?
01020?kg

Method. Start at the labelled number, count the small steps, then add.

  1. Find the labelled number below the arrow. Labels show the bigger steps.
    0 kg
  2. Count the small steps of 2 from 0. Each small step adds 2.
    2 steps of 2 = 4 kg more
  3. Add to find the reading. Add the steps to the labelled number.
    0 + 4 = 4
  4. Write the reading with the unit. Give the unit of the scale.
    4 kg

Check. Check: 4 is 2 steps of 2 from zero.

Watch out. Count each small mark. Do not count the labels as steps.

Worked example 8.4.3
The juice bottle: each small mark is 10 ml. The arrow points to a value. What is it?
050100?ml

Method. Start at the labelled number, count the small steps, then add.

  1. Find the labelled number below the arrow. Labels show the bigger steps.
    0 ml
  2. Count the small steps of 10 from 0. Each small step adds 10.
    3 steps of 10 = 30 ml more
  3. Add to find the reading. Add the steps to the labelled number.
    0 + 30 = 30
  4. Write the reading with the unit. Give the unit of the scale.
    30 ml

Check. Check: 30 is 3 steps of 10 from zero.

Watch out. Count each small mark. Do not count the labels as steps.

Watch out

Watch out. Count the small marks, not the labels. Check the step size the question gives you.

Exam tip

Grown-up tip. Use a real ruler or measuring jug. Ask: “How many small steps from the label to the mark?”

Exercise 8D  Practice: reading scales and choosing units

Non-calculator
1
RWhich unit would you use to measure the distance between two towns?
2
RWhich unit would you use to measure the water in a glass?
3
FThe sugar scale: each small mark is 5 g. The arrow points to a value. What is it?
02550?g
4
FThe juice bottle: each small mark is 10 ml. The arrow points to a value. What is it?
050100?ml
5
FThe juice bottle: each small mark is 10 ml. The arrow points to a value. What is it?
050100?ml
6
FThe measuring jug: each small mark is 10 ml. The arrow points to a value. What is it?
050100?ml
7
FThe parcel scale: each small mark is 2 kg. The arrow points to a value. What is it?
01020?kg
8
RWhich unit would you use to measure the mass of a bag of flour?
9
FThe sugar scale: each small mark is 5 g. The arrow points to a value. What is it?
02550?g
10
FThe measuring jug: each small mark is 10 ml. The arrow points to a value. What is it?
050100?ml
11
FThe juice bottle: each small mark is 10 ml. The arrow points to a value. What is it?
050100?ml
12
FThe parcel scale: each small mark is 2 kg. The arrow points to a value. What is it?
01020?kg
13
FThe shop scale: each small mark is 2 kg. The arrow points to a value. What is it?
01020?kg
14
FThe shop scale: each small mark is 2 kg. The arrow points to a value. What is it?
01020?kg
15
FThe sugar scale: each small mark is 5 g. The arrow points to a value. What is it?
02550?g
16
RWhich unit would you use to measure the length of a pencil?
8.5

Problems with totals of length, mass and capacity

Level 5
Solve a problem with a total length, mass or capacity
Video lesson: Problems with totals of length, mass and capacityComing soon

For a total, multiply the measure by the number of items. Work in the smaller unit, then change the total back into mixed units.

Check that the answer makes sense for the story.

Key ideas

  • Multiply the measure by the number of items.
  • Work in the smaller unit to avoid mistakes.
  • Give the answer in mixed units if the question asks.
Worked example 8.5.1
A bag of rice weighs 1 kg 250 g. Sam buys 3 bags. What is the total mass?

Method. Multiply the measure by the number of items, then change to mixed units.

  1. Work out the total in the smallest unit. Each one is 1,250 g.
    1,250 g × 3 = 3,750 g
  2. Change back to kg and g. Share the g into groups of 1,000.
    3,750 g = 3 kg 750 g
  3. Write the answer. Give the total in mixed units.
    3 kg 750 g

Check. Check: 3,750 ÷ 3 = 1,250.

Watch out. Multiply in the small unit, then change back at the end.

Worked example 8.5.2
A ribbon is 2 m 15 cm long. Sam buys 3 ribbons of this length. What is the total length?

Method. Multiply the measure by the number of items, then change to mixed units.

  1. Work out the total in the smallest unit. Each one is 215 cm.
    215 cm × 3 = 645 cm
  2. Change back to m and cm. Share the cm into groups of 100.
    645 cm = 6 m 45 cm
  3. Write the answer. Give the total in mixed units.
    6 m 45 cm

Check. Check: 645 ÷ 3 = 215.

Watch out. Multiply in the small unit, then change back at the end.

Worked example 8.5.3
A jug holds 1 l 500 ml. Sam fills 2 jugs. How much do the 2 jugs hold altogether?

Method. Multiply the measure by the number of items, then change to mixed units.

  1. Work out the total in the smallest unit. Each one is 1,500 ml.
    1,500 ml × 2 = 3,000 ml
  2. Change back to l and ml. Share the ml into groups of 1,000.
    3,000 ml = 3 l
  3. Write the answer. Give the total in mixed units.
    3 l

Check. Check: 3,000 ÷ 2 = 1,500.

Watch out. Multiply in the small unit, then change back at the end.

Watch out

Watch out. Read the question: does it ask for the total of one item or for several? Check the number of items.

Exam tip

Grown-up tip. Ask the child to say the total in the smallest unit first, then in mixed units.

Exercise 8E  Practice: problems with totals

Non-calculator
1
PSA jug holds 3 l 763 ml. Sam fills 2 jugs. How much do the 2 jugs hold altogether?
2
PSA jug holds 3 l 720 ml. Sam fills 2 jugs. How much do the 2 jugs hold altogether?
3
PSA jug holds 2 l 297 ml. Sam fills 2 jugs. How much do the 2 jugs hold altogether?
4
PSA jug holds 2 l 428 ml. Sam fills 2 jugs. How much do the 2 jugs hold altogether?
5
PSA ribbon is 1 m 97 cm long. Sam buys 3 ribbons of this length. What is the total length?
6
PSA ribbon is 1 m 85 cm long. Sam buys 3 ribbons of this length. What is the total length?
7
PSA ribbon is 1 m 91 cm long. Sam buys 3 ribbons of this length. What is the total length?
8
PSA ribbon is 1 m 68 cm long. Sam buys 3 ribbons of this length. What is the total length?
9
PSA ribbon is 1 m long. Sam buys 3 ribbons of this length. What is the total length?
10
PSA jug holds 1 l 594 ml. Sam fills 2 jugs. How much do the 2 jugs hold altogether?
11
PSA bag of rice weighs 2 kg 284 g. Sam buys 3 bags. What is the total mass?
12
PSA bag of rice weighs 1 kg 152 g. Sam buys 3 bags. What is the total mass?
13
PSA bag of rice weighs 1 kg 783 g. Sam buys 3 bags. What is the total mass?
14
PSA ribbon is 1 m 74 cm long. Sam buys 3 ribbons of this length. What is the total length?
15
PSA bag of rice weighs 3 kg 729 g. Sam buys 3 bags. What is the total mass?
16
PSA jug holds 2 l 845 ml. Sam fills 2 jugs. How much do the 2 jugs hold altogether?

Chapter summary

SkillMethod
Length1 km = 1,000 m; 1 m = 100 cm; 1 cm = 10 mm
Mass and capacity1 kg = 1,000 g; 1 litre = 1,000 ml
Adding and subtractingChange to the same unit first; calculate; change back
ScalesCount the small steps from the label below; each step is the given interval
TotalsMultiply the measure by the number of items; change to mixed units

Can you…?

  • I can convert between km and m, m and cm, and cm and mm
  • I can convert between kg and g, and between litres and ml
  • I can add and subtract measures in mixed units
  • I can read a scale in steps of 2, 5 or 10 units
  • I can choose a sensible unit for a measure
  • I can solve problems with totals of length, mass and capacity

Key terms

metric
the units based on tens, such as metres, grams and litres
convert
change a measure into another unit
scale
the marks and numbers on a measuring tool
interval
the size of the step between marks on a scale

Exercise 8Z  Check-up

Non-calculator
1
Change 5,890 ml to l and ml.
2
Change 134 mm to cm and mm.
3
Work out 1 cm 3 mm + 2 mm.
4
A bag of rice weighs 2 kg 658 g. Sam buys 3 bags. What is the total mass?
5
Work out 3 kg 235 g - 2 kg 718 g.
6
A jug holds 1 l 458 ml. Sam fills 2 jugs. How much do the 2 jugs hold altogether?
7
Change 15,524 g to kg and g.
8
Change 3,329 g to kg and g.
9
Work out 1 m 9 cm + 22 cm.
10
Work out 3 l 770 ml - 2 l 147 ml.

Total 19 marks. Allow about 19 minutes.

Exercise 8X  Practice test questions

Non-calculator
1
FChange 2 l to ml.[1 mark]
2
FChange 508 cm to m and cm.[1 mark]
3
FChange 6 km to metres.[1 mark]
4
FThe shop scale: each small mark is 2 kg. The arrow points to a value. What is it?[1 mark]
01020?kg
5
RWhich unit would you use to measure the distance between two towns?[2 marks]
6
PSWork out 4 m 33 cm - 1 m 82 cm.[2 marks]
7
PSA bag of rice weighs 3 kg 330 g. Sam buys 3 bags. What is the total mass?[2 marks]
8
PSA bag of rice weighs 1 kg 436 g. Sam buys 3 bags. What is the total mass?[3 marks]
9
FChange 63 mm to cm and mm.[3 marks]
10
PSWork out 4 l 913 ml + 871 ml.[3 marks]
← Chapter 7: Decimals to tenths and hundredthsChapter 9: Perimeter of rectilinear shapes, time and money problems →

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