Length and mass
By the end of this chapter you will be able to
- Choose metres, centimetres, kilograms or grams
- Measure a length with a ruler to the nearest centimetre
- Read a scale to the nearest mark
- Know 100 cm = 1 m and 1000 g = 1 kg
- Compare, order, add and subtract lengths and masses
You should already know
- Counting in tens and hundreds (chapter 1)
- Adding and subtracting within 1000 (chapters 4 and 5)
Where this leads
- Level 3 check (chapter 10)
Step-by-step practice: maths (Level 3). Small steps, repeated until fluent. Content: Choose and use metres or centimetres to estimate and measure a length (M1), Choose and use kilograms or grams to estimate and weigh a mass (M2), Measure to the nearest appropriate unit with a ruler or a scale (M5), Compare and order lengths and masses, using <, > and = (M6), Add and subtract lengths and masses in m and cm, and kg and g.
Exercise P Do you remember?
Non-calculatorMethod. Use the ruler: find the start and the end of the line, then the difference.
- Put the 0 at the start of the line. Line up the ruler so the line begins at 0.0 cm
- Read where the line ends. The end of the line is on this number.The end is at 6
- Write the length. The length is the end number, because we started at 0.6 cm
Check. Count the centimetres from 0 to 6: 6 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Use the ruler: find the start and the end of the line, then the difference.
- Put the 0 at the start of the line. Line up the ruler so the line begins at 0.0 cm
- Read where the line ends. The end of the line is on this number.The end is at 9
- Write the length. The length is the end number, because we started at 0.9 cm
Check. Count the centimetres from 0 to 9: 9 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Change to cm, work it out, then change back.
- Change both to the smaller unit. 100 cm make one bigger unit.45 cm = 45 cm, 30 cm = 30 cm
- Add the cm. Work with the numbers in cm.45 + 30 = 75
- Change back to the bigger units. 75 cm is written with 100 cm as one bigger unit.75 cm = 75 cm
- Write the answer. This is the answer.75 cm
Check. Check: 75 cm - 30 cm = 45 cm.
Watch out. Work in cm to avoid mistakes. Change back at the end.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Remember the rule. 1 m is 100 cm.1 m = 100 cm
- Multiply the metres by 100. There are 2 metres, so 2 lots of 100.2 × 100 = 200
- Write the answer in centimetres. This is the length in centimetres.200 cm
Check. Divide 200 cm by 100 to get 2 m.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Find the operation, then work out what is left.
- Find the operation. Words like cut off and used mean take away.500 - 120
- Work out what is left. Change to the smaller unit, then take away.500 - 120 = 380
- Write the answer. Change back to the bigger units.380 g
Check. Check: 380 g plus 120 g is 500 g.
Watch out. Use the same unit for both amounts before you take away.
Choosing metres, centimetres, kilograms and grams
Length is how long something is. Use metres (m) for big things, and centimetres (cm) for small things.
Mass is how heavy something is. Use kilograms (kg) for heavy things, and grams (g) for light things.
Key ideas
- m and cm measure length.
- kg and g measure mass.
- Small things use cm and g. Big or heavy things use m and kg.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A pencil is about the size of a thing we can check easily.a pencil
- Choose the unit that fits. Big things are measured in metres. Small things are measured in centimetres.cm
- Write the answer. This is the unit to use.cm
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A bag of sugar is about the size of a thing we can check easily.a bag of sugar
- Choose the unit that fits. Heavy things are weighed in kilograms. Light things are weighed in grams.kg
- Write the answer. This is the unit to use.kg
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A door is about the size of a thing we can check easily.a door
- Choose the unit that fits. Big things are measured in metres. Small things are measured in centimetres.m
- Write the answer. This is the unit to use.m
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Watch out
Watch out. A door is measured in metres, not centimetres. A paper clip is weighed in grams, not kilograms.
Exam tip
Grown-up tip. Ask: “Would you carry it, or would you need a trolley?” to help choose kg or g.
Exercise 9A Practice: choosing units
Non-calculatorMethod. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A bedroom wall is about the size of a thing we can check easily.a bedroom wall
- Choose the unit that fits. Big things are measured in metres. Small things are measured in centimetres.m
- Write the answer. This is the unit to use.m
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A garden fence is about the size of a thing we can check easily.a garden fence
- Choose the unit that fits. Big things are measured in metres. Small things are measured in centimetres.m
- Write the answer. This is the unit to use.m
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A bus is about the size of a thing we can check easily.a bus
- Choose the unit that fits. Big things are measured in metres. Small things are measured in centimetres.m
- Write the answer. This is the unit to use.m
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A football pitch is about the size of a thing we can check easily.a football pitch
- Choose the unit that fits. Big things are measured in metres. Small things are measured in centimetres.m
- Write the answer. This is the unit to use.m
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A rubber is about the size of a thing we can check easily.a rubber
- Choose the unit that fits. Big things are measured in metres. Small things are measured in centimetres.cm
- Write the answer. This is the unit to use.cm
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A paper clip is about the size of a thing we can check easily.a paper clip
- Choose the unit that fits. Heavy things are weighed in kilograms. Light things are weighed in grams.g
- Write the answer. This is the unit to use.g
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A strawberry is about the size of a thing we can check easily.a strawberry
- Choose the unit that fits. Heavy things are weighed in kilograms. Light things are weighed in grams.g
- Write the answer. This is the unit to use.g
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A bicycle is about the size of a thing we can check easily.a bicycle
- Choose the unit that fits. Heavy things are weighed in kilograms. Light things are weighed in grams.kg
- Write the answer. This is the unit to use.kg
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A book is about the size of a thing we can check easily.a book
- Choose the unit that fits. Big things are measured in metres. Small things are measured in centimetres.cm
- Write the answer. This is the unit to use.cm
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A bag of apples is about the size of a thing we can check easily.a bag of apples
- Choose the unit that fits. Heavy things are weighed in kilograms. Light things are weighed in grams.kg
- Write the answer. This is the unit to use.kg
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A sheet of paper is about the size of a thing we can check easily.a sheet of paper
- Choose the unit that fits. Heavy things are weighed in kilograms. Light things are weighed in grams.g
- Write the answer. This is the unit to use.g
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A pencil is about the size of a thing we can check easily.a pencil
- Choose the unit that fits. Big things are measured in metres. Small things are measured in centimetres.cm
- Write the answer. This is the unit to use.cm
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A bag of potatoes is about the size of a thing we can check easily.a bag of potatoes
- Choose the unit that fits. Heavy things are weighed in kilograms. Light things are weighed in grams.kg
- Write the answer. This is the unit to use.kg
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A door is about the size of a thing we can check easily.a door
- Choose the unit that fits. Big things are measured in metres. Small things are measured in centimetres.m
- Write the answer. This is the unit to use.m
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A bag of sugar is about the size of a thing we can check easily.a bag of sugar
- Choose the unit that fits. Heavy things are weighed in kilograms. Light things are weighed in grams.kg
- Write the answer. This is the unit to use.kg
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A teaspoon of sugar is about the size of a thing we can check easily.a teaspoon of sugar
- Choose the unit that fits. Heavy things are weighed in kilograms. Light things are weighed in grams.g
- Write the answer. This is the unit to use.g
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Measuring with a ruler and reading a scale
To measure with a ruler, put the 0 at the start of the line. Read the number where the line ends.
On a scale, find the label before the pointer, then count the small marks.
Key ideas
- Line up the 0 with the start.
- Read the end of the line.
- On a scale, count the small marks from the label.
Method. Use the ruler: find the start and the end of the line, then the difference.
- Put the 0 at the start of the line. Line up the ruler so the line begins at 0.0 cm
- Read where the line ends. The end of the line is on this number.The end is at 7
- Write the length. The length is the end number, because we started at 0.7 cm
Check. Count the centimetres from 0 to 7: 7 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Use the ruler: find the start and the end of the line, then the difference.
- Find where the line starts. The line starts at this mark.start = 2 cm
- Find where the line ends. The line ends at this mark.end = 7 cm
- Subtract the start from the end. The length is the distance between the two marks.7 - 2 = 5
- Write the length. This is how long the line is.5 cm
Check. Add the length to the start: 2 + 5 = 7 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Find the label before the pointer, then count the small marks.
- Find the labels on the scale. The labels show every 100 g.0 g, 100 g, 200 g
- Count the marks from the label before. Each small mark is 50 g.the pointer is 350 g
- Write the reading. This is what the scale shows.350 g
Check. 350 g is between two labels, halfway or on a label.
Watch out. Each small mark is 50 g. Count them carefully.
Watch out
Watch out. Do not start measuring at 1. Start at the 0 mark, or subtract the start from the end.
Exam tip
Grown-up tip. Use a real ruler and a book. Ask the child to measure things at home, and to say the length in cm.
Exercise 9B Practice: measuring and reading
Non-calculatorMethod. Use the ruler: find the start and the end of the line, then the difference.
- Find where the line starts. The line starts at this mark.start = 5 cm
- Find where the line ends. The line ends at this mark.end = 11 cm
- Subtract the start from the end. The length is the distance between the two marks.11 - 5 = 6
- Write the length. This is how long the line is.6 cm
Check. Add the length to the start: 5 + 6 = 11 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Use the ruler: find the start and the end of the line, then the difference.
- Put the 0 at the start of the line. Line up the ruler so the line begins at 0.0 cm
- Read where the line ends. The end of the line is on this number.The end is at 12
- Write the length. The length is the end number, because we started at 0.12 cm
Check. Count the centimetres from 0 to 12: 12 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Use the ruler: find the start and the end of the line, then the difference.
- Find where the line starts. The line starts at this mark.start = 3 cm
- Find where the line ends. The line ends at this mark.end = 8 cm
- Subtract the start from the end. The length is the distance between the two marks.8 - 3 = 5
- Write the length. This is how long the line is.5 cm
Check. Add the length to the start: 3 + 5 = 8 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Use the ruler: find the start and the end of the line, then the difference.
- Find where the line starts. The line starts at this mark.start = 6 cm
- Find where the line ends. The line ends at this mark.end = 9 cm
- Subtract the start from the end. The length is the distance between the two marks.9 - 6 = 3
- Write the length. This is how long the line is.3 cm
Check. Add the length to the start: 6 + 3 = 9 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Use the ruler: find the start and the end of the line, then the difference.
- Find where the line starts. The line starts at this mark.start = 1 cm
- Find where the line ends. The line ends at this mark.end = 4 cm
- Subtract the start from the end. The length is the distance between the two marks.4 - 1 = 3
- Write the length. This is how long the line is.3 cm
Check. Add the length to the start: 1 + 3 = 4 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Use the ruler: find the start and the end of the line, then the difference.
- Find where the line starts. The line starts at this mark.start = 1 cm
- Find where the line ends. The line ends at this mark.end = 5 cm
- Subtract the start from the end. The length is the distance between the two marks.5 - 1 = 4
- Write the length. This is how long the line is.4 cm
Check. Add the length to the start: 1 + 4 = 5 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Use the ruler: find the start and the end of the line, then the difference.
- Put the 0 at the start of the line. Line up the ruler so the line begins at 0.0 cm
- Read where the line ends. The end of the line is on this number.The end is at 4
- Write the length. The length is the end number, because we started at 0.4 cm
Check. Count the centimetres from 0 to 4: 4 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Use the ruler: find the start and the end of the line, then the difference.
- Put the 0 at the start of the line. Line up the ruler so the line begins at 0.0 cm
- Read where the line ends. The end of the line is on this number.The end is at 5
- Write the length. The length is the end number, because we started at 0.5 cm
Check. Count the centimetres from 0 to 5: 5 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Find the label before the pointer, then count the small marks.
- Find the labels on the scale. The labels show every 100 g.0 g, 100 g, 200 g
- Count the marks from the label before. Each small mark is 50 g.the pointer is 100 g
- Write the reading. This is what the scale shows.100 g
Check. 100 g is between two labels, halfway or on a label.
Watch out. Each small mark is 50 g. Count them carefully.
Method. Find the label before the pointer, then count the small marks.
- Find the labels on the scale. The labels show every 100 g.0 g, 100 g, 200 g
- Count the marks from the label before. Each small mark is 50 g.the pointer is 400 g
- Write the reading. This is what the scale shows.400 g
Check. 400 g is between two labels, halfway or on a label.
Watch out. Each small mark is 50 g. Count them carefully.
Method. Find the label before the pointer, then count the small marks.
- Find the labels on the scale. The labels show every 100 g.0 g, 100 g, 200 g
- Count the marks from the label before. Each small mark is 50 g.the pointer is 250 g
- Write the reading. This is what the scale shows.250 g
Check. 250 g is between two labels, halfway or on a label.
Watch out. Each small mark is 50 g. Count them carefully.
Method. Find the label before the pointer, then count the small marks.
- Find the labels on the scale. The labels show every 100 g.0 g, 100 g, 200 g
- Count the marks from the label before. Each small mark is 50 g.the pointer is 450 g
- Write the reading. This is what the scale shows.450 g
Check. 450 g is between two labels, halfway or on a label.
Watch out. Each small mark is 50 g. Count them carefully.
Method. Find the label before the pointer, then count the small marks.
- Find the labels on the scale. The labels show every 100 g.0 g, 100 g, 200 g
- Count the marks from the label before. Each small mark is 50 g.the pointer is 850 g
- Write the reading. This is what the scale shows.850 g
Check. 850 g is between two labels, halfway or on a label.
Watch out. Each small mark is 50 g. Count them carefully.
Method. Find the label before the pointer, then count the small marks.
- Find the labels on the scale. The labels show every 100 g.0 g, 100 g, 200 g
- Count the marks from the label before. Each small mark is 50 g.the pointer is 750 g
- Write the reading. This is what the scale shows.750 g
Check. 750 g is between two labels, halfway or on a label.
Watch out. Each small mark is 50 g. Count them carefully.
Method. Find the label before the pointer, then count the small marks.
- Find the labels on the scale. The labels show every 100 g.0 g, 100 g, 200 g
- Count the marks from the label before. Each small mark is 50 g.the pointer is 500 g
- Write the reading. This is what the scale shows.500 g
Check. 500 g is between two labels, halfway or on a label.
Watch out. Each small mark is 50 g. Count them carefully.
Method. Find the label before the pointer, then count the small marks.
- Find the labels on the scale. The labels show every 100 g.0 g, 100 g, 200 g
- Count the marks from the label before. Each small mark is 50 g.the pointer is 700 g
- Write the reading. This is what the scale shows.700 g
Check. 700 g is between two labels, halfway or on a label.
Watch out. Each small mark is 50 g. Count them carefully.
Changing units, and comparing lengths and masses
100 cm is the same as 1 m. 1000 g is the same as 1 kg.
To compare two measures, change them to the same unit first. Then compare the numbers.
Key ideas
- 100 cm = 1 m.
- 1000 g = 1 kg.
- Change to the same unit before comparing.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Remember the rule. 1 m is 100 cm.1 m = 100 cm
- Multiply the metres by 100. There are 3 metres, so 3 lots of 100.3 × 100 = 300
- Write the answer in centimetres. This is the length in centimetres.300 cm
Check. Divide 300 cm by 100 to get 3 m.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Find the number of whole kilograms. 1000 g make 1 kg.4250 ÷ 1000 = 4 rem 250
- Write the grams that are left. The rest are grams.4 kg and 250 g
- Write the answer. Use kilograms and grams.4 kg 250 g
Check. Add back: 4 kg + 250 g = 4250 g.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 100 cm = 1 m, so change both to the smaller unit.2 m = 200 cm, 2 m 50 cm = 250 cm
- Compare the numbers. Compare the bigger numbers.200 cm and 250 cm
- Write the sign. 2 m is less than 2 m 50 cm.<
Check. 2 m < 2 m 50 cm is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Watch out
Watch out. 2 m is more than 150 cm. Do not compare 2 with 150 directly, because the units are different.
Exam tip
Grown-up tip. Use a metre stick or a 1 kg bag of flour to see the size of the units, and ask which is more.
Exercise 9C Practice: changing units and comparing
Non-calculatorMethod. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Remember the rule. 1 m is 100 cm.1 m = 100 cm
- Multiply the metres by 100. There are 2 metres, so 2 lots of 100.2 × 100 = 200
- Write the answer in centimetres. This is the length in centimetres.200 cm
Check. Divide 200 cm by 100 to get 2 m.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Find the number of whole kilograms. 1000 g make 1 kg.2250 ÷ 1000 = 2 rem 250
- Write the grams that are left. The rest are grams.2 kg and 250 g
- Write the answer. Use kilograms and grams.2 kg 250 g
Check. Add back: 2 kg + 250 g = 2250 g.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Remember the rule. 1 kg is 1000 g.1 kg = 1000 g
- Multiply the kilograms by 1000. There are 2 kilograms, so 2 lots of 1000.2 × 1000 = 2000
- Write the answer in grams. This is the mass in grams.2000 g
Check. Divide 2000 g by 1000 to get 2 kg.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Remember the rule. 1 kg is 1000 g.1 kg = 1000 g
- Multiply the kilograms by 1000. There are 3 kilograms, so 3 lots of 1000.3 × 1000 = 3000
- Write the answer in grams. This is the mass in grams.3000 g
Check. Divide 3000 g by 1000 to get 3 kg.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Find the number of whole kilograms. 1000 g make 1 kg.3250 ÷ 1000 = 3 rem 250
- Write the grams that are left. The rest are grams.3 kg and 250 g
- Write the answer. Use kilograms and grams.3 kg 250 g
Check. Add back: 3 kg + 250 g = 3250 g.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Find the number of whole kilograms. 1000 g make 1 kg.8250 ÷ 1000 = 8 rem 250
- Write the grams that are left. The rest are grams.8 kg and 250 g
- Write the answer. Use kilograms and grams.8 kg 250 g
Check. Add back: 8 kg + 250 g = 8250 g.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Find the number of whole kilograms. 1000 g make 1 kg.1250 ÷ 1000 = 1 rem 250
- Write the grams that are left. The rest are grams.1 kg and 250 g
- Write the answer. Use kilograms and grams.1 kg 250 g
Check. Add back: 1 kg + 250 g = 1250 g.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Remember the rule. 1 kg is 1000 g.1 kg = 1000 g
- Multiply the kilograms by 1000. There are 6 kilograms, so 6 lots of 1000.6 × 1000 = 6000
- Write the answer in grams. This is the mass in grams.6000 g
Check. Divide 6000 g by 1000 to get 6 kg.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 100 cm = 1 m, so change both to the smaller unit.3 m 26 cm = 326 cm, 19 cm = 19 cm
- Compare the numbers. Compare the bigger numbers.326 cm and 19 cm
- Write the sign. 3 m 26 cm is more than 19 cm.>
Check. 3 m 26 cm > 19 cm is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 100 cm = 1 m, so change both to the smaller unit.1 m = 100 cm, 3 m 50 cm = 350 cm
- Compare the numbers. Compare the bigger numbers.100 cm and 350 cm
- Write the sign. 1 m is less than 3 m 50 cm.<
Check. 1 m < 3 m 50 cm is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 1000 g = 1 kg, so change both to the smaller unit.2 kg 250 g = 2250 g, 3 kg = 3000 g
- Compare the numbers. Compare the bigger numbers.2250 g and 3000 g
- Write the sign. 2 kg 250 g is less than 3 kg.<
Check. 2 kg 250 g < 3 kg is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 100 cm = 1 m, so change both to the smaller unit.4 m 51 cm = 451 cm, 2 m = 200 cm
- Compare the numbers. Compare the bigger numbers.451 cm and 200 cm
- Write the sign. 4 m 51 cm is more than 2 m.>
Check. 4 m 51 cm > 2 m is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 100 cm = 1 m, so change both to the smaller unit.4 m 19 cm = 419 cm, 2 m 9 cm = 209 cm
- Compare the numbers. Compare the bigger numbers.419 cm and 209 cm
- Write the sign. 4 m 19 cm is more than 2 m 9 cm.>
Check. 4 m 19 cm > 2 m 9 cm is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 100 cm = 1 m, so change both to the smaller unit.2 m 17 cm = 217 cm, 2 m 23 cm = 223 cm
- Compare the numbers. Compare the bigger numbers.217 cm and 223 cm
- Write the sign. 2 m 17 cm is less than 2 m 23 cm.<
Check. 2 m 17 cm < 2 m 23 cm is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 1000 g = 1 kg, so change both to the smaller unit.2 kg 500 g = 2500 g, 100 g = 100 g
- Compare the numbers. Compare the bigger numbers.2500 g and 100 g
- Write the sign. 2 kg 500 g is more than 100 g.>
Check. 2 kg 500 g > 100 g is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 1000 g = 1 kg, so change both to the smaller unit.4 kg = 4000 g, 1 kg 500 g = 1500 g
- Compare the numbers. Compare the bigger numbers.4000 g and 1500 g
- Write the sign. 4 kg is more than 1 kg 500 g.>
Check. 4 kg > 1 kg 500 g is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Ordering lengths and masses
To put lengths or masses in order, change them all to the same unit first.
Then put the numbers in order, and write the measurements the way they were given.
Key ideas
- Change to the same unit.
- Order the numbers.
- Write the measurements in order.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.2 m = 200 cm, 1 m 50 cm = 150 cm, 90 cm = 90 cm
- Put the numbers in order. Compare the numbers, then write the measurements in that order.90, 150, 200
- Write the order. Write the original measurements in order.90 cm, 1 m 50 cm, 2 m
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.500 g = 500 g, 1 kg = 1000 g, 750 g = 750 g
- Put the numbers in order. Compare the numbers, then write the measurements in that order.500, 750, 1000
- Write the order. Write the original measurements in order.500 g, 750 g, 1 kg
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.3 m = 300 cm, 2 m 80 cm = 280 cm, 2 m 50 cm = 250 cm
- Put the numbers in order. Compare the numbers, then write the measurements in that order.300, 280, 250
- Write the order. Write the original measurements in order.3 m, 2 m 80 cm, 2 m 50 cm
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Watch out
Watch out. 1 kg is less than 1 kg 500 g. Do not look only at the first number.
Exam tip
Grown-up tip. Write each measure on a card and move the cards into order. Ask: “Which one is first, and why?”
Exercise 9D Practice: ordering lengths and masses
Non-calculatorMethod. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.2 m 75 cm = 275 cm, 2 m 50 cm = 250 cm, 3 m 50 cm = 350 cm
- Put the numbers in order. Compare the numbers, then write the measurements in that order.350, 275, 250
- Write the order. Write the original measurements in order.3 m 50 cm, 2 m 75 cm, 2 m 50 cm
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.3 m 20 cm = 320 cm, 50 cm = 50 cm, 1 m 75 cm = 175 cm
- Put the numbers in order. Compare the numbers, then write the measurements in that order.320, 175, 50
- Write the order. Write the original measurements in order.3 m 20 cm, 1 m 75 cm, 50 cm
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.3 kg 250 g = 3250 g, 2 kg 500 g = 2500 g, 1 kg 800 g = 1800 g
- Put the numbers in order. Compare the numbers, then write the measurements in that order.3250, 2500, 1800
- Write the order. Write the original measurements in order.3 kg 250 g, 2 kg 500 g, 1 kg 800 g
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.1 kg 500 g = 1500 g, 800 g = 800 g, 1 kg = 1000 g
- Put the numbers in order. Compare the numbers, then write the measurements in that order.800, 1000, 1500
- Write the order. Write the original measurements in order.800 g, 1 kg, 1 kg 500 g
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.1 m = 100 cm, 2 m 50 cm = 250 cm, 50 cm = 50 cm
- Put the numbers in order. Compare the numbers, then write the measurements in that order.250, 100, 50
- Write the order. Write the original measurements in order.2 m 50 cm, 1 m, 50 cm
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.1 kg 800 g = 1800 g, 800 g = 800 g, 2 kg 500 g = 2500 g
- Put the numbers in order. Compare the numbers, then write the measurements in that order.800, 1800, 2500
- Write the order. Write the original measurements in order.800 g, 1 kg 800 g, 2 kg 500 g
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.3 m 20 cm = 320 cm, 3 m = 300 cm, 1 m 20 cm = 120 cm
- Put the numbers in order. Compare the numbers, then write the measurements in that order.120, 300, 320
- Write the order. Write the original measurements in order.1 m 20 cm, 3 m, 3 m 20 cm
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.20 cm = 20 cm, 2 m 50 cm = 250 cm, 2 m 75 cm = 275 cm
- Put the numbers in order. Compare the numbers, then write the measurements in that order.20, 250, 275
- Write the order. Write the original measurements in order.20 cm, 2 m 50 cm, 2 m 75 cm
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.75 cm = 75 cm, 2 m = 200 cm, 2 m 50 cm = 250 cm
- Put the numbers in order. Compare the numbers, then write the measurements in that order.250, 200, 75
- Write the order. Write the original measurements in order.2 m 50 cm, 2 m, 75 cm
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.1 m 20 cm = 120 cm, 3 m 75 cm = 375 cm, 20 cm = 20 cm
- Put the numbers in order. Compare the numbers, then write the measurements in that order.20, 120, 375
- Write the order. Write the original measurements in order.20 cm, 1 m 20 cm, 3 m 75 cm
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.1 kg 800 g = 1800 g, 2 kg 500 g = 2500 g, 500 g = 500 g
- Put the numbers in order. Compare the numbers, then write the measurements in that order.2500, 1800, 500
- Write the order. Write the original measurements in order.2 kg 500 g, 1 kg 800 g, 500 g
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.1 kg = 1000 g, 2 kg = 2000 g, 1 kg 500 g = 1500 g
- Put the numbers in order. Compare the numbers, then write the measurements in that order.2000, 1500, 1000
- Write the order. Write the original measurements in order.2 kg, 1 kg 500 g, 1 kg
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.1 m 20 cm = 120 cm, 3 m = 300 cm, 50 cm = 50 cm
- Put the numbers in order. Compare the numbers, then write the measurements in that order.50, 120, 300
- Write the order. Write the original measurements in order.50 cm, 1 m 20 cm, 3 m
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.1 kg = 1000 g, 250 g = 250 g, 2 kg = 2000 g
- Put the numbers in order. Compare the numbers, then write the measurements in that order.250, 1000, 2000
- Write the order. Write the original measurements in order.250 g, 1 kg, 2 kg
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.2 m = 200 cm, 3 m = 300 cm, 3 m 50 cm = 350 cm
- Put the numbers in order. Compare the numbers, then write the measurements in that order.200, 300, 350
- Write the order. Write the original measurements in order.2 m, 3 m, 3 m 50 cm
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.75 cm = 75 cm, 3 m = 300 cm, 1 m = 100 cm
- Put the numbers in order. Compare the numbers, then write the measurements in that order.75, 100, 300
- Write the order. Write the original measurements in order.75 cm, 1 m, 3 m
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Adding and subtracting lengths and masses
To add or subtract, change both measures to the smaller unit. Work it out, then change back.
For example, 1 m 20 cm + 45 cm: 120 cm + 45 cm = 165 cm, which is 1 m 65 cm.
Key ideas
- Change to the smaller unit.
- Add or take away.
- Change back to m and cm, or kg and g.
Method. Change to cm, work it out, then change back.
- Change both to the smaller unit. 100 cm make one bigger unit.1 m 20 cm = 120 cm, 45 cm = 45 cm
- Add the cm. Work with the numbers in cm.120 + 45 = 165
- Change back to the bigger units. 165 cm is written with 100 cm as one bigger unit.165 cm = 1 m 65 cm
- Write the answer. This is the answer.1 m 65 cm
Check. Check: 1 m 65 cm - 45 cm = 1 m 20 cm.
Watch out. Work in cm to avoid mistakes. Change back at the end.
Method. Change to g, work it out, then change back.
- Change both to the smaller unit. 1000 g make one bigger unit.2 kg 300 g = 2300 g, 1 kg 400 g = 1400 g
- Add the g. Work with the numbers in g.2300 + 1400 = 3700
- Change back to the bigger units. 3700 g is written with 1000 g as one bigger unit.3700 g = 3 kg 700 g
- Write the answer. This is the answer.3 kg 700 g
Check. Check: 3 kg 700 g - 1 kg 400 g = 2 kg 300 g.
Watch out. Work in g to avoid mistakes. Change back at the end.
Method. Find the operation, then work out what is left.
- Find the operation. Words like cut off and used mean take away.250 - 45
- Work out what is left. Change to the smaller unit, then take away.250 - 45 = 205
- Write the answer. Change back to the bigger units.2 m 5 cm
Check. Check: 2 m 5 cm plus 45 cm is 2 m 50 cm.
Watch out. Use the same unit for both amounts before you take away.
Watch out
Watch out. 100 cm is 1 m, so 165 cm is 1 m 65 cm, not 165 m.
Exam tip
Grown-up tip. Ask: “How many centimetres is that altogether?” before writing the answer in metres.
Exercise 9E Practice: adding, subtracting and problems
Non-calculatorMethod. Change to g, work it out, then change back.
- Change both to the smaller unit. 1000 g make one bigger unit.4 kg 250 g = 4250 g, 1 kg 150 g = 1150 g
- Take away the g. Work with the numbers in g.4250 - 1150 = 3100
- Change back to the bigger units. 3100 g is written with 1000 g as one bigger unit.3100 g = 3 kg 100 g
- Write the answer. This is the answer.3 kg 100 g
Check. Check: 3 kg 100 g + 1 kg 150 g = 4 kg 250 g.
Watch out. Work in g to avoid mistakes. Change back at the end.
Method. Change to g, work it out, then change back.
- Change both to the smaller unit. 1000 g make one bigger unit.3 kg 750 g = 3750 g, 2 kg 450 g = 2450 g
- Add the g. Work with the numbers in g.3750 + 2450 = 6200
- Change back to the bigger units. 6200 g is written with 1000 g as one bigger unit.6200 g = 6 kg 200 g
- Write the answer. This is the answer.6 kg 200 g
Check. Check: 6 kg 200 g - 2 kg 450 g = 3 kg 750 g.
Watch out. Work in g to avoid mistakes. Change back at the end.
Method. Change to g, work it out, then change back.
- Change both to the smaller unit. 1000 g make one bigger unit.3 kg 250 g = 3250 g, 450 g = 450 g
- Add the g. Work with the numbers in g.3250 + 450 = 3700
- Change back to the bigger units. 3700 g is written with 1000 g as one bigger unit.3700 g = 3 kg 700 g
- Write the answer. This is the answer.3 kg 700 g
Check. Check: 3 kg 700 g - 450 g = 3 kg 250 g.
Watch out. Work in g to avoid mistakes. Change back at the end.
Method. Change to g, work it out, then change back.
- Change both to the smaller unit. 1000 g make one bigger unit.1 kg 100 g = 1100 g, 2 kg 300 g = 2300 g
- Add the g. Work with the numbers in g.1100 + 2300 = 3400
- Change back to the bigger units. 3400 g is written with 1000 g as one bigger unit.3400 g = 3 kg 400 g
- Write the answer. This is the answer.3 kg 400 g
Check. Check: 3 kg 400 g - 2 kg 300 g = 1 kg 100 g.
Watch out. Work in g to avoid mistakes. Change back at the end.
Method. Change to cm, work it out, then change back.
- Change both to the smaller unit. 100 cm make one bigger unit.3 m 20 cm = 320 cm, 1 m 40 cm = 140 cm
- Take away the cm. Work with the numbers in cm.320 - 140 = 180
- Change back to the bigger units. 180 cm is written with 100 cm as one bigger unit.180 cm = 1 m 80 cm
- Write the answer. This is the answer.1 m 80 cm
Check. Check: 1 m 80 cm + 1 m 40 cm = 3 m 20 cm.
Watch out. Work in cm to avoid mistakes. Change back at the end.
Method. Change to g, work it out, then change back.
- Change both to the smaller unit. 1000 g make one bigger unit.1 kg 600 g = 1600 g, 2 kg 300 g = 2300 g
- Add the g. Work with the numbers in g.1600 + 2300 = 3900
- Change back to the bigger units. 3900 g is written with 1000 g as one bigger unit.3900 g = 3 kg 900 g
- Write the answer. This is the answer.3 kg 900 g
Check. Check: 3 kg 900 g - 2 kg 300 g = 1 kg 600 g.
Watch out. Work in g to avoid mistakes. Change back at the end.
Method. Change to cm, work it out, then change back.
- Change both to the smaller unit. 100 cm make one bigger unit.2 m 30 cm = 230 cm, 1 m 55 cm = 155 cm
- Take away the cm. Work with the numbers in cm.230 - 155 = 75
- Change back to the bigger units. 75 cm is written with 100 cm as one bigger unit.75 cm = 75 cm
- Write the answer. This is the answer.75 cm
Check. Check: 75 cm + 1 m 55 cm = 2 m 30 cm.
Watch out. Work in cm to avoid mistakes. Change back at the end.
Method. Change to cm, work it out, then change back.
- Change both to the smaller unit. 100 cm make one bigger unit.4 m 75 cm = 475 cm, 1 m 25 cm = 125 cm
- Take away the cm. Work with the numbers in cm.475 - 125 = 350
- Change back to the bigger units. 350 cm is written with 100 cm as one bigger unit.350 cm = 3 m 50 cm
- Write the answer. This is the answer.3 m 50 cm
Check. Check: 3 m 50 cm + 1 m 25 cm = 4 m 75 cm.
Watch out. Work in cm to avoid mistakes. Change back at the end.
Method. Find the operation, then work out what is left.
- Find the operation. Words like cut off and used mean take away.3500 - 2000
- Work out what is left. Change to the smaller unit, then take away.3500 - 2000 = 1500
- Write the answer. Change back to the bigger units.1 kg 500 g
Check. Check: 1 kg 500 g plus 2 kg is 3 kg 500 g.
Watch out. Use the same unit for both amounts before you take away.
Method. Find the operation, then work out what is left.
- Find the operation. Words like cut off and used mean take away.400 - 288
- Work out what is left. Change to the smaller unit, then take away.400 - 288 = 112
- Write the answer. Change back to the bigger units.1 m 12 cm
Check. Check: 1 m 12 cm plus 2 m 88 cm is 4 m.
Watch out. Use the same unit for both amounts before you take away.
Method. Find the operation, then work out what is left.
- Find the operation. Words like cut off and used mean take away.280 - 108
- Work out what is left. Change to the smaller unit, then take away.280 - 108 = 172
- Write the answer. Change back to the bigger units.1 m 72 cm
Check. Check: 1 m 72 cm plus 1 m 8 cm is 2 m 80 cm.
Watch out. Use the same unit for both amounts before you take away.
Method. Find the operation, then work out what is left.
- Find the operation. Words like cut off and used mean take away.380 - 325
- Work out what is left. Change to the smaller unit, then take away.380 - 325 = 55
- Write the answer. Change back to the bigger units.55 cm
Check. Check: 55 cm plus 3 m 25 cm is 3 m 80 cm.
Watch out. Use the same unit for both amounts before you take away.
Method. Find the operation, then work out what is left.
- Find the operation. Words like cut off and used mean take away.2200 - 1500
- Work out what is left. Change to the smaller unit, then take away.2200 - 1500 = 700
- Write the answer. Change back to the bigger units.700 g
Check. Check: 700 g plus 1 kg 500 g is 2 kg 200 g.
Watch out. Use the same unit for both amounts before you take away.
Method. Find the operation, then work out what is left.
- Find the operation. Words like cut off and used mean take away.380 - 149
- Work out what is left. Change to the smaller unit, then take away.380 - 149 = 231
- Write the answer. Change back to the bigger units.2 m 31 cm
Check. Check: 2 m 31 cm plus 1 m 49 cm is 3 m 80 cm.
Watch out. Use the same unit for both amounts before you take away.
Method. Find the operation, then work out what is left.
- Find the operation. Words like cut off and used mean take away.280 - 120
- Work out what is left. Change to the smaller unit, then take away.280 - 120 = 160
- Write the answer. Change back to the bigger units.1 m 60 cm
Check. Check: 1 m 60 cm plus 1 m 20 cm is 2 m 80 cm.
Watch out. Use the same unit for both amounts before you take away.
Method. Find the operation, then work out what is left.
- Find the operation. Words like cut off and used mean take away.400 - 196
- Work out what is left. Change to the smaller unit, then take away.400 - 196 = 204
- Write the answer. Change back to the bigger units.2 m 4 cm
Check. Check: 2 m 4 cm plus 1 m 96 cm is 4 m.
Watch out. Use the same unit for both amounts before you take away.
Chapter summary
| Skill | Method |
|---|---|
| Choose a unit | m and cm for length; kg and g for mass; small things use the smaller unit |
| Measure with a ruler | Put the 0 at the start; read the end of the line |
| Read a scale | Find the label before the pointer; count the small marks |
| Change units | 100 cm = 1 m; 1000 g = 1 kg |
| Compare and order | Change to the same unit, then compare or order the numbers |
| Add and subtract | Change to the smaller unit, work it out, change back |
Can you…?
- I can choose metres, centimetres, kilograms or grams for an object
- I can measure a line to the nearest centimetre
- I can read a scale to the nearest mark
- I know that 100 cm is 1 m and 1000 g is 1 kg
- I can compare and order lengths and masses
- I can add and subtract lengths and masses in the same unit
Key terms
- length
- how long something is; measured in cm or m
- mass
- how heavy something is; measured in g or kg
- ruler
- a tool with centimetre marks, used to measure length
- scale
- a tool used to read the mass of an object
Exercise 9Z Check-up
Non-calculatorMethod. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.3 kg 500 g = 3500 g, 2 kg 500 g = 2500 g, 2 kg = 2000 g
- Put the numbers in order. Compare the numbers, then write the measurements in that order.2000, 2500, 3500
- Write the order. Write the original measurements in order.2 kg, 2 kg 500 g, 3 kg 500 g
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Find the number of whole kilograms. 1000 g make 1 kg.8250 ÷ 1000 = 8 rem 250
- Write the grams that are left. The rest are grams.8 kg and 250 g
- Write the answer. Use kilograms and grams.8 kg 250 g
Check. Add back: 8 kg + 250 g = 8250 g.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the ruler: find the start and the end of the line, then the difference.
- Put the 0 at the start of the line. Line up the ruler so the line begins at 0.0 cm
- Read where the line ends. The end of the line is on this number.The end is at 4
- Write the length. The length is the end number, because we started at 0.4 cm
Check. Count the centimetres from 0 to 4: 4 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.2 kg 800 g = 2800 g, 1 kg 500 g = 1500 g, 800 g = 800 g
- Put the numbers in order. Compare the numbers, then write the measurements in that order.2800, 1500, 800
- Write the order. Write the original measurements in order.2 kg 800 g, 1 kg 500 g, 800 g
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Find the number of whole metres. 100 cm make 1 m.450 ÷ 100 = 4 rem 50
- Write the centimetres that are left. The rest are centimetres.4 m and 50 cm
- Write the answer. Use metres and centimetres.4 m 50 cm
Check. Add back: 4 m + 50 cm = 450 cm.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Use the ruler: find the start and the end of the line, then the difference.
- Put the 0 at the start of the line. Line up the ruler so the line begins at 0.0 cm
- Read where the line ends. The end of the line is on this number.The end is at 13
- Write the length. The length is the end number, because we started at 0.13 cm
Check. Count the centimetres from 0 to 13: 13 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Use the ruler: find the start and the end of the line, then the difference.
- Find where the line starts. The line starts at this mark.start = 2 cm
- Find where the line ends. The line ends at this mark.end = 9 cm
- Subtract the start from the end. The length is the distance between the two marks.9 - 2 = 7
- Write the length. This is how long the line is.7 cm
Check. Add the length to the start: 2 + 7 = 9 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Find the number of whole kilograms. 1000 g make 1 kg.2250 ÷ 1000 = 2 rem 250
- Write the grams that are left. The rest are grams.2 kg and 250 g
- Write the answer. Use kilograms and grams.2 kg 250 g
Check. Add back: 2 kg + 250 g = 2250 g.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.3 m 50 cm = 350 cm, 1 m 20 cm = 120 cm, 3 m 75 cm = 375 cm
- Put the numbers in order. Compare the numbers, then write the measurements in that order.375, 350, 120
- Write the order. Write the original measurements in order.3 m 75 cm, 3 m 50 cm, 1 m 20 cm
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.1 kg = 1000 g, 3 kg 800 g = 3800 g, 250 g = 250 g
- Put the numbers in order. Compare the numbers, then write the measurements in that order.3800, 1000, 250
- Write the order. Write the original measurements in order.3 kg 800 g, 1 kg, 250 g
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Total 19 marks. Allow about 19 minutes.
Exercise 9X Practice test questions
Non-calculatorMethod. Change to g, work it out, then change back.
- Change both to the smaller unit. 1000 g make one bigger unit.4 kg 750 g = 4750 g, 2 kg 150 g = 2150 g
- Add the g. Work with the numbers in g.4750 + 2150 = 6900
- Change back to the bigger units. 6900 g is written with 1000 g as one bigger unit.6900 g = 6 kg 900 g
- Write the answer. This is the answer.6 kg 900 g
Check. Check: 6 kg 900 g - 2 kg 150 g = 4 kg 750 g.
Watch out. Work in g to avoid mistakes. Change back at the end.
Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.
- Remember the rule. 1 m is 100 cm.1 m = 100 cm
- Multiply the metres by 100. There are 2 metres, so 2 lots of 100.2 × 100 = 200
- Write the answer in centimetres. This is the length in centimetres.200 cm
Check. Divide 200 cm by 100 to get 2 m.
Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.
Method. Find the operation, then work out what is left.
- Find the operation. Words like cut off and used mean take away.4500 - 3250
- Work out what is left. Change to the smaller unit, then take away.4500 - 3250 = 1250
- Write the answer. Change back to the bigger units.1 kg 250 g
Check. Check: 1 kg 250 g plus 3 kg 250 g is 4 kg 500 g.
Watch out. Use the same unit for both amounts before you take away.
Method. Change every measurement to the same unit, then order the numbers.
- Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.3 kg 800 g = 3800 g, 2 kg 500 g = 2500 g, 3 kg 250 g = 3250 g
- Put the numbers in order. Compare the numbers, then write the measurements in that order.3800, 3250, 2500
- Write the order. Write the original measurements in order.3 kg 800 g, 3 kg 250 g, 2 kg 500 g
Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.
Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 1000 g = 1 kg, so change both to the smaller unit.4 kg 500 g = 4500 g, 2 kg 500 g = 2500 g
- Compare the numbers. Compare the bigger numbers.4500 g and 2500 g
- Write the sign. 4 kg 500 g is more than 2 kg 500 g.>
Check. 4 kg 500 g > 2 kg 500 g is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 100 cm = 1 m, so change both to the smaller unit.2 m = 200 cm, 3 m 50 cm = 350 cm
- Compare the numbers. Compare the bigger numbers.200 cm and 350 cm
- Write the sign. 2 m is less than 3 m 50 cm.<
Check. 2 m < 3 m 50 cm is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Change to cm, work it out, then change back.
- Change both to the smaller unit. 100 cm make one bigger unit.4 m 30 cm = 430 cm, 55 cm = 55 cm
- Take away the cm. Work with the numbers in cm.430 - 55 = 375
- Change back to the bigger units. 375 cm is written with 100 cm as one bigger unit.375 cm = 3 m 75 cm
- Write the answer. This is the answer.3 m 75 cm
Check. Check: 3 m 75 cm + 55 cm = 4 m 30 cm.
Watch out. Work in cm to avoid mistakes. Change back at the end.
Method. Find the operation, then work out what is left.
- Find the operation. Words like cut off and used mean take away.4200 - 800
- Work out what is left. Change to the smaller unit, then take away.4200 - 800 = 3400
- Write the answer. Change back to the bigger units.3 kg 400 g
Check. Check: 3 kg 400 g plus 800 g is 4 kg 200 g.
Watch out. Use the same unit for both amounts before you take away.
Method. Put both measurements in the same unit, then compare them.
- Change both to the same unit. 1000 g = 1 kg, so change both to the smaller unit.3 kg = 3000 g, 3 kg 100 g = 3100 g
- Compare the numbers. Compare the bigger numbers.3000 g and 3100 g
- Write the sign. 3 kg is less than 3 kg 100 g.<
Check. 3 kg < 3 kg 100 g is true.
Watch out. Change to the smaller unit first. Then compare the numbers.
Method. Change to g, work it out, then change back.
- Change both to the smaller unit. 1000 g make one bigger unit.4 kg 750 g = 4750 g, 2 kg 450 g = 2450 g
- Add the g. Work with the numbers in g.4750 + 2450 = 7200
- Change back to the bigger units. 7200 g is written with 1000 g as one bigger unit.7200 g = 7 kg 200 g
- Write the answer. This is the answer.7 kg 200 g
Check. Check: 7 kg 200 g - 2 kg 450 g = 4 kg 750 g.
Watch out. Work in g to avoid mistakes. Change back at the end.