Year 1 Length and Height: worked examples and questions with answers
By the end of this chapter you will be able to
- Say which thing is longer or shorter, and which is the longest or shortest
- Say which thing is taller or shorter, and which is the tallest or shortest
- Measure with cubes, paper clips and hand spans, using units of the same size
- Work out how much longer one thing is than another
- Find double and half of a length
- Read a length in centimetres on a ruler, starting at 0, and write it down
You should already know
- Counting and comparing numbers to 10 (Chapter 1)
- Taking away within 10 (Chapter 2)
- Naming 2-D and 3-D shapes such as cubes (Chapter 3)
Where this leads
- Mass and capacity: heavy and light, full and empty (Chapter 8)
- Measuring lengths in centimetres and metres in more detail (Year 2)
National Curriculum for England, Key Stage 1 mathematics, Year 1. Content: Compare and describe lengths: long, short, longer, shorter, Compare and describe heights: tall, short, taller, shorter, tallest, shortest, Solve practical problems about lengths and heights, including how much longer, Double and half, Measure with non-standard units: cubes, paper clips, hand spans, Begin to use centimetres (cm) on a ruler, starting at 0, Record lengths in a table.
- 7.1 Long and short: Worksheet (PDF) · Answers (PDF) · lesson page
- 7.2 Tall and short: Worksheet (PDF) · Answers (PDF) · lesson page
- 7.3 Measuring with things: cubes, paper clips and hand spans: Worksheet (PDF) · Answers (PDF) · lesson page
- 7.4 How much longer or shorter?: Worksheet (PDF) · Answers (PDF) · lesson page
- 7.5 Double and half: Worksheet (PDF) · Answers (PDF) · lesson page
- 7.6 Using a ruler and recording lengths: Worksheet (PDF) · Answers (PDF) · lesson page
- Check-up and end-of-chapter quiz: Worksheet (PDF) · Answers (PDF) · lesson page
Exercise P Do you remember?
Non-calculatorKey words. A unit is the thing we measure with, like a cube or a paper clip.
Method. Line the units up end to end, then count them one at a time.
- Look at the row of units. The row is the length we measure.A row of 7 cubes
- Count them one at a time. Touch each unit once as you say its number.1, 2, 3, 4, 5, 6, 7
- Write the answer. The last number you say is how long the row is.7 cubes
Check. Count again from the other end. You get 7 again. ✓
Watch out. Do not miss a unit at the end, and do not count one twice.
Method. Start at 7. One more is the number after 7.
- Start at 7. Put your finger on 7.7
- Count on one. The next number is one more.7 + 1 = 8
- Write the answer. 8
Check. Count back one from 8: 8 − 1 = 7. ✓
Watch out. One more is the next number. Do not write 7 again.
Method. Smallest first means the smallest number goes first.
- Find the smallest number. Look for the number nearest to 0.1 is the smallest
- Find the next smallest. 4 is smaller than 9.1, 4, 9
- Write the answer. 1, 4, 9
Check. Start at 1 and count on to 9 in order: 1, 4, 9. ✓
Watch out. Compare the numbers. The names do not matter.
Method. A 3-D shape is solid. It has length, width and height.
- Look at the shapes. A circle and a triangle are flat.circle and triangle are flat
- Find the solid shape. A cube is a solid shape with square faces.cube is 3-D
- Write the answer. cube
Check. Pick up a real cube and feel that it is solid. ✓
Watch out. A circle and a triangle are flat, so they are 2-D.
Method. Count on one at a time from 5.
- Start at 5. We count on from the number we have.5
- Say the next three numbers. Each number is one more than the one before.6, 7, 8
- Write the answer. 6, 7, 8
Check. Count back from 8 to 5 to check: 8, 7, 6, 5. ✓
Watch out. Start with the number after 5, not 5 itself.
Long and short
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
Some things are long. Some things are short. The length of something is how far it goes from one end to the other.
To compare two things, put them side by side with one end level. The one that reaches further is the longer one. The one that stops sooner is the shorter one.
With three or more things, the one that reaches furthest is the longest. The one that stops first is the shortest.
Key ideas
- Line up the starts so that you can compare.
- Longer means it reaches further.
- Shorter means it stops sooner.
- Longest and shortest are for three or more things.
Key words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Line them up at the same start. Then see which one is longer.
- Line them up at the same start. Start both at the same place, so the comparison is fair.A and B start together
- Count the units to check. Count each one, one unit at a time.A: 8 cubes, B: 5 cubes
- Compare the two. Look at the far ends. The one that goes further is longer, and the one that stops sooner is shorter.8 > 5
- Write the answer. A is longer.
Check. Look at the picture again. A and B start together, and A is the longer one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Line them up at the same start. Then see which one is shorter.
- Line them up at the same start. Start both at the same place, so the comparison is fair.A and B start together
- Count the units to check. Count each one, one unit at a time.A: 3 cubes, B: 6 cubes
- Compare the two. Look at the far ends. The one that goes further is longer, and the one that stops sooner is shorter.3 < 6
- Write the answer. A is shorter.
Check. Look at the picture again. A and B start together, and A is the shorter one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. Longest and tallest mean the biggest. Shortest means the smallest.
Method. Measure each one. The longest one has the biggest number.
- Measure each one. Count or read the length of each one.A: 4 cubes
B: 9 cubes
C: 6 cubes - Find the biggest number. Compare the numbers, not the names.9 is the biggest number
- Write the answer. B is the longest one.
Check. The other ones have less than 9. ✓
Watch out. Look at every one before you choose. The first one you see is not always the answer.
Watch out
Watch out: start the lines at the same place. A line that is higher up the page is not always longer. Check the far ends.
Exam tip
Grown-up tip. Use two strips of paper, or two pencils. Lay them side by side with the ends level, then ask: “Which one is longer? How do you know?”
Exercise 7A Longer and shorter
Non-calculatorKey words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Line them up at the same start. Then see which one is longer.
- Line them up at the same start. Start both at the same place, so the comparison is fair.A and B start together
- Count the units to check. Count each one, one unit at a time.A: 6 cubes, B: 2 cubes
- Compare the two. Look at the far ends. The one that goes further is longer, and the one that stops sooner is shorter.6 > 2
- Write the answer. A is longer.
Check. Look at the picture again. A and B start together, and A is the longer one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Line them up at the same start. Then see which one is shorter.
- Line them up at the same start. Start both at the same place, so the comparison is fair.A and B start together
- Count the units to check. Count each one, one unit at a time.A: 5 cubes, B: 8 cubes
- Compare the two. Look at the far ends. The one that goes further is longer, and the one that stops sooner is shorter.5 < 8
- Write the answer. A is shorter.
Check. Look at the picture again. A and B start together, and A is the shorter one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Line them up at the same start. Then see which one is longer.
- Line them up at the same start. Start both at the same place, so the comparison is fair.A and B start together
- Count the units to check. Count each one, one unit at a time.A: 3 cubes, B: 7 cubes
- Compare the two. Look at the far ends. The one that goes further is longer, and the one that stops sooner is shorter.3 < 7
- Write the answer. B is longer.
Check. Look at the picture again. A and B start together, and B is the longer one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Line them up at the same start. Then see which one is shorter.
- Line them up at the same start. Start both at the same place, so the comparison is fair.A and B start together
- Count the units to check. Count each one, one unit at a time.A: 9 cubes, B: 4 cubes
- Compare the two. Look at the far ends. The one that goes further is longer, and the one that stops sooner is shorter.9 > 4
- Write the answer. B is shorter.
Check. Look at the picture again. A and B start together, and B is the shorter one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. Longest and tallest mean the biggest. Shortest means the smallest.
Method. Measure each one. The longest one has the biggest number.
- Measure each one. Count or read the length of each one.A: 2 cubes
B: 5 cubes
C: 3 cubes - Find the biggest number. Compare the numbers, not the names.5 is the biggest number
- Write the answer. B is the longest one.
Check. The other ones have less than 5. ✓
Watch out. Look at every one before you choose. The first one you see is not always the answer.
Key words. Longest and tallest mean the biggest. Shortest means the smallest.
Method. Measure each one. The shortest one has the smallest number.
- Measure each one. Count or read the length of each one.A: 6 cubes
B: 8 cubes
C: 4 cubes - Find the smallest number. Compare the numbers, not the names.4 is the smallest number
- Write the answer. C is the shortest one.
Check. The other ones have more than 4. ✓
Watch out. Look at every one before you choose. The first one you see is not always the answer.
Key words. Smallest first means the shortest or lowest number comes first.
Method. Measure each one, then put them in order, starting with the smallest number.
- Measure each one. Count or read the length of each one.A: 7 cubes
B: 3 cubes
C: 5 cubes - Put them in order, starting with the smallest. Put the next one after the one before it.B, C, A
- Write the names in order. B, C, A
Check. There are 3 names in the question and 3 in the answer. ✓
Watch out. Check you have not left one out.
Key words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Line them up at the same start. Then see which one is shorter.
- Line them up at the same start. Start both at the same place, so the comparison is fair.A and B start together
- Count the units to check. Count each one, one unit at a time.A: 4 cubes, B: 7 cubes
- Compare the two. Look at the far ends. The one that goes further is longer, and the one that stops sooner is shorter.4 < 7
- Write the answer. A is shorter.
Check. Look at the picture again. A and B start together, and A is the shorter one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Line them up at the same start. Then see which one is longer.
- Line them up at the same start. Start both at the same place, so the comparison is fair.A and B start together
- Count the units to check. Count each one, one unit at a time.A: 7 cubes, B: 4 cubes
- Compare the two. Look at the far ends. The one that goes further is longer, and the one that stops sooner is shorter.7 > 4
- Write the answer. A is longer.
Check. Look at the picture again. A and B start together, and A is the longer one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Line them up at the same start. Then see which one is shorter.
- Line them up at the same start. Start both at the same place, so the comparison is fair.B and C start together
- Count the units to check. Count each one, one unit at a time.B: 4 cubes, C: 6 cubes
- Compare the two. Look at the far ends. The one that goes further is longer, and the one that stops sooner is shorter.4 < 6
- Write the answer. B is shorter.
Check. Look at the picture again. B and C start together, and B is the shorter one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Line them up at the same start. Then see which one is longer.
- Line them up at the same start. Start both at the same place, so the comparison is fair.A and C start together
- Count the units to check. Count each one, one unit at a time.A: 7 cubes, C: 6 cubes
- Compare the two. Look at the far ends. The one that goes further is longer, and the one that stops sooner is shorter.7 > 6
- Write the answer. A is longer.
Check. Look at the picture again. A and C start together, and A is the longer one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Method. Ignore how high the ribbon is on the page. Look at the far ends.
- Look at the top ribbon, A. It is higher up, but it stops at 3 cubes.A: 3 cubes
- Look at the bottom ribbon, B. It reaches further, to 7 cubes.B: 7 cubes
- Write the answer. Aisha is not right, because B reaches further.No. Ribbon B is longer.
Check. Line the two ribbons up at the start. B goes further. ✓
Watch out. Being higher up the page does not make a line longer.
Method. Measure each one. Two of them match exactly, so they are the same length.
- Measure each one. Read or count the length of each one.A: 5 cubes
B: 5 cubes
C: 2 cubes - Find the two that match. Things with the same length are the same length.A = 5, B = 5
- Write the answer. A and B
Check. Compare each pair to check. Only A and B match. ✓
Watch out. Measure, do not guess from the picture.
Tall and short
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
Some things stand up. We measure how tall they are, from the bottom to the top. This is their height.
A tall thing is high. A short thing is low. When things stand on the same ground, the one that reaches higher is taller. The one that is lower is shorter.
With three or more things, the tallest is the highest and the shortest is the lowest.
Key ideas
- Stand things on the same ground to compare heights.
- Taller means higher from the bottom.
- Shorter means lower from the bottom.
- Tallest is the highest. Shortest is the lowest.
Key words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Stand them on the same ground, at the bottom. Then see which one is taller.
- Stand them on the same ground, at the bottom. Start both at the same place, so the comparison is fair.A and B start together
- Count the units to check. Count each one, one unit at a time.A: 6 cubes, B: 4 cubes
- Compare the two. Look at the tops. The one that is higher is taller, and the one that is lower is shorter.6 > 4
- Write the answer. A is taller.
Check. Look at the picture again. A and B start together, and A is the taller one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. Longest and tallest mean the biggest. Shortest means the smallest.
Method. Measure each one. The tallest one has the biggest number.
- Measure each one. Count or read the length of each one.Noah: 5 cubes
Priya: 7 cubes
Amira: 3 cubes - Find the biggest number. Compare the numbers, not the names.7 is the biggest number
- Write the answer. Priya is the tallest one.
Check. The other ones have less than 7. ✓
Watch out. Look at every one before you choose. The first one you see is not always the answer.
Key words. Smallest first means the shortest or lowest number comes first.
Method. Measure each one, then put them in order, starting with the smallest number.
- Measure each one. Count or read the length of each one.A: 5 cubes
B: 2 cubes
C: 4 cubes - Put them in order, starting with the smallest. Put the next one after the one before it.B, C, A
- Write the names in order. B, C, A
Check. There are 3 names in the question and 3 in the answer. ✓
Watch out. Check you have not left one out.
Watch out
Watch out: a tower looks taller when it is nearer to you or on a stool. Compare them on the same ground, from the bottom.
Exam tip
Grown-up tip. Stand two cups or boxes on a table. Ask: “Which is taller? Which is the shortest of the three?” Let your child stack cubes or coins to show each height.
Exercise 7B Taller and shorter
Non-calculatorKey words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Stand them on the same ground, at the bottom. Then see which one is taller.
- Stand them on the same ground, at the bottom. Start both at the same place, so the comparison is fair.A and B start together
- Count the units to check. Count each one, one unit at a time.A: 3 cubes, B: 8 cubes
- Compare the two. Look at the tops. The one that is higher is taller, and the one that is lower is shorter.3 < 8
- Write the answer. B is taller.
Check. Look at the picture again. A and B start together, and B is the taller one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Stand them on the same ground, at the bottom. Then see which one is shorter.
- Stand them on the same ground, at the bottom. Start both at the same place, so the comparison is fair.A and B start together
- Count the units to check. Count each one, one unit at a time.A: 7 cubes, B: 5 cubes
- Compare the two. Look at the tops. The one that is higher is taller, and the one that is lower is shorter.7 > 5
- Write the answer. B is shorter.
Check. Look at the picture again. A and B start together, and B is the shorter one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. Longest and tallest mean the biggest. Shortest means the smallest.
Method. Measure each one. The tallest one has the biggest number.
- Measure each one. Count or read the length of each one.A: 4 cubes
B: 9 cubes
C: 6 cubes - Find the biggest number. Compare the numbers, not the names.9 is the biggest number
- Write the answer. B is the tallest one.
Check. The other ones have less than 9. ✓
Watch out. Look at every one before you choose. The first one you see is not always the answer.
Key words. Longest and tallest mean the biggest. Shortest means the smallest.
Method. Measure each one. The shortest one has the smallest number.
- Measure each one. Count or read the length of each one.A: 5 cubes
B: 2 cubes
C: 8 cubes - Find the smallest number. Compare the numbers, not the names.2 is the smallest number
- Write the answer. B is the shortest one.
Check. The other ones have more than 2. ✓
Watch out. Look at every one before you choose. The first one you see is not always the answer.
Key words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Stand them on the same ground, at the bottom. Then see which one is taller.
- Stand them on the same ground, at the bottom. Start both at the same place, so the comparison is fair.Ruby and Chloe start together
- Count the units to check. Count each one, one unit at a time.Ruby: 6 cubes, Chloe: 8 cubes
- Compare the two. Look at the tops. The one that is higher is taller, and the one that is lower is shorter.6 < 8
- Write the answer. Chloe is taller.
Check. Look at the picture again. Ruby and Chloe start together, and Chloe is the taller one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. Smallest first means the shortest or lowest number comes first.
Method. Measure each one, then put them in order, starting with the biggest number.
- Measure each one. Count or read the length of each one.A: 3 cubes
B: 7 cubes
C: 5 cubes - Put them in order, starting with the biggest. Put the next one after the one before it.B, C, A
- Write the names in order. B, C, A
Check. There are 3 names in the question and 3 in the answer. ✓
Watch out. Check you have not left one out.
Key words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Stand them on the same ground, at the bottom. Then see which one is shorter.
- Stand them on the same ground, at the bottom. Start both at the same place, so the comparison is fair.A and B start together
- Count the units to check. Count each one, one unit at a time.A: 2 cubes, B: 6 cubes
- Compare the two. Look at the tops. The one that is higher is taller, and the one that is lower is shorter.2 < 6
- Write the answer. A is shorter.
Check. Look at the picture again. A and B start together, and A is the shorter one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Method. Measure each one. Two of them match exactly, so they are the same length.
- Measure each one. Read or count the length of each one.A: 4 cubes
B: 4 cubes
C: 7 cubes - Find the two that match. Things with the same length are the same length.A = 4, B = 4
- Write the answer. A and B
Check. Compare each pair to check. Only A and B match. ✓
Watch out. Measure, do not guess from the picture.
Method. Find who is taller than whom, one step at a time.
- Jack is taller than Leo. Write down the first pair.Jack > Leo
- Leo is taller than Mei. Now put Mei on the list.Jack > Leo > Mei
- Find the shortest. Mei is the lowest on the list.Mei is the shortest
Check. The tallest is at the top, and the shortest is at the bottom: Jack, Leo, Mei. ✓
Watch out. Put the names in a line, tallest at the top, and check each pair.
Method. Compare the two towers from the bottom to the top.
- Count tower A. Count the cubes from the bottom.A: 5 cubes
- Count tower B. Count the cubes from the bottom.B: 8 cubes
- Compare them. The one with more cubes is higher.8 > 5
- Write the answer. Fatima is not right, because B is taller.No. Tower B is taller.
Check. Stand the cubes in a tower and count them. B has 8. ✓
Watch out. Tower A is wider, but it is not taller.
Method. Think about how a tower is built.
- Look at the towers. Each tower is made of cubes stacked on top of each other.A: 4 cubes, B: 7 cubes
- Think about the heights. Cubes of the same size, stacked on the same ground, make the tower taller.More cubes means higher
- Write the answer. So a tower with more cubes is taller, when the cubes are the same size.Yes, if the cubes are the same size.
Check. Count each tower again: 4 and 7. 7 is more than 4. ✓
Watch out. This is true only when the cubes are the same size and stacked on the same ground.
Measuring with things: cubes, paper clips and hand spans
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
We can measure length using things we have to hand. These are called non-standard units. We can use cubes, paper clips or hand spans. A hand span is the distance from the tip of your thumb to the tip of your little finger, when your hand is spread wide.
Lay the units end to end, with no gaps and no overlaps. Then count how many there are. Every unit must be the same size.
Key ideas
- Use units of the same size.
- Lay them end to end, with no gaps.
- Count them one at a time.
- Say the unit too: 5 cubes, 5 paper clips, 5 hand spans.
Key words. A unit is the thing we measure with, like a cube or a paper clip.
Method. Line the units up end to end, then count them one at a time.
- Look at the row of units. The row is the length we measure.A row of 7 cubes
- Count them one at a time. Touch each unit once as you say its number.1, 2, 3, 4, 5, 6, 7
- Write the answer. The last number you say is how long the row is.7 cubes
Check. Count again from the other end. You get 7 again. ✓
Watch out. Do not miss a unit at the end, and do not count one twice.
Key words. A unit is the thing we measure with, like a cube or a paper clip.
Method. Line the units up end to end, then count them one at a time.
- Look at the row of units. The row is the length we measure.A row of 5 paper clips
- Count them one at a time. Touch each unit once as you say its number.1, 2, 3, 4, 5
- Write the answer. The last number you say is how long the row is.5 paper clips
Check. Count again from the other end. You get 5 again. ✓
Watch out. Do not miss a unit at the end, and do not count one twice.
Key words. A unit is the thing we measure with, like a cube or a paper clip.
Method. Line the units up end to end, then count them one at a time.
- Look at the row of units. The row is the length we measure.A row of 8 hand spans
- Count them one at a time. Touch each unit once as you say its number.1, 2, 3, 4, 5, 6, 7, 8
- Write the answer. The last number you say is how long the row is.8 hand spans
Check. Count again from the other end. You get 8 again. ✓
Watch out. Do not miss a unit at the end, and do not count one twice.
Watch out
Watch out: every unit must be the same size. If you mix big cubes and small cubes, your count will not match. Also check there are no gaps between the units.
Exam tip
Grown-up tip. Measure things at home with paper clips, pasta shapes or hand spans. Ask: “Is your hand span the same as mine?” Grown-up hands and child hands are different sizes, so the answers differ. That shows why we need the same size of unit.
Exercise 7C Measuring with units
Non-calculatorKey words. A unit is the thing we measure with, like a cube or a paper clip.
Method. Line the units up end to end, then count them one at a time.
- Look at the row of units. The row is the length we measure.A row of 4 cubes
- Count them one at a time. Touch each unit once as you say its number.1, 2, 3, 4
- Write the answer. The last number you say is how long the row is.4 cubes
Check. Count again from the other end. You get 4 again. ✓
Watch out. Do not miss a unit at the end, and do not count one twice.
Key words. A unit is the thing we measure with, like a cube or a paper clip.
Method. Line the units up end to end, then count them one at a time.
- Look at the row of units. The row is the length we measure.A row of 9 cubes
- Count them one at a time. Touch each unit once as you say its number.1, 2, 3, 4, 5, 6, 7, 8, 9
- Write the answer. The last number you say is how long the row is.9 cubes
Check. Count again from the other end. You get 9 again. ✓
Watch out. Do not miss a unit at the end, and do not count one twice.
Key words. A unit is the thing we measure with, like a cube or a paper clip.
Method. Line the units up end to end, then count them one at a time.
- Look at the row of units. The row is the length we measure.A row of 6 paper clips
- Count them one at a time. Touch each unit once as you say its number.1, 2, 3, 4, 5, 6
- Write the answer. The last number you say is how long the row is.6 paper clips
Check. Count again from the other end. You get 6 again. ✓
Watch out. Do not miss a unit at the end, and do not count one twice.
Key words. A unit is the thing we measure with, like a cube or a paper clip.
Method. Line the units up end to end, then count them one at a time.
- Look at the row of units. The row is the length we measure.A row of 3 paper clips
- Count them one at a time. Touch each unit once as you say its number.1, 2, 3
- Write the answer. The last number you say is how long the row is.3 paper clips
Check. Count again from the other end. You get 3 again. ✓
Watch out. Do not miss a unit at the end, and do not count one twice.
Key words. A unit is the thing we measure with, like a cube or a paper clip.
Method. Line the units up end to end, then count them one at a time.
- Look at the row of units. The row is the length we measure.A row of 10 hand spans
- Count them one at a time. Touch each unit once as you say its number.1, 2, 3, 4, 5, 6, 7, 8, 9, 10
- Write the answer. The last number you say is how long the row is.10 hand spans
Check. Count again from the other end. You get 10 again. ✓
Watch out. Do not miss a unit at the end, and do not count one twice.
Key words. A unit is the thing we measure with, like a cube or a paper clip.
Method. Line the units up end to end, then count them one at a time.
- Look at the row of units. The row is the length we measure.A row of 5 cubes
- Count them one at a time. Touch each unit once as you say its number.1, 2, 3, 4, 5
- Write the answer. The last number you say is how long the row is.5 cubes
Check. Count again from the other end. You get 5 again. ✓
Watch out. Do not miss a unit at the end, and do not count one twice.
Key words. A unit is the thing we measure with, like a cube or a paper clip.
Method. Line the units up end to end, then count them one at a time.
- Look at the row of units. The row is the length we measure.A row of 9 paper clips
- Count them one at a time. Touch each unit once as you say its number.1, 2, 3, 4, 5, 6, 7, 8, 9
- Write the answer. The last number you say is how long the row is.9 paper clips
Check. Count again from the other end. You get 9 again. ✓
Watch out. Do not miss a unit at the end, and do not count one twice.
Key words. A unit is the thing we measure with, like a cube or a paper clip.
Method. Line the units up end to end, then count them one at a time.
- Look at the row of units. The row is the length we measure.A row of 4 hand spans
- Count them one at a time. Touch each unit once as you say its number.1, 2, 3, 4
- Write the answer. The last number you say is how long the row is.4 hand spans
Check. Count again from the other end. You get 4 again. ✓
Watch out. Do not miss a unit at the end, and do not count one twice.
Method. Compare the two numbers. The bigger number is the longer ribbon.
- Count the red ribbon. Count its cubes one at a time.Red: 5 cubes
- Count the blue ribbon. Count its cubes one at a time.Blue: 3 cubes
- Compare the two numbers. Five is more than three.5 > 3
- Write the answer. Red ribbon is longer.
Check. Line them up: the red ribbon reaches further. ✓
Watch out. Compare the numbers, not the colours.
Method. Count each cube once, one at a time, then check what was said.
- Count the cubes again. Touch each one once.1, 2, 3, 4, 5, 6
- Compare with what was said. The count was 4, but the real count is 6.6 − 4 = 2
- Write the correct answer. 2 cubes were missed, so the count was too small.6
Check. Count from the other end. You still get 6. ✓
Watch out. If you lose your place, move each unit to the side as you count it.
Method. Think about what each person did. Both can count correctly, but the units are different.
- Look at Jack’s count. He used big cubes, so there are fewer of them.Jack: 4 big cubes
- Look at Oliver’s count. He used small cubes, so there are more of them.Oliver: 9 small cubes
- Compare the answers. The numbers cannot be compared, because the cubes are different sizes.Different units, different numbers
- Write the answer. Both counted right, but the cubes were different sizes.
Check. Measure again with one size of cube, and the numbers will match. ✓
Watch out. Always use units of the same size when you want to compare two lengths.
Method. Think about how big each unit is.
- Think about a hand span. A hand span is a long unit.A hand span is long
- Think about a paper clip. A paper clip is a short unit.A paper clip is short
- Compare the two. A short unit needs more of them to reach the same length.More clips than hand spans
- Write the answer. Paper clips give the bigger number.
Check. Measure the table again with clips to see that the count is bigger. ✓
Watch out. The smaller the unit, the more of them you need.
How much longer or shorter?
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
How much longer is one ribbon than another? Line the two ribbons up at the start. The extra units at the end of the longer one show how much longer it is.
You can also count the units in each ribbon. Then take the smaller number away from the bigger number. The answer tells you how much longer.
Key ideas
- Line up the start of each one.
- The extra part at the end shows how much longer.
- Count the extra, or take the smaller number away from the bigger number.
- Use longer for the one that reaches further.
Key words. How much longer means the extra amount that one has.
Method. Line them up at the start. Count the extra part on the longer one.
- Measure A. Count or read its length.A: 9 cubes
- Measure B. Count or read its length.B: 4 cubes
- Find the extra part. Take the smaller number away from the bigger number.9 − 4 = 5
- Write the answer. 5 cubes
Check. Check: 4 + 5 = 9. ✓
Watch out. Count only the extra part at the end of the longer one, not the whole of it.
Key words. How much longer means the extra amount that one has.
Method. Line them up at the start. Count the extra part on the longer one.
- Measure D. Count or read its length.D: 8 paper clips
- Measure C. Count or read its length.C: 2 paper clips
- Find the extra part. Take the smaller number away from the bigger number.8 − 2 = 6
- Write the answer. 6 paper clips
Check. Check: 2 + 6 = 8. ✓
Watch out. Count only the extra part at the end of the longer one, not the whole of it.
Method. If both are the same length, neither one is longer. The difference is zero.
- Measure E. Count or read its length.E: 6 cubes
- Measure F. Count or read its length.F: 6 cubes
- Compare them. They are equal, so there is no extra part.6 − 6 = 0
- Write the answer. 0. They are the same length.
Check. Line them up: every unit has a partner, and nothing is left over. ✓
Watch out. When the lengths are the same, there is no extra part.
Watch out
Watch out: count only the extra part at the end of the longer one. Do not count the part that both ribbons share.
Exam tip
Grown-up tip. Lay two pencils side by side, starting at the same place. Ask: “How many extra pencils do we need to make the short one as long?” Let your child count the extra with a finger.
Exercise 7D How much longer?
Non-calculatorKey words. How much longer means the extra amount that one has.
Method. Line them up at the start. Count the extra part on the longer one.
- Measure A. Count or read its length.A: 7 cubes
- Measure B. Count or read its length.B: 3 cubes
- Find the extra part. Take the smaller number away from the bigger number.7 − 3 = 4
- Write the answer. 4 cubes
Check. Check: 3 + 4 = 7. ✓
Watch out. Count only the extra part at the end of the longer one, not the whole of it.
Key words. How much longer means the extra amount that one has.
Method. Line them up at the start. Count the extra part on the longer one.
- Measure A. Count or read its length.A: 6 cubes
- Measure B. Count or read its length.B: 4 cubes
- Find the extra part. Take the smaller number away from the bigger number.6 − 4 = 2
- Write the answer. 2 cubes
Check. Check: 4 + 2 = 6. ✓
Watch out. Count only the extra part at the end of the longer one, not the whole of it.
Key words. How much longer means the extra amount that one has.
Method. Line them up at the start. Count the extra part on the longer one.
- Measure D. Count or read its length.D: 9 paper clips
- Measure C. Count or read its length.C: 6 paper clips
- Find the extra part. Take the smaller number away from the bigger number.9 − 6 = 3
- Write the answer. 3 paper clips
Check. Check: 6 + 3 = 9. ✓
Watch out. Count only the extra part at the end of the longer one, not the whole of it.
Key words. How much longer means the extra amount that one has.
Method. Line them up at the start. Count the extra part on the longer one.
- Measure F. Count or read its length.F: 8 hand spans
- Measure E. Count or read its length.E: 3 hand spans
- Find the extra part. Take the smaller number away from the bigger number.8 − 3 = 5
- Write the answer. 5 hand spans
Check. Check: 3 + 5 = 8. ✓
Watch out. Count only the extra part at the end of the longer one, not the whole of it.
Key words. How much longer means the extra amount that one has.
Method. Line them up at the start. Count the extra part on the longer one.
- Measure G. Count or read its length.G: 10 cubes
- Measure H. Count or read its length.H: 7 cubes
- Find the extra part. Take the smaller number away from the bigger number.10 − 7 = 3
- Write the answer. 3 cubes
Check. Check: 7 + 3 = 10. ✓
Watch out. Count only the extra part at the end of the longer one, not the whole of it.
Method. Start with the whole. Take away the part that is cut off.
- Start with 9 cubes. This is the whole rope before the cut.9
- Take away 4. Count back 4 from 9.9 − 4 = 5
- Write the answer. The rope is now shorter.5 cubes
Check. Put the cut part back on: 5 + 4 = 9. ✓
Watch out. Take away the cut part. Check you did not take away the part that is left.
Key words. How much taller means the extra amount that one has.
Method. Line them up at the start. Count the extra part on the taller one.
- Measure Chloe. Count or read its length.Chloe: 7 cubes
- Measure Tom. Count or read its length.Tom: 2 cubes
- Find the extra part. Take the smaller number away from the bigger number.7 − 2 = 5
- Write the answer. 5 cubes
Check. Check: 2 + 5 = 7. ✓
Watch out. Count only the extra part at the end of the taller one, not the whole of it.
Key words. How much longer means the extra amount that one has.
Method. Line them up at the start. Count the extra part on the longer one.
- Measure Rope 1. Count or read its length.Rope 1: 8 cubes
- Measure Rope 2. Count or read its length.Rope 2: 3 cubes
- Find the extra part. Take the smaller number away from the bigger number.8 − 3 = 5
- Write the answer. 5 cubes
Check. Check: 3 + 5 = 8. ✓
Watch out. Count only the extra part at the end of the longer one, not the whole of it.
Key words. How much longer means the extra amount that one has.
Method. Line them up at the start. Count the extra part on the longer one.
- Measure Rope 1. Count or read its length.Rope 1: 7 cubes
- Measure Rope 2. Count or read its length.Rope 2: 4 cubes
- Find the extra part. Take the smaller number away from the bigger number.7 − 4 = 3
- Write the answer. 3 cubes
Check. Check: 4 + 3 = 7. ✓
Watch out. Count only the extra part at the end of the longer one, not the whole of it.
Key words. How much longer means the extra amount that one has.
Method. Line them up at the start. Count the extra part on the longer one.
- Measure Rope 1. Count or read its length.Rope 1: 10 cubes
- Measure Rope 2. Count or read its length.Rope 2: 6 cubes
- Find the extra part. Take the smaller number away from the bigger number.10 − 6 = 4
- Write the answer. 4 cubes
Check. Check: 6 + 4 = 10. ✓
Watch out. Count only the extra part at the end of the longer one, not the whole of it.
Method. Start with the whole. Take away the part that is cut off.
- Start with 7 cubes. This is the whole rope before the cut.7
- Take away 2. Count back 2 from 7.7 − 2 = 5
- Write the answer. The rope is now shorter.5 cubes
Check. Put the cut part back on: 5 + 2 = 7. ✓
Watch out. Take away the cut part. Check you did not take away the part that is left.
Method. Think about lining the two things up at the start.
- Line up the starts. Put the two things side by side, starting at the same place.Both start together
- Find the extra part. The extra units at the end of the longer one are the difference.Count only the extra units
- Write the answer. Count the extra units. Do not count the whole longer thing.Count the extra units at the end.
Check. Take the smaller number from the bigger one, and check the answer. ✓
Watch out. Do not count the whole longer thing. Count only the extra part.
Method. Work out each ribbon, one at a time, then compare.
- Find ribbon B. Ribbon B is 4 shorter than ribbon A.10 − 4 = 6
- Find ribbon C. Ribbon C is 3 longer than ribbon B.6 + 3 = 9
- Compare the three. The biggest number is the longest ribbon.A: 10, B: 6, C: 9
- Write the answer. A is the longest.
Check. Check: 6 + 4 = 10, and 9 is 3 more than 6. ✓
Watch out. Work out each one in order. Each ribbon depends on the one before it.
Double and half
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
Double means two times as much. A rope that is double another rope is two times as long. To double a number of cubes, make two equal lots of it.
Half means share into two equal parts. When you halve a strip, each half is the same length. Halving is the opposite of doubling.
Key ideas
- Double means two equal lots of the same amount.
- Half means share into two equal parts.
- Double 4 is 8, because 4 + 4 = 8.
- Half of 8 is 4, because 4 + 4 = 8.
Method. Double means two equal lots of the same number.
- Start with 4. This is the length we want to double.4
- Add 4 again. Two equal lots make double.4 + 4 = 8
- Write the answer. 8 cubes
Check. Half of 8 is 4, so double 4 must be 8. ✓
Watch out. Double means add the same number again. It is not add one more.
Method. Half means share it into two equal parts.
- Start with 10. This is the whole strip.10
- Share it into two equal parts. Each part must be exactly the same length.10 ÷ 2 = 5
- Write the answer. 5 cubes
Check. Put the two halves back together: 5 + 5 = 10. ✓
Watch out. The two parts must be equal. Count each part to check.
Method. Double means two equal lots of the same number.
- Start with 3. This is the length we want to double.3
- Add 3 again. Two equal lots make double.3 + 3 = 6
- Write the answer. 6 paper clips
Check. Half of 6 is 3, so double 3 must be 6. ✓
Watch out. Double means add the same number again. It is not add one more.
Watch out
Watch out: double means add the same amount again. It does not mean add one more. Double 3 is 6, not 4.
Exam tip
Grown-up tip. Use two rows of buttons or cubes. Make one row, then build an identical row next to it. Ask: “How many altogether? Is it double?” For halves, share a row of buttons one at a time, so each person gets the same.
Exercise 7E Double and half
Non-calculatorMethod. Double means two equal lots of the same number.
- Start with 2. This is the length we want to double.2
- Add 2 again. Two equal lots make double.2 + 2 = 4
- Write the answer. 4 cubes
Check. Half of 4 is 2, so double 2 must be 4. ✓
Watch out. Double means add the same number again. It is not add one more.
Method. Double means two equal lots of the same number.
- Start with 4. This is the length we want to double.4
- Add 4 again. Two equal lots make double.4 + 4 = 8
- Write the answer. 8 cubes
Check. Half of 8 is 4, so double 4 must be 8. ✓
Watch out. Double means add the same number again. It is not add one more.
Method. Double means two equal lots of the same number.
- Start with 5. This is the length we want to double.5
- Add 5 again. Two equal lots make double.5 + 5 = 10
- Write the answer. 10
Check. Half of 10 is 5, so double 5 must be 10. ✓
Watch out. Double means add the same number again. It is not add one more.
Method. Half means share it into two equal parts.
- Start with 6. This is the whole strip.6
- Share it into two equal parts. Each part must be exactly the same length.6 ÷ 2 = 3
- Write the answer. 3 cubes
Check. Put the two halves back together: 3 + 3 = 6. ✓
Watch out. The two parts must be equal. Count each part to check.
Method. Half means share it into two equal parts.
- Start with 8. This is the whole strip.8
- Share it into two equal parts. Each part must be exactly the same length.8 ÷ 2 = 4
- Write the answer. 4 cubes
Check. Put the two halves back together: 4 + 4 = 8. ✓
Watch out. The two parts must be equal. Count each part to check.
Method. Half means share it into two equal parts.
- Start with 8. This is the whole strip.8
- Share it into two equal parts. Each part must be exactly the same length.8 ÷ 2 = 4
- Write the answer. 4
Check. Put the two halves back together: 4 + 4 = 8. ✓
Watch out. The two parts must be equal. Count each part to check.
Method. Double B is the same as two lots of A.
- Look at strip A. Strip A has 3 cubes.A = 3
- Find double 3. Double 3 means 3 + 3.3 + 3 = 6
- Compare with strip B. Strip B has 6 cubes, which matches double 3.B = 6
- Write the answer. Yes. B is double A.
Check. Halve 6 to check: 6 ÷ 2 = 3. That is A. ✓
Watch out. Double means two lots of the same number.
Method. Find double 4, then compare it with strip D.
- Look at strip C. Strip C has 4 cubes.C = 4
- Find double 4. Double 4 means 4 + 4.4 + 4 = 8
- Compare with strip D. Strip D has 9 cubes. That is not 8.D = 9, and 9 is not 8
- Write the answer. No. Double 4 is 8, not 9.
Check. Double 4 is 8, and strip D has 9, so the two strips are not double. ✓
Watch out. Count the cubes in both strips before you decide.
Method. Double means two equal lots of the same number.
- Start with 5. This is the length we want to double.5
- Add 5 again. Two equal lots make double.5 + 5 = 10
- Write the answer. 10 cubes
Check. Half of 10 is 5, so double 5 must be 10. ✓
Watch out. Double means add the same number again. It is not add one more.
Method. Double means two equal lots of the same number.
- Start with 1. This is the length we want to double.1
- Add 1 again. Two equal lots make double.1 + 1 = 2
- Write the answer. 2
Check. Half of 2 is 1, so double 1 must be 2. ✓
Watch out. Double means add the same number again. It is not add one more.
Method. Double means two equal lots of the same number.
- Start with 2. This is the length we want to double.2
- Add 2 again. Two equal lots make double.2 + 2 = 4
- Write the answer. 4
Check. Half of 4 is 2, so double 2 must be 4. ✓
Watch out. Double means add the same number again. It is not add one more.
Method. Double means two equal lots of the same number.
- Start with 4. This is the length we want to double.4
- Add 4 again. Two equal lots make double.4 + 4 = 8
- Write the answer. 8
Check. Half of 8 is 4, so double 4 must be 8. ✓
Watch out. Double means add the same number again. It is not add one more.
Method. Double means two equal lots of the same number.
- Start with 5. This is the length we want to double.5
- Add 5 again. Two equal lots make double.5 + 5 = 10
- Write the answer. 10
Check. Half of 10 is 5, so double 5 must be 10. ✓
Watch out. Double means add the same number again. It is not add one more.
Method. Half means share it into two equal parts.
- Start with 4. This is the whole strip.4
- Share it into two equal parts. Each part must be exactly the same length.4 ÷ 2 = 2
- Write the answer. 2
Check. Put the two halves back together: 2 + 2 = 4. ✓
Watch out. The two parts must be equal. Count each part to check.
Method. Half means share it into two equal parts.
- Start with 2. This is the whole strip.2
- Share it into two equal parts. Each part must be exactly the same length.2 ÷ 2 = 1
- Write the answer. 1
Check. Put the two halves back together: 1 + 1 = 2. ✓
Watch out. The two parts must be equal. Count each part to check.
Method. Half means share it into two equal parts.
- Start with 10. This is the whole strip.10
- Share it into two equal parts. Each part must be exactly the same length.10 ÷ 2 = 5
- Write the answer. 5
Check. Put the two halves back together: 5 + 5 = 10. ✓
Watch out. The two parts must be equal. Count each part to check.
Method. Half means share it into two equal parts.
- Start with 6. This is the whole strip.6
- Share it into two equal parts. Each part must be exactly the same length.6 ÷ 2 = 3
- Write the answer. 3
Check. Put the two halves back together: 3 + 3 = 6. ✓
Watch out. The two parts must be equal. Count each part to check.
Method. Try doubling and then halving, one step at a time.
- Start with 3. This is the length of the rope.3
- Double it. Double 3 is 3 + 3.3 + 3 = 6
- Halve it again. Half of 6 is 3.6 ÷ 2 = 3
- Write the answer. Tom is right, because he gets back to 3.Yes. Double 3 is 6, and half of 6 is 3.
Check. Doubling and halving undo each other. ✓
Watch out. Halving undoes doubling, so you get back to where you started.
Using a ruler and recording lengths
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
A ruler measures length in centimetres. We write centimetres as cm. Each big number on the ruler is one centimetre. The small marks between the numbers are the same size.
To measure something, put the 0 at one end. Then look at the number at the other end. That number tells you the length in centimetres.
Write each length in a table, with the name of the thing and its length. Then you can compare them later.
Key ideas
- Start measuring at 0.
- Read the number at the other end.
- cm means centimetres.
- Write the length with its unit, like 6 cm.
Method. Find the start and the end on the ruler. Then take the start away from the end.
- Find where the line starts. Put your finger on the start.Start: 0 cm
- Find where the line ends. Read the number at the other end.End: 4 cm
- Take the start away from the end. The length is the distance between the two numbers.4 − 0 = 4
- Write the answer. 4 cm
Check. Count along the ruler from 0 to 4: that is 4 centimetres. ✓
Watch out. Start at 0 when you can. If the line starts at 2, take 2 away from the end number.
Method. Find the start and the end on the ruler. Then take the start away from the end.
- Find where the line starts. Put your finger on the start.Start: 0 cm
- Find where the line ends. Read the number at the other end.End: 9 cm
- Take the start away from the end. The length is the distance between the two numbers.9 − 0 = 9
- Write the answer. 9 cm
Check. Count along the ruler from 0 to 9: that is 9 centimetres. ✓
Watch out. Start at 0 when you can. If the line starts at 2, take 2 away from the end number.
| Thing | Length |
|---|---|
| Pencil | 6 cm |
| Crayon | 4 cm |
| Ribbon | 9 cm |
Key words. Longest and tallest mean the biggest. Shortest means the smallest.
Method. Measure each one. The longest one has the biggest number.
- Measure each one. Count or read the length of each one.Pencil: 6 cm
Crayon: 4 cm
Ribbon: 9 cm - Find the biggest number. Compare the numbers, not the names.9 is the biggest number
- Write the answer. Ribbon is the longest one.
Check. The other ones have less than 9. ✓
Watch out. Look at every one before you choose. The first one you see is not always the answer.
Watch out
Watch out: many children start at the 1, not at the 0. If the pencil starts at 1, the number at its end is one too big. Start at 0.
Exam tip
Grown-up tip. Use a real ruler. Let your child lay it along a pencil, a book or a sock. Ask: “Where does it start? Where does it end?” Write each length on a sticky note with cm after it.
Exercise 7F Measuring in centimetres
Non-calculatorMethod. Find the start and the end on the ruler. Then take the start away from the end.
- Find where the line starts. Put your finger on the start.Start: 0 cm
- Find where the line ends. Read the number at the other end.End: 5 cm
- Take the start away from the end. The length is the distance between the two numbers.5 − 0 = 5
- Write the answer. 5 cm
Check. Count along the ruler from 0 to 5: that is 5 centimetres. ✓
Watch out. Start at 0 when you can. If the line starts at 2, take 2 away from the end number.
Method. Find the start and the end on the ruler. Then take the start away from the end.
- Find where the line starts. Put your finger on the start.Start: 0 cm
- Find where the line ends. Read the number at the other end.End: 8 cm
- Take the start away from the end. The length is the distance between the two numbers.8 − 0 = 8
- Write the answer. 8 cm
Check. Count along the ruler from 0 to 8: that is 8 centimetres. ✓
Watch out. Start at 0 when you can. If the line starts at 2, take 2 away from the end number.
Method. Find the start and the end on the ruler. Then take the start away from the end.
- Find where the line starts. Put your finger on the start.Start: 0 cm
- Find where the line ends. Read the number at the other end.End: 3 cm
- Take the start away from the end. The length is the distance between the two numbers.3 − 0 = 3
- Write the answer. 3 cm
Check. Count along the ruler from 0 to 3: that is 3 centimetres. ✓
Watch out. Start at 0 when you can. If the line starts at 2, take 2 away from the end number.
Method. Start each line at 0, then find the one that ends at 6.
- Read where each line ends. Every line starts at 0.A ends at 4
B ends at 6
C ends at 9 - Find the line that ends at 6. We want a line that is 6 cm long.B ends at 6
- Write the answer. B
Check. Count along the ruler from 0 to 6. ✓
Watch out. Look at the far end of each line, not the middle.
Key words. Longest and tallest mean the biggest. Shortest means the smallest.
Method. Measure each one. The longest one has the biggest number.
- Measure each one. Count or read the length of each one.A: 7 cm
B: 2 cm
C: 5 cm - Find the biggest number. Compare the numbers, not the names.7 is the biggest number
- Write the answer. A is the longest one.
Check. The other ones have less than 7. ✓
Watch out. Look at every one before you choose. The first one you see is not always the answer.
Key words. How much longer means the extra amount that one has.
Method. Line them up at the start. Count the extra part on the longer one.
- Measure Aisha. Count or read its length.Aisha: 7 cm
- Measure Tom. Count or read its length.Tom: 4 cm
- Find the extra part. Take the smaller number away from the bigger number.7 − 4 = 3
- Write the answer. 3 cm
Check. Check: 4 + 3 = 7. ✓
Watch out. Count only the extra part at the end of the longer one, not the whole of it.
Method. Find the start and the end on the ruler. Then take the start away from the end.
- Find where the line starts. Put your finger on the start.Start: 2 cm
- Find where the line ends. Read the number at the other end.End: 7 cm
- Take the start away from the end. The length is the distance between the two numbers.7 − 2 = 5
- Write the answer. 5 cm
Check. Count along the ruler from 2 to 7: that is 5 centimetres. ✓
Watch out. Start at 0 when you can. If the line starts at 2, take 2 away from the end number.
Method. Find the start and the end on the ruler. Then take the start away from the end.
- Find where the line starts. Put your finger on the start.Start: 0 cm
- Find where the line ends. Read the number at the other end.End: 3 cm
- Take the start away from the end. The length is the distance between the two numbers.3 − 0 = 3
- Write the answer. 3 cm
Check. Count along the ruler from 0 to 3: that is 3 centimetres. ✓
Watch out. Start at 0 when you can. If the line starts at 2, take 2 away from the end number.
Method. Find the start and the end on the ruler. Then take the start away from the end.
- Find where the line starts. Put your finger on the start.Start: 0 cm
- Find where the line ends. Read the number at the other end.End: 7 cm
- Take the start away from the end. The length is the distance between the two numbers.7 − 0 = 7
- Write the answer. 7 cm
Check. Count along the ruler from 0 to 7: that is 7 centimetres. ✓
Watch out. Start at 0 when you can. If the line starts at 2, take 2 away from the end number.
Method. Find the start and the end on the ruler. Then take the start away from the end.
- Find where the line starts. Put your finger on the start.Start: 0 cm
- Find where the line ends. Read the number at the other end.End: 5 cm
- Take the start away from the end. The length is the distance between the two numbers.5 − 0 = 5
- Write the answer. 5 cm
Check. Count along the ruler from 0 to 5: that is 5 centimetres. ✓
Watch out. Start at 0 when you can. If the line starts at 2, take 2 away from the end number.
| Thing | Length |
|---|---|
| Pencil | 5 cm |
| Crayon | 8 cm |
| Ribbon | 3 cm |
Key words. Longest and tallest mean the biggest. Shortest means the smallest.
Method. Measure each one. The shortest one has the smallest number.
- Measure each one. Count or read the length of each one.Pencil: 5 cm
Crayon: 8 cm
Ribbon: 3 cm - Find the smallest number. Compare the numbers, not the names.3 is the smallest number
- Write the answer. Ribbon is the shortest one.
Check. The other ones have more than 3. ✓
Watch out. Look at every one before you choose. The first one you see is not always the answer.
Method. Measure each one. Two of them match exactly, so they are the same length.
- Measure each one. Read or count the length of each one.A: 5 cm
B: 8 cm
C: 5 cm - Find the two that match. Things with the same length are the same length.A = 5, C = 5
- Write the answer. A and C
Check. Compare each pair to check. Only A and C match. ✓
Watch out. Measure, do not guess from the picture.
Chapter summary
| Skill | Method |
|---|---|
| Compare lengths | Line up the starts. The one that reaches further is longer. Use shortest and longest for three or more. |
| Compare heights | Stand them on the same ground. The one that is higher is taller. |
| Measure with units | Lay cubes, paper clips or hand spans end to end, all the same size. Count them. |
| How much longer? | Line up the starts. Count the extra part at the end of the longer one. |
| Double and half | Double means two equal lots. Half means share into two equal parts. |
| Ruler in cm | Start at 0. Read the number at the other end. Write the length with cm. |
Can you…?
- I can say which thing is longer or shorter, and which is the longest or shortest
- I can say which thing is taller or shorter, and which is the tallest or shortest
- I can measure with cubes, paper clips and hand spans, using units of the same size
- I can say how much longer one thing is than another
- I can find double and half of a length
- I can read a length in cm on a ruler, starting at 0, and write it down
Key terms
- length
- how long something is, from one end to the other
- height
- how tall something is, from the bottom to the top
- longer
- reaches further than another thing
- shorter
- stops sooner than another thing
- tall
- high from the bottom to the top
- taller
- reaches higher than another thing that stands on the same ground
- unit
- the thing we measure with, such as a cube or a paper clip
- hand span
- the distance from the tip of your thumb to the tip of your little finger, hand spread wide
- centimetre (cm)
- a unit of length that we measure with on a ruler
- ruler
- a tool with numbers in centimetres, used to measure length
- double
- two equal lots of the same number
- half
- one of two equal parts
Exercise 7Z Check-up
Non-calculatorKey words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Line them up at the same start. Then see which one is longer.
- Line them up at the same start. Start both at the same place, so the comparison is fair.A and B start together
- Count the units to check. Count each one, one unit at a time.A: 8 cubes, B: 3 cubes
- Compare the two. Look at the far ends. The one that goes further is longer, and the one that stops sooner is shorter.8 > 3
- Write the answer. A is longer.
Check. Look at the picture again. A and B start together, and A is the longer one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. Longest and tallest mean the biggest. Shortest means the smallest.
Method. Measure each one. The tallest one has the biggest number.
- Measure each one. Count or read the length of each one.A: 3 cubes
B: 6 cubes
C: 4 cubes - Find the biggest number. Compare the numbers, not the names.6 is the biggest number
- Write the answer. B is the tallest one.
Check. The other ones have less than 6. ✓
Watch out. Look at every one before you choose. The first one you see is not always the answer.
Key words. A unit is the thing we measure with, like a cube or a paper clip.
Method. Line the units up end to end, then count them one at a time.
- Look at the row of units. The row is the length we measure.A row of 5 cubes
- Count them one at a time. Touch each unit once as you say its number.1, 2, 3, 4, 5
- Write the answer. The last number you say is how long the row is.5 cubes
Check. Count again from the other end. You get 5 again. ✓
Watch out. Do not miss a unit at the end, and do not count one twice.
Key words. A unit is the thing we measure with, like a cube or a paper clip.
Method. Line the units up end to end, then count them one at a time.
- Look at the row of units. The row is the length we measure.A row of 7 paper clips
- Count them one at a time. Touch each unit once as you say its number.1, 2, 3, 4, 5, 6, 7
- Write the answer. The last number you say is how long the row is.7 paper clips
Check. Count again from the other end. You get 7 again. ✓
Watch out. Do not miss a unit at the end, and do not count one twice.
Key words. How much longer means the extra amount that one has.
Method. Line them up at the start. Count the extra part on the longer one.
- Measure A. Count or read its length.A: 9 cubes
- Measure B. Count or read its length.B: 6 cubes
- Find the extra part. Take the smaller number away from the bigger number.9 − 6 = 3
- Write the answer. 3 cubes
Check. Check: 6 + 3 = 9. ✓
Watch out. Count only the extra part at the end of the longer one, not the whole of it.
Method. Double means two equal lots of the same number.
- Start with 3. This is the length we want to double.3
- Add 3 again. Two equal lots make double.3 + 3 = 6
- Write the answer. 6
Check. Half of 6 is 3, so double 3 must be 6. ✓
Watch out. Double means add the same number again. It is not add one more.
Method. Half means share it into two equal parts.
- Start with 4. This is the whole strip.4
- Share it into two equal parts. Each part must be exactly the same length.4 ÷ 2 = 2
- Write the answer. 2 cubes
Check. Put the two halves back together: 2 + 2 = 4. ✓
Watch out. The two parts must be equal. Count each part to check.
Method. Find the start and the end on the ruler. Then take the start away from the end.
- Find where the line starts. Put your finger on the start.Start: 0 cm
- Find where the line ends. Read the number at the other end.End: 6 cm
- Take the start away from the end. The length is the distance between the two numbers.6 − 0 = 6
- Write the answer. 6 cm
Check. Count along the ruler from 0 to 6: that is 6 centimetres. ✓
Watch out. Start at 0 when you can. If the line starts at 2, take 2 away from the end number.
Key words. Smallest first means the shortest or lowest number comes first.
Method. Measure each one, then put them in order, starting with the smallest number.
- Measure each one. Count or read the length of each one.A: 7 cubes
B: 2 cubes
C: 5 cubes - Put them in order, starting with the smallest. Put the next one after the one before it.B, C, A
- Write the names in order. B, C, A
Check. There are 3 names in the question and 3 in the answer. ✓
Watch out. Check you have not left one out.
Method. Find the start and the end on the ruler. Then take the start away from the end.
- Find where the line starts. Put your finger on the start.Start: 0 cm
- Find where the line ends. Read the number at the other end.End: 9 cm
- Take the start away from the end. The length is the distance between the two numbers.9 − 0 = 9
- Write the answer. 9 cm
Check. Count along the ruler from 0 to 9: that is 9 centimetres. ✓
Watch out. Start at 0 when you can. If the line starts at 2, take 2 away from the end number.
Total 14 marks. Allow about 14 minutes.
Exercise 7X End-of-chapter quiz
Non-calculatorKey words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Line them up at the same start. Then see which one is longer.
- Line them up at the same start. Start both at the same place, so the comparison is fair.A and B start together
- Count the units to check. Count each one, one unit at a time.A: 4 cubes, B: 7 cubes
- Compare the two. Look at the far ends. The one that goes further is longer, and the one that stops sooner is shorter.4 < 7
- Write the answer. B is longer.
Check. Look at the picture again. A and B start together, and B is the longer one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. A unit is the thing we measure with, like a cube or a paper clip.
Method. Line the units up end to end, then count them one at a time.
- Look at the row of units. The row is the length we measure.A row of 6 cubes
- Count them one at a time. Touch each unit once as you say its number.1, 2, 3, 4, 5, 6
- Write the answer. The last number you say is how long the row is.6 cubes
Check. Count again from the other end. You get 6 again. ✓
Watch out. Do not miss a unit at the end, and do not count one twice.
Key words. Longer means it reaches further. Shorter means it stops sooner. Taller means it is higher.
Method. Stand them on the same ground, at the bottom. Then see which one is shorter.
- Stand them on the same ground, at the bottom. Start both at the same place, so the comparison is fair.A and B start together
- Count the units to check. Count each one, one unit at a time.A: 7 cubes, B: 5 cubes
- Compare the two. Look at the tops. The one that is higher is taller, and the one that is lower is shorter.7 > 5
- Write the answer. B is shorter.
Check. Look at the picture again. A and B start together, and B is the shorter one. ✓
Watch out. Do not judge only by where a thing is on the page. Line them up first.
Key words. How much longer means the extra amount that one has.
Method. Line them up at the start. Count the extra part on the longer one.
- Measure A. Count or read its length.A: 8 cubes
- Measure B. Count or read its length.B: 5 cubes
- Find the extra part. Take the smaller number away from the bigger number.8 − 5 = 3
- Write the answer. 3 cubes
Check. Check: 5 + 3 = 8. ✓
Watch out. Count only the extra part at the end of the longer one, not the whole of it.
Method. Find the start and the end on the ruler. Then take the start away from the end.
- Find where the line starts. Put your finger on the start.Start: 0 cm
- Find where the line ends. Read the number at the other end.End: 7 cm
- Take the start away from the end. The length is the distance between the two numbers.7 − 0 = 7
- Write the answer. 7 cm
Check. Count along the ruler from 0 to 7: that is 7 centimetres. ✓
Watch out. Start at 0 when you can. If the line starts at 2, take 2 away from the end number.
Method. Double means two equal lots of the same number.
- Start with 4. This is the length we want to double.4
- Add 4 again. Two equal lots make double.4 + 4 = 8
- Write the answer. 8
Check. Half of 8 is 4, so double 4 must be 8. ✓
Watch out. Double means add the same number again. It is not add one more.
Method. Start with the whole. Take away the part that is cut off.
- Start with 6 cubes. This is the whole rope before the cut.6
- Take away 2. Count back 2 from 6.6 − 2 = 4
- Write the answer. The rope is now shorter.4 cubes
Check. Put the cut part back on: 4 + 2 = 6. ✓
Watch out. Take away the cut part. Check you did not take away the part that is left.
Key words. Smallest first means the shortest or lowest number comes first.
Method. Measure each one, then put them in order, starting with the biggest number.
- Measure each one. Count or read the length of each one.Noah: 4 cubes
Priya: 2 cubes
Amira: 6 cubes - Put them in order, starting with the biggest. Put the next one after the one before it.Amira, Noah, Priya
- Write the names in order. Amira, Noah, Priya
Check. There are 3 names in the question and 3 in the answer. ✓
Watch out. Check you have not left one out.
Method. Measure each one. Two of them match exactly, so they are the same length.
- Measure each one. Read or count the length of each one.A: 4 cm
B: 7 cm
C: 4 cm - Find the two that match. Things with the same length are the same length.A = 4, C = 4
- Write the answer. A and C
Check. Compare each pair to check. Only A and C match. ✓
Watch out. Measure, do not guess from the picture.
Method. Think about the units. The units must be the same size, and they must be in a line.
- Lay the units in a line. Put them end to end, with no gaps.Units in a row
- Use units of the same size. Otherwise the count cannot be compared.Same size, one after the other
- Count them. Count one at a time, and say the last number.Lay the clips end to end, with no gaps. Use clips of the same size.
Check. Count them again to check you get the same number. ✓
Watch out. Two rules: end to end, and the same size.