Year 1 Mass and Capacity: worked examples and questions with answers
By the end of this chapter you will be able to
- Say which object is heavier or lighter, using a balance scale
- Count cubes to find out how heavy something is
- Say which container is full, empty or part full
- Say which container holds more or less, by counting cups
- Recognise a half full and a quarter full container
- Measure how much a container holds, using cups
You should already know
- Counting and comparing groups to 10 (Chapter 1)
- Adding and subtracting within 20 (Chapters 2 and 5)
- Comparing lengths and heights (Chapter 7)
Where this leads
- Measuring in grams, kilograms, millilitres and litres (Year 2)
National Curriculum for England, Key Stage 1 mathematics, Year 1. Content: Compare objects by mass: heavy, light, heavier than, lighter than, Use a balance scale to compare mass, Measure mass with non-standard units (cubes), Compare capacity: full, empty, more than, less than, Recognise half full and quarter full, Measure capacity with non-standard units (cups).
- 8.1 Heavy and light: Worksheet (PDF) · Answers (PDF) · lesson page
- 8.2 Balance scales and counting cubes: Worksheet (PDF) · Answers (PDF) · lesson page
- 8.3 Full, empty and more or less: Worksheet (PDF) · Answers (PDF) · lesson page
- 8.4 Half full and quarter full: Worksheet (PDF) · Answers (PDF) · lesson page
- 8.5 Measuring capacity with cups: 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. To count is to say one number for each thing, in order.
Method. Touch each one once and say its number. The last number you say is how many there are.
- Count each one, in order. Each one gets one number. Do not miss one.1, 2, 3, 4, 5, 6, 7
- Look at the last number. The last number tells us how many altogether.The last number is 7.
- Write the answer. There are 7 balls.
Check. Count again from the other side. You get 7 again. ✓
Watch out. Move each one to one side as you count it, so you do not count it twice.
Method. One more is the number after 6.
- Start at 6. Put your finger on the number.Start: 6
- Move one step forward. Each step on the number line is one number.6 + 1 = 7
- Write the answer. 7
Check. Check: 7 − 1 = 6. ✓
Watch out. Move one step only. Do not write the number you started with.
Method. Count on one at a time from 4.
- Start at 4. We count on from the number we have.4
- Say the next numbers. Each number is one more than the one before.5, 6, 7
- Write the answer. 5, 6, 7
Check. Count back from the last number to 4 to check. ✓
Watch out. Start with the number after 4, not 4 itself.
Method. Look at the triangle. Count its corners, one at a time.
- Look at the triangle. Corners are the sharp points.1, 2, 3
- Write the answer. The last number is how many corners there are.3
Check. Count the sides too. A triangle has as many sides as corners. ✓
Watch out. Count the corners, not the sides.
Method. The biggest number is the one furthest to the right on the number line.
- Look at each number. Think about which is bigger.3, 8, 5
- Find the biggest. Bigger numbers are further to the right.8 is the biggest
- Write the answer. 8
Check. Each of the others is smaller than 8. ✓
Watch out. Compare the numbers. Do not choose by how big the writing looks.
Heavy and light
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
Some things are heavy. Some things are light. Heavy things weigh more. Light things weigh less.
You can feel it. Hold one thing in each hand. The hand with the heavier thing goes down.
A balance scale works in the same way. Put one thing on each pan. The pan with the heavier thing goes down, and the other pan goes up.
We can say the book is heavier than the apple. We can say the apple is lighter than the book.
Key ideas
- Heavy means it weighs a lot. Light means it weighs less.
- The side that goes down is the heavier side.
- The side that goes up is the lighter side.
- Heavier than and lighter than compare two things.
Key words. Heavier than means weighs more. Lighter than means weighs less.
Method. The heavier one is the one that makes its side go down on the scale.
- Look at the scale. The side that goes down holds the heavier object.Pan B goes down
- Find the heavier object. The heavier object is on the low side.B is the book
- Write the answer. B, the book
Check. The other side goes up, so it is the other one. ✓
Watch out. A big thing can be light, and a small thing can be heavy. Look at the scale, not the size.
Key words. Heavier than means weighs more. Lighter than means weighs less.
Method. The lighter one is the one that makes its side go up on the scale.
- Look at the scale. The side that goes down holds the heavier object.Pan B goes down
- Find the lighter object. The lighter object is on the high side.A is the ball
- Write the answer. A, the ball
Check. The other side goes down, so it is the other one. ✓
Watch out. A big thing can be light, and a small thing can be heavy. Look at the scale, not the size.
Method. Compare the two objects, then decide if the sentence is true.
- Find the two objects. Read the sentence carefully.bag and apple
- Say which one is heavier. The heavier one makes its side go down.The bag is heavier
- Write the answer. Does the sentence match what we found?True
Check. Read the sentence the other way round to check. ✓
Watch out. Heavier and lighter mean opposite things. Read them carefully.
Watch out
Watch out: a big thing is not always heavy. A small thing can be heavy too. Look at the scale, not at the size.
Exam tip
Grown-up tip. Let your child lift two things, one in each hand. Ask: “Which is heavier? How do you know?” Then ask them to use the word heavier in a sentence.
Exercise 8A Heavy and light
Non-calculatorKey words. Heavier than means weighs more. Lighter than means weighs less.
Method. The heavier one is the one that makes its side go down on the scale.
- Look at the scale. The side that goes down holds the heavier object.Pan A goes down
- Find the heavier object. The heavier object is on the low side.A is the ball
- Write the answer. A, the ball
Check. The other side goes up, so it is the other one. ✓
Watch out. A big thing can be light, and a small thing can be heavy. Look at the scale, not the size.
Key words. Heavier than means weighs more. Lighter than means weighs less.
Method. The lighter one is the one that makes its side go up on the scale.
- Look at the scale. The side that goes down holds the heavier object.Pan B goes down
- Find the lighter object. The lighter object is on the high side.A is the bag
- Write the answer. A, the bag
Check. The other side goes down, so it is the other one. ✓
Watch out. A big thing can be light, and a small thing can be heavy. Look at the scale, not the size.
Key words. Heavier than means weighs more. Lighter than means weighs less.
Method. The heavier one is the one that makes its side go down on the scale.
- Look at the scale. The side that goes down holds the heavier object.Pan A goes down
- Find the heavier object. The heavier object is on the low side.A is the bag
- Write the answer. A, the bag
Check. The other side goes up, so it is the other one. ✓
Watch out. A big thing can be light, and a small thing can be heavy. Look at the scale, not the size.
Key words. Heavier than means weighs more. Lighter than means weighs less.
Method. The lighter one is the one that makes its side go up on the scale.
- Look at the scale. The side that goes down holds the heavier object.Pan B goes down
- Find the lighter object. The lighter object is on the high side.A is the book
- Write the answer. A, the book
Check. The other side goes down, so it is the other one. ✓
Watch out. A big thing can be light, and a small thing can be heavy. Look at the scale, not the size.
Key words. Heavier than means weighs more. Lighter than means weighs less.
Method. The heavier one is the one that makes its side go down on the scale.
- Look at the scale. The side that goes down holds the heavier object.Pan B goes down
- Find the heavier object. The heavier object is on the low side.B is the brick
- Write the answer. B, the brick
Check. The other side goes up, so it is the other one. ✓
Watch out. A big thing can be light, and a small thing can be heavy. Look at the scale, not the size.
Key words. Heavier than means weighs more. Lighter than means weighs less.
Method. The lighter one is the one that makes its side go up on the scale.
- Look at the scale. The side that goes down holds the heavier object.Pan A goes down
- Find the lighter object. The lighter object is on the high side.B is the bag
- Write the answer. B, the bag
Check. The other side goes down, so it is the other one. ✓
Watch out. A big thing can be light, and a small thing can be heavy. Look at the scale, not the size.
Key words. Heavier than means weighs more. Lighter than means weighs less.
Method. The heavier one is the one that makes its side go down on the scale.
- Look at the scale. The side that goes down holds the heavier object.Pan B goes down
- Find the heavier object. The heavier object is on the low side.B is the brick
- Write the answer. B, the brick
Check. The other side goes up, so it is the other one. ✓
Watch out. A big thing can be light, and a small thing can be heavy. Look at the scale, not the size.
Key words. Heaviest means the most heavy. Lightest means the least heavy.
Method. Put the objects in a line, from the heaviest to the lightest. Then find the heaviest one.
- Put the objects in a line. The heaviest goes at the front.brick > bag > book
- Find the heaviest one. The heaviest one is at the front of the line.brick is the heaviest
- Write the answer. The brick is the heaviest.
Check. The first one is heavier than the last one, so the line is right. ✓
Watch out. Read every sentence. Do not pick the first object you read about.
Key words. Heaviest means the most heavy. Lightest means the least heavy.
Method. Put the objects in a line, from the heaviest to the lightest. Then find the lightest one.
- Put the objects in a line. The heaviest goes at the front.bag > book > ball
- Find the lightest one. The lightest one is at the end of the line.ball is the lightest
- Write the answer. The ball is the lightest.
Check. The first one is heavier than the last one, so the line is right. ✓
Watch out. Read every sentence. Do not pick the first object you read about.
Key words. Lightest is the least heavy. Heaviest is the most heavy.
Method. Lightest first. Compare two objects at a time.
- Compare two objects. Use the scale or the cubes to see which is heavier.apple < book < brick
- Put them in a line. Start with the lightest one.apple, book, brick
- Write the answer. apple, book, brick
Check. There are 3 objects in the question and 3 in the answer. ✓
Watch out. Check that you have not left one out.
Method. Compare the two objects, then decide if the sentence is true.
- Find the two objects. Read the sentence carefully.bag and apple
- Say which one is heavier. The heavier one makes its side go down.The bag is heavier
- Write the answer. Does the sentence match what we found?True
Check. Read the sentence the other way round to check. ✓
Watch out. Heavier and lighter mean opposite things. Read them carefully.
Method. Think about which thing is heavier. The heavier thing pulls its hand down.
- Find the heavier thing. The heavier thing pulls harder.The brick is heavier than the ball
- Find the lower hand. The hand with the heavier thing goes down.The hand with the brick is lower
- Write the answer. The hand with the brick is lower.
Check. The hand with the ball is higher up. ✓
Watch out. Think about the weight, not the size of the thing.
Balance scales and counting cubes
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
A balance scale can show how heavy things are. Put an object on one pan. Add cubes to the other pan, one at a time, until the scale is level.
Then count the cubes. The number of cubes tells us how heavy the object is. Cubes are a non-standard unit. We use them to measure because we can count them.
Key ideas
- A balance scale is level when both sides weigh the same.
- We measure how heavy something is by counting cubes.
- The cubes must all be the same size.
- The number of cubes is the weight in cubes.
Key words. A balance scale is level when both sides weigh the same. A cube is a unit we can count.
Method. Add cubes to one pan until the scale is level. Then count the cubes.
- Look at the book and the scale. When the beam is level, both sides weigh the same.The book weighs the same as the cubes.
- Count the cubes, one at a time. Touch each cube once so you do not miss one.1, 2, 3, 4, 5
- Write the answer. The last number is how many cubes there are.5 cubes
Check. Take one cube away. The scale tips, so 5 cubes is exactly right. ✓
Watch out. Use cubes that are all the same size. Different sizes give a wrong count.
Key words. More means a bigger number. Take away to find out how many more.
Method. Find how many more. Take the smaller number away from the bigger number.
- Count the cubes for each. Use the numbers you counted.brick: 8 cubes, book: 5 cubes
- Take the smaller number away. What is left is how many more.8 − 5 = 3
- Write the answer. 3 more cubes
Check. Add them back: 5 + 3 = 8. ✓
Watch out. Start with the bigger number and take the smaller one away.
Method. Count the cubes on each scale. Then choose the one that needs more cubes.
- Count the cubes for A. Each cube is one unit.A: 3 cubes
- Count the cubes for B. Each cube is one unit.B: 2 cubes
- Compare the two numbers. The bigger number is more cubes.3 > 2
- Write the answer. A (the ball)
Check. 2 is smaller than 3, so the answer is right. ✓
Watch out. Count the cubes on both scales. Do not guess from the size of the objects.
Watch out
Watch out: every cube must be the same size. If one cube is bigger, the count will be wrong. Count each cube only once.
Exam tip
Grown-up tip. Use a kitchen balance or a simple DIY scale with two bowls, and small toy bricks or coins as cubes. Ask: “How many bricks balance the apple?” Let your child move the bricks and count.
Exercise 8B Counting cubes on a balance
Non-calculatorKey words. A balance scale is level when both sides weigh the same. A cube is a unit we can count.
Method. Add cubes to one pan until the scale is level. Then count the cubes.
- Look at the apple and the scale. When the beam is level, both sides weigh the same.The apple weighs the same as the cubes.
- Count the cubes, one at a time. Touch each cube once so you do not miss one.1, 2
- Write the answer. The last number is how many cubes there are.2 cubes
Check. Take one cube away. The scale tips, so 2 cubes is exactly right. ✓
Watch out. Use cubes that are all the same size. Different sizes give a wrong count.
Key words. A balance scale is level when both sides weigh the same. A cube is a unit we can count.
Method. Add cubes to one pan until the scale is level. Then count the cubes.
- Look at the ball and the scale. When the beam is level, both sides weigh the same.The ball weighs the same as the cubes.
- Count the cubes, one at a time. Touch each cube once so you do not miss one.1, 2, 3
- Write the answer. The last number is how many cubes there are.3 cubes
Check. Take one cube away. The scale tips, so 3 cubes is exactly right. ✓
Watch out. Use cubes that are all the same size. Different sizes give a wrong count.
Key words. A balance scale is level when both sides weigh the same. A cube is a unit we can count.
Method. Add cubes to one pan until the scale is level. Then count the cubes.
- Look at the brick and the scale. When the beam is level, both sides weigh the same.The brick weighs the same as the cubes.
- Count the cubes, one at a time. Touch each cube once so you do not miss one.1, 2, 3, 4, 5, 6, 7, 8
- Write the answer. The last number is how many cubes there are.8 cubes
Check. Take one cube away. The scale tips, so 8 cubes is exactly right. ✓
Watch out. Use cubes that are all the same size. Different sizes give a wrong count.
Key words. A balance scale is level when both sides weigh the same. A cube is a unit we can count.
Method. Add cubes to one pan until the scale is level. Then count the cubes.
- Look at the bag and the scale. When the beam is level, both sides weigh the same.The bag weighs the same as the cubes.
- Count the cubes, one at a time. Touch each cube once so you do not miss one.1, 2, 3, 4, 5, 6, 7
- Write the answer. The last number is how many cubes there are.7 cubes
Check. Take one cube away. The scale tips, so 7 cubes is exactly right. ✓
Watch out. Use cubes that are all the same size. Different sizes give a wrong count.
Key words. A balance scale is level when both sides weigh the same. A cube is a unit we can count.
Method. Add cubes to one pan until the scale is level. Then count the cubes.
- Look at the apple and the scale. When the beam is level, both sides weigh the same.The apple weighs the same as the cubes.
- Count the cubes, one at a time. Touch each cube once so you do not miss one.1, 2
- Write the answer. The last number is how many cubes there are.2 cubes
Check. Take one cube away. The scale tips, so 2 cubes is exactly right. ✓
Watch out. Use cubes that are all the same size. Different sizes give a wrong count.
Key words. A balance scale is level when both sides weigh the same. A cube is a unit we can count.
Method. Add cubes to one pan until the scale is level. Then count the cubes.
- Look at the book and the scale. When the beam is level, both sides weigh the same.The book weighs the same as the cubes.
- Count the cubes, one at a time. Touch each cube once so you do not miss one.1, 2, 3, 4, 5
- Write the answer. The last number is how many cubes there are.5 cubes
Check. Take one cube away. The scale tips, so 5 cubes is exactly right. ✓
Watch out. Use cubes that are all the same size. Different sizes give a wrong count.
Method. Count the cubes on each scale. Then choose the one that needs fewer cubes.
- Count the cubes for A. Each cube is one unit.A: 5 cubes
- Count the cubes for B. Each cube is one unit.B: 3 cubes
- Compare the two numbers. The bigger number is more cubes.5 > 3
- Write the answer. B (the ball)
Check. 3 is smaller than 5, so the answer is right. ✓
Watch out. Count the cubes on both scales. Do not guess from the size of the objects.
Key words. More means a bigger number. Take away to find out how many more.
Method. Find how many more. Take the smaller number away from the bigger number.
- Count the cubes for each. Use the numbers you counted.bag: 7 cubes, ball: 3 cubes
- Take the smaller number away. What is left is how many more.7 − 3 = 4
- Write the answer. 4 more cubes
Check. Add them back: 3 + 4 = 7. ✓
Watch out. Start with the bigger number and take the smaller one away.
Key words. More means a bigger number. Take away to find out how many more.
Method. Find how many more. Take the smaller number away from the bigger number.
- Count the cubes for each. Use the numbers you counted.bag: 7 cubes, apple: 2 cubes
- Take the smaller number away. What is left is how many more.7 − 2 = 5
- Write the answer. 5 more cubes
Check. Add them back: 2 + 5 = 7. ✓
Watch out. Start with the bigger number and take the smaller one away.
Method. Look at how many cubes each one balances. More cubes means heavier.
- Sam's bag balances 7 cubes. Use the number of cubes.Sam: 7
- Ruby's apple balances 2 cubes. Use the number of cubes.Ruby: 2
- Compare the two numbers. The bigger number is heavier.7 > 2
- Write the answer. Sam's bag is heavier.
Check. The lighter one balances fewer cubes. ✓
Watch out. Compare the cubes, not the names of the people.
Method. Start with what is already there. Then add the ones you put in.
- Start with 5. That is how many are already there.5
- Add 5 more. Count on from the first number.5 + 5 = 10
- Write the answer. 10 cubes
Check. Take 5 away from 10 to get back to 5. ✓
Watch out. Count on from the first number. Do not start again at one.
Method. The same book needs the same number of cubes every time.
- Look at the two numbers. They should match if both people counted correctly.4 and 6
- Decide if both can be right. The same object cannot need two different numbers of cubes.4 is not 6
- Write the answer. At least one of them has miscounted.
Check. Count the cubes again, one at a time, to find the right number. ✓
Watch out. Check every count. Balance the scale again if you are not sure.
Method. Think about what the count is for.
- Think about the cubes. If one cube were heavier, the count would be wrong.All cubes must weigh the same
- Think about the count. Then the number of cubes tells us how heavy the object is.Count = how heavy
- Write the answer. Each cube must weigh the same, so the count tells us how heavy the object is.
Check. Think about using two different sizes of cube on the same scale. ✓
Watch out. Use cubes that are the same size, every time.
Full, empty and more or less
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
A container holds liquid, such as water or juice. A container is full when there is no room for more. A container is empty when there is nothing inside it.
Capacity means how much a container can hold. To find out which holds more, fill each one with cups of water and count the cups. The one that takes more cups holds more.
Key ideas
- Full means there is no room for more.
- Empty means there is nothing inside.
- Capacity is how much a container holds.
- To compare capacity, count how many cups fill each container.
Key words. Full means the water reaches the top.
Method. Look for the container that is full.
- Look at each container. Check how high the water reaches.A: empty; B: full; C: half full
- Find the one that is full. Only one container matches.B: full
- Write the answer. B
Check. The other containers are not full. ✓
Watch out. Look at the water, not at the shape of the container.
Method. Count the cups for each container. Then see which one holds more.
- Count the cups for A. Each cup is one unit.A: 6 cups
- Count the cups for B. Each cup is one unit.B: 4 cups
- Compare the two numbers. The bigger number holds more.6 > 4
- Write the answer. A
Check. 4 cups is less than 6 cups. ✓
Watch out. Count the cups. Do not guess from the shape of the container.
Key words. Empty means nothing inside. Quarter full means a quarter of the way up.
Method. Look at how high the water reaches.
- Look at the water. Compare it with the top and the bottom of the container.This container: there is nothing in it
- Find the matching word. Empty, quarter full, half full or full.empty
- Write the answer. empty
Check. Check: the water is there is nothing in it. ✓
Watch out. The water starts at the bottom. Do not count the empty space at the top.
Watch out
Watch out: a tall container does not always hold more. A wide bowl can hold more than a tall glass. Count the cups to find out.
Exam tip
Grown-up tip. At bath time or at the sink, fill two cups with water and ask: “Which holds more?” Pour the water from one to the other to check. Use the words full and empty.
Exercise 8C Full, empty and holding more
Non-calculatorKey words. Full means the water reaches the top.
Method. Look for the container that is full.
- Look at each container. Check how high the water reaches.A: full; B: empty; C: half full
- Find the one that is full. Only one container matches.A: full
- Write the answer. A
Check. The other containers are not full. ✓
Watch out. Look at the water, not at the shape of the container.
Key words. Empty means there is nothing in it.
Method. Look for the container that is empty.
- Look at each container. Check how high the water reaches.A: full; B: empty
- Find the one that is empty. Only one container matches.B: empty
- Write the answer. B
Check. The other containers are not empty. ✓
Watch out. Look at the water, not at the shape of the container.
Key words. Empty means there is nothing in it.
Method. Look for the container that is empty.
- Look at each container. Check how high the water reaches.A: full; B: empty; C: full
- Find the one that is empty. Only one container matches.B: empty
- Write the answer. B
Check. The other containers are not empty. ✓
Watch out. Look at the water, not at the shape of the container.
Method. Count the cups for each container. Then see which one holds more.
- Count the cups for A. Each cup is one unit.A: 6 cups
- Count the cups for B. Each cup is one unit.B: 3 cups
- Compare the two numbers. The bigger number holds more.6 > 3
- Write the answer. A
Check. 3 cups is less than 6 cups. ✓
Watch out. Count the cups. Do not guess from the shape of the container.
Method. Count the cups for each container. Then see which one holds less.
- Count the cups for A. Each cup is one unit.A: 4 cups
- Count the cups for B. Each cup is one unit.B: 7 cups
- Compare the two numbers. The bigger number holds more.7 > 4
- Write the answer. A
Check. 4 cups is less than 7 cups. ✓
Watch out. Count the cups. Do not guess from the shape of the container.
Method. Count the cups for each container. Then find the most.
- Count the cups for each one. Each cup is one unit.A: 4 cups; B: 7 cups; C: 2 cups
- Find the biggest number. The biggest number holds the most.7 cups
- Write the answer. B
Check. The others hold less than 7. ✓
Watch out. Count the cups. Do not guess from the size of the container.
Method. Count the cups for each container. Then find the least.
- Count the cups for each one. Each cup is one unit.A: 3 cups; B: 6 cups; C: 5 cups
- Find the smallest number. The smallest number holds the least.3 cups
- Write the answer. A
Check. The others hold more than 3. ✓
Watch out. Count the cups. Do not guess from the size of the container.
Method. Count the cups for each one. Then put them in order, least first.
- Count the cups for each one. Each cup is one unit.A: 2 cups; B: 5 cups; C: 3 cups
- Put them in order. Start with the smallest number.A, C, B
- Write the answer. A, C, B
Check. There are 3 containers in the question and 3 in the answer. ✓
Watch out. Check you have written every letter once.
Key words. Empty means nothing inside. Quarter full means a quarter of the way up.
Method. Look at how high the water reaches.
- Look at the water. Compare it with the top and the bottom of the container.This container: the water reaches the top
- Find the matching word. Empty, quarter full, half full or full.full
- Write the answer. full
Check. Check: the water is the water reaches the top. ✓
Watch out. The water starts at the bottom. Do not count the empty space at the top.
Method. Count the cups already in the jug. Then count how many more fill the empty spaces.
- Count the cups already in the jug. Count the full spaces.2 cups
- Count the empty spaces left. Each empty space needs one more cup.6 − 2 = 4
- Write the answer. 4 more cups
Check. 2 + 4 = 6. ✓
Watch out. Count the empty spaces, not the full ones.
Method. Use cups of water to measure. Count the cups, then compare the two numbers.
- Fill the first container with cups. Count how many cups it takes.Count the cups for the first one
- Fill the second container with cups. Count how many cups it takes.Count the cups for the second one
- Compare the two numbers. The bigger number holds more.Count the cups for each one and compare the two numbers.
Check. Use the same kind of cup each time, so the count is fair. ✓
Watch out. Use the same cup for both containers.
Method. Use cups of water to measure. Count the cups, then compare the two numbers.
- Fill the first container with cups. Count how many cups it takes.Count the cups for the first one
- Fill the second container with cups. Count how many cups it takes.Count the cups for the second one
- Compare the two numbers. The bigger number holds more.Fill one bowl with cups and count them. Then do the same for the other bowl. Compare the two numbers.
Check. Use the same kind of cup each time, so the count is fair. ✓
Watch out. Use the same cup for both containers.
Half full and quarter full
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
A container can be empty, quarter full, half full or full.
Half full means the water reaches halfway up. A half is one of two equal parts.
Quarter full means the water reaches a quarter of the way up. A quarter is one of four equal parts. Four quarters make one whole. A half full jug has more water than a quarter full jug.
Key ideas
- A half is one of two equal parts.
- A quarter is one of four equal parts.
- Four quarters make one whole.
- Half full has more water than quarter full.
Key words. Half full means the water is halfway up.
Method. Look for the container that is half full.
- Look at each container. Check how high the water reaches.A: quarter full; B: half full; C: full
- Find the one that is half full. Only one container matches.B: half full
- Write the answer. B
Check. The other containers are not half full. ✓
Watch out. Look at the water, not at the shape of the container.
Method. Look at the water. The one with more water is higher up.
- Look at each container. Check how high the water reaches.A: quarter full; B: half full
- Find the one with more water. The higher the water, the more it holds.B has more water
- Write the answer. B
Check. The water in B is higher than in the others. ✓
Watch out. Compare the same kind of container. Look at how high the water reaches.
Method. Start with the full jug. Then pour some of the water out.
- Start with the full jug. A full jug has all of the water in it.full
- Pour out half of the water. Some of the water is poured away.Take away half
- Look at what is left. Check how high the water reaches now.the water is halfway up
- Write the answer. half full
Check. Half of a full jug is half full. ✓
Watch out. Look at how high the water is. Do not guess from the picture of the empty part.
Watch out
Watch out: a quarter is smaller than a half. A quarter full jug has less water than a half full jug.
Exam tip
Grown-up tip. Fold a piece of paper in half, then in half again. Show your child that four quarters make one whole. Then pour water into a cup and mark the halfway line together.
Exercise 8D Half full and quarter full
Non-calculatorKey words. Half full means the water is halfway up.
Method. Look for the container that is half full.
- Look at each container. Check how high the water reaches.A: quarter full; B: full; C: half full; D: empty
- Find the one that is half full. Only one container matches.C: half full
- Write the answer. C
Check. The other containers are not half full. ✓
Watch out. Look at the water, not at the shape of the container.
Key words. Quarter full means the water is a quarter of the way up.
Method. Look for the container that is quarter full.
- Look at each container. Check how high the water reaches.A: half full; B: quarter full; C: empty
- Find the one that is quarter full. Only one container matches.B: quarter full
- Write the answer. B
Check. The other containers are not quarter full. ✓
Watch out. Look at the water, not at the shape of the container.
Key words. Full means the water reaches the top.
Method. Look for the container that is full.
- Look at each container. Check how high the water reaches.A: half full; B: full; C: quarter full
- Find the one that is full. Only one container matches.B: full
- Write the answer. B
Check. The other containers are not full. ✓
Watch out. Look at the water, not at the shape of the container.
Key words. Empty means there is nothing in it.
Method. Look for the container that is empty.
- Look at each container. Check how high the water reaches.A: quarter full; B: empty
- Find the one that is empty. Only one container matches.B: empty
- Write the answer. B
Check. The other containers are not empty. ✓
Watch out. Look at the water, not at the shape of the container.
Method. Look at the water. The one with more water is higher up.
- Look at each container. Check how high the water reaches.A: half full; B: full
- Find the one with more water. The higher the water, the more it holds.B has more water
- Write the answer. B
Check. The water in B is higher than in the others. ✓
Watch out. Compare the same kind of container. Look at how high the water reaches.
Method. Look at the water. The one with less water is lower down.
- Look at each container. Check how high the water reaches.A: full; B: quarter full
- Find the one with less water. The higher the water, the more it holds.B has less water
- Write the answer. B
Check. The water in B is lower than in the others. ✓
Watch out. Compare the same kind of container. Look at how high the water reaches.
Method. Look at how full each one is. Start with the emptiest.
- Look at each container. Check how high the water reaches.A: half full; B: empty; C: quarter full; D: full
- Put them in order. Start with the one that has the least water.B, C, A, D
- Write the answer. B, C, A, D
Check. There are 4 containers in the question and 4 in the answer. ✓
Watch out. Empty comes first, then quarter full, then half full, then full.
Key words. Empty means nothing inside. Quarter full means a quarter of the way up.
Method. Look at how high the water reaches.
- Look at the water. Compare it with the top and the bottom of the container.Container A: the water is a quarter of the way up
- Find the matching word. Empty, quarter full, half full or full.quarter full
- Write the answer. quarter full
Check. Check: the water is the water is a quarter of the way up. ✓
Watch out. The water starts at the bottom. Do not count the empty space at the top.
Key words. Empty means nothing inside. Quarter full means a quarter of the way up.
Method. Look at how high the water reaches.
- Look at the water. Compare it with the top and the bottom of the container.Container B: the water is halfway up
- Find the matching word. Empty, quarter full, half full or full.half full
- Write the answer. half full
Check. Check: the water is the water is halfway up. ✓
Watch out. The water starts at the bottom. Do not count the empty space at the top.
Key words. Empty means nothing inside. Quarter full means a quarter of the way up.
Method. Look at how high the water reaches.
- Look at the water. Compare it with the top and the bottom of the container.Container C: the water reaches the top
- Find the matching word. Empty, quarter full, half full or full.full
- Write the answer. full
Check. Check: the water is the water reaches the top. ✓
Watch out. The water starts at the bottom. Do not count the empty space at the top.
Method. Look at how much is empty before the water is added.
- Look at the jug. The top half is empty at the start.Half of the jug is empty
- Fill the empty half. Filling to the top fills the empty half.The jug is filled with one more half
- Write the answer. Half the jug
Check. Half and half make a whole, so the jug is now full. ✓
Watch out. Half full plus half more makes full.
Method. Look at the water. The one with more water is higher up.
- Look at each container. Check how high the water reaches.A: quarter full; B: half full
- Find the one with more water. The higher the water, the more it holds.B has more water
- Write the answer. B
Check. The water in B is higher than in the others. ✓
Watch out. Compare the same kind of container. Look at how high the water reaches.
Method. Think about what one whole jug looks like when it is shared into equal parts.
- Share a whole jug into equal parts. Each part is one quarter.1 quarter + 1 quarter + 1 quarter + 1 quarter
- Count the quarters. Four quarters make one whole.4 quarters = 1 whole
- Write the answer. 4 quarters
Check. A quarter is one of four equal parts. ✓
Watch out. A quarter is one of four equal parts, not one of two.
Method. Compare the two jugs. Look at how high the water reaches.
- Compare the two fractions. Half is bigger than a quarter.1/2 is bigger than 1/4
- Look at the water levels. The half full jug has water higher up.Half full is higher than quarter full
- Write the answer. No. Half full has more water than quarter full.
Check. Half of a jug is more than a quarter of it. ✓
Watch out. Two fractions can look alike, but the bigger one has more water.
Measuring capacity with cups
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
We can measure how much a jug holds with cups. Fill a cup with water. Pour it into the jug. Count the cups until the jug is full.
Each cup is one unit. The number of cups tells us how much the jug holds. Look at the lines inside the jug. Each space between two lines is one cup.
Key ideas
- A cup is a non-standard unit for capacity.
- Count the cups to find how much a container holds.
- The cups must all be the same size.
- To find how many more, take the cups already in from the total.
Key words. To count is to say one number for each thing, in order.
Method. Touch each one once and say its number. The last number you say is how many there are.
- Count each one, in order. Each one gets one number. Do not miss one.1, 2, 3, 4, 5, 6
- Look at the last number. The last number tells us how many altogether.The last number is 6.
- Write the answer. There are 6 cups.
Check. Count again from the other side. You get 6 again. ✓
Watch out. Move each one to one side as you count it, so you do not count it twice.
Method. Count the cups already in the jug. Then count how many more fill the empty spaces.
- Count the cups already in the jug. Count the full spaces.5 cups
- Count the empty spaces left. Each empty space needs one more cup.8 − 5 = 3
- Write the answer. 3 more cups
Check. 5 + 3 = 8. ✓
Watch out. Count the empty spaces, not the full ones.
Key words. More means a bigger number. Take away to find out how many more.
Method. Find how many more. Take the smaller number away from the bigger number.
- Count the cups for each. Use the numbers you counted.bowl: 5 cups, glass: 2 cups
- Take the smaller number away. What is left is how many more.5 − 2 = 3
- Write the answer. 3 more cups
Check. Add them back: 2 + 3 = 5. ✓
Watch out. Start with the bigger number and take the smaller one away.
Watch out
Watch out: a bigger cup holds more, so fewer big cups fill the same jug. Always say which cup you used.
Exam tip
Grown-up tip. Use a jug and two cups of different sizes at the sink. Ask: “How many cups fill the jug?” Then try the other cup. Talk about why the numbers are different.
Exercise 8E Measuring with cups
Non-calculatorKey words. To count is to say one number for each thing, in order.
Method. Touch each one once and say its number. The last number you say is how many there are.
- Count each one, in order. Each one gets one number. Do not miss one.1, 2, 3, 4, 5
- Look at the last number. The last number tells us how many altogether.The last number is 5.
- Write the answer. There are 5 cups.
Check. Count again from the other side. You get 5 again. ✓
Watch out. Move each one to one side as you count it, so you do not count it twice.
Key words. To count is to say one number for each thing, in order.
Method. Touch each one once and say its number. The last number you say is how many there are.
- Count each one, in order. Each one gets one number. Do not miss one.1, 2, 3, 4
- Look at the last number. The last number tells us how many altogether.The last number is 4.
- Write the answer. There are 4 cups.
Check. Count again from the other side. You get 4 again. ✓
Watch out. Move each one to one side as you count it, so you do not count it twice.
Method. Count the cups already in the jug. Then count how many more fill the empty spaces.
- Count the cups already in the jug. Count the full spaces.2 cups
- Count the empty spaces left. Each empty space needs one more cup.6 − 2 = 4
- Write the answer. 4 more cups
Check. 2 + 4 = 6. ✓
Watch out. Count the empty spaces, not the full ones.
Method. Count the cups already in the jug. Then count how many more fill the empty spaces.
- Count the cups already in the jug. Count the full spaces.3 cups
- Count the empty spaces left. Each empty space needs one more cup.8 − 3 = 5
- Write the answer. 5 more cups
Check. 3 + 5 = 8. ✓
Watch out. Count the empty spaces, not the full ones.
Method. Count the cups already in the jug. Then count how many more fill the empty spaces.
- Count the cups already in the jug. Count the full spaces.4 cups
- Count the empty spaces left. Each empty space needs one more cup.7 − 4 = 3
- Write the answer. 3 more cups
Check. 4 + 3 = 7. ✓
Watch out. Count the empty spaces, not the full ones.
Method. Count the cups for each container. Then see which one holds more.
- Count the cups for A. Each cup is one unit.A: 5 cups
- Count the cups for B. Each cup is one unit.B: 8 cups
- Compare the two numbers. The bigger number holds more.8 > 5
- Write the answer. B
Check. 5 cups is less than 8 cups. ✓
Watch out. Count the cups. Do not guess from the shape of the container.
Key words. More means a bigger number. Take away to find out how many more.
Method. Find how many more. Take the smaller number away from the bigger number.
- Count the cups for each. Use the numbers you counted.bowl: 6 cups, glass: 3 cups
- Take the smaller number away. What is left is how many more.6 − 3 = 3
- Write the answer. 3 more cups
Check. Add them back: 3 + 3 = 6. ✓
Watch out. Start with the bigger number and take the smaller one away.
Method. Start with what is already there. Then add the ones you put in.
- Start with 3. That is how many are already there.3
- Add 4 more. Count on from the first number.3 + 4 = 7
- Write the answer. 7 cups
Check. Take 4 away from 7 to get back to 3. ✓
Watch out. Count on from the first number. Do not start again at one.
Method. Count the cups already in the jug. Then count how many more fill the empty spaces.
- Count the cups already in the jug. Count the full spaces.6 cups
- Count the empty spaces left. Each empty space needs one more cup.9 − 6 = 3
- Write the answer. 3 more cups
Check. 6 + 3 = 9. ✓
Watch out. Count the empty spaces, not the full ones.
Method. Count the cups already in the jug. Then count how many more fill the empty spaces.
- Count the cups already in the jug. Count the full spaces.8 cups
- Count the empty spaces left. Each empty space needs one more cup.10 − 8 = 2
- Write the answer. 2 more cups
Check. 8 + 2 = 10. ✓
Watch out. Count the empty spaces, not the full ones.
Method. Count in groups of 2. How many groups of 2 fill the jug?
- Count the cups in the jug. The jug holds this many cups.6 cups
- Count on in 2s. Each glass takes 2 cups.2, 4, 6
- Write the answer. Count the groups you said.3 glasses
Check. 3 glasses of 2 cups make 6 cups. ✓
Watch out. Count the glasses, not the cups.
Method. Think about what the count is for. Each cup is one unit.
- Look at the two counts. Different cups give different counts.3 big cups and 6 small cups
- Think about the cups. A big cup holds more, so fewer of them fill the bowl.Big cups = fewer cups
- Write the answer. Both are right. The number depends on the size of the cup.
Check. Use the same kind of cup each time to get the same count. ✓
Watch out. Always say which cup you used when you measure.
Chapter summary
| Skill | Method |
|---|---|
| Heavy and light | The side of the balance scale that goes down is the heavier side. |
| Heavier and lighter | Compare two things on a scale. Use the words heavier than or lighter than. |
| Counting cubes | Add cubes until the scale is level. Count the cubes. That is how heavy it is in cubes. |
| Full and empty | A full container has no room for more. An empty container has nothing inside. |
| Half and quarter full | Half full is halfway up. Quarter full is a quarter of the way up. Four quarters make one whole. |
| Measuring with cups | Fill the container with cups and count them. The number of cups is how much it holds. |
Can you…?
- I can say which object is heavy and which is light
- I can say which thing is heavier than another, using a balance scale
- I can count cubes to find out how heavy something is
- I can say which container is full, empty or part full
- I can say which container holds more, by counting cups
- I can say what half full and quarter full mean
Key terms
- mass
- how heavy something is
- heavy and light
- heavy means it weighs a lot; light means it weighs less
- heavier than
- weighs more than another thing
- lighter than
- weighs less than another thing
- balance scale
- a scale with a pan on each side, which shows which side is heavier
- cube
- a non-standard unit we count to measure how heavy something is
- capacity
- how much a container can hold
- full
- there is no room for more
- empty
- there is nothing inside
- half full
- the water reaches halfway up the container
- quarter full
- the water reaches a quarter of the way up the container
- cup
- a non-standard unit we use to measure capacity
Exercise 8Z Check-up
Non-calculatorKey words. Heavier than means weighs more. Lighter than means weighs less.
Method. The heavier one is the one that makes its side go down on the scale.
- Look at the scale. The side that goes down holds the heavier object.Pan A goes down
- Find the heavier object. The heavier object is on the low side.A is the bag
- Write the answer. A, the bag
Check. The other side goes up, so it is the other one. ✓
Watch out. A big thing can be light, and a small thing can be heavy. Look at the scale, not the size.
Key words. A balance scale is level when both sides weigh the same. A cube is a unit we can count.
Method. Add cubes to one pan until the scale is level. Then count the cubes.
- Look at the ball and the scale. When the beam is level, both sides weigh the same.The ball weighs the same as the cubes.
- Count the cubes, one at a time. Touch each cube once so you do not miss one.1, 2, 3
- Write the answer. The last number is how many cubes there are.3 cubes
Check. Take one cube away. The scale tips, so 3 cubes is exactly right. ✓
Watch out. Use cubes that are all the same size. Different sizes give a wrong count.
Key words. Full means the water reaches the top.
Method. Look for the container that is full.
- Look at each container. Check how high the water reaches.A: half full; B: full; C: empty
- Find the one that is full. Only one container matches.B: full
- Write the answer. B
Check. The other containers are not full. ✓
Watch out. Look at the water, not at the shape of the container.
Method. Count the cups for each container. Then see which one holds more.
- Count the cups for A. Each cup is one unit.A: 5 cups
- Count the cups for B. Each cup is one unit.B: 3 cups
- Compare the two numbers. The bigger number holds more.5 > 3
- Write the answer. A
Check. 3 cups is less than 5 cups. ✓
Watch out. Count the cups. Do not guess from the shape of the container.
Key words. Half full means the water is halfway up.
Method. Look for the container that is half full.
- Look at each container. Check how high the water reaches.A: quarter full; B: half full; C: full
- Find the one that is half full. Only one container matches.B: half full
- Write the answer. B
Check. The other containers are not half full. ✓
Watch out. Look at the water, not at the shape of the container.
Key words. To count is to say one number for each thing, in order.
Method. Touch each one once and say its number. The last number you say is how many there are.
- Count each one, in order. Each one gets one number. Do not miss one.1, 2, 3, 4, 5, 6, 7
- Look at the last number. The last number tells us how many altogether.The last number is 7.
- Write the answer. There are 7 cups.
Check. Count again from the other side. You get 7 again. ✓
Watch out. Move each one to one side as you count it, so you do not count it twice.
Method. Count the cups already in the jug. Then count how many more fill the empty spaces.
- Count the cups already in the jug. Count the full spaces.2 cups
- Count the empty spaces left. Each empty space needs one more cup.5 − 2 = 3
- Write the answer. 3 more cups
Check. 2 + 3 = 5. ✓
Watch out. Count the empty spaces, not the full ones.
Key words. Heaviest means the most heavy. Lightest means the least heavy.
Method. Put the objects in a line, from the heaviest to the lightest. Then find the heaviest one.
- Put the objects in a line. The heaviest goes at the front.brick > book > apple
- Find the heaviest one. The heaviest one is at the front of the line.brick is the heaviest
- Write the answer. The brick is the heaviest.
Check. The first one is heavier than the last one, so the line is right. ✓
Watch out. Read every sentence. Do not pick the first object you read about.
Key words. Empty means nothing inside. Quarter full means a quarter of the way up.
Method. Look at how high the water reaches.
- Look at the water. Compare it with the top and the bottom of the container.This container: the water is a quarter of the way up
- Find the matching word. Empty, quarter full, half full or full.quarter full
- Write the answer. quarter full
Check. Check: the water is the water is a quarter of the way up. ✓
Watch out. The water starts at the bottom. Do not count the empty space at the top.
Key words. Lightest is the least heavy. Heaviest is the most heavy.
Method. Lightest first. Compare two objects at a time.
- Compare two objects. Use the scale or the cubes to see which is heavier.apple < bag < brick
- Put them in a line. Start with the lightest one.apple, bag, brick
- Write the answer. apple, bag, brick
Check. There are 3 objects in the question and 3 in the answer. ✓
Watch out. Check that you have not left one out.
Total 16 marks. Allow about 16 minutes.
Exercise 8X End-of-chapter quiz
Non-calculatorKey words. Heavier than means weighs more. Lighter than means weighs less.
Method. The lighter one is the one that makes its side go up on the scale.
- Look at the scale. The side that goes down holds the heavier object.Pan A goes down
- Find the lighter object. The lighter object is on the high side.B is the book
- Write the answer. B, the book
Check. The other side goes down, so it is the other one. ✓
Watch out. A big thing can be light, and a small thing can be heavy. Look at the scale, not the size.
Key words. A balance scale is level when both sides weigh the same. A cube is a unit we can count.
Method. Add cubes to one pan until the scale is level. Then count the cubes.
- Look at the bag and the scale. When the beam is level, both sides weigh the same.The bag weighs the same as the cubes.
- Count the cubes, one at a time. Touch each cube once so you do not miss one.1, 2, 3, 4, 5, 6, 7
- Write the answer. The last number is how many cubes there are.7 cubes
Check. Take one cube away. The scale tips, so 7 cubes is exactly right. ✓
Watch out. Use cubes that are all the same size. Different sizes give a wrong count.
Key words. Empty means there is nothing in it.
Method. Look for the container that is empty.
- Look at each container. Check how high the water reaches.A: half full; B: empty; C: full
- Find the one that is empty. Only one container matches.B: empty
- Write the answer. B
Check. The other containers are not empty. ✓
Watch out. Look at the water, not at the shape of the container.
Key words. Empty means nothing inside. Quarter full means a quarter of the way up.
Method. Look at how high the water reaches.
- Look at the water. Compare it with the top and the bottom of the container.This container: the water is halfway up
- Find the matching word. Empty, quarter full, half full or full.half full
- Write the answer. half full
Check. Check: the water is the water is halfway up. ✓
Watch out. The water starts at the bottom. Do not count the empty space at the top.
Method. Count the cups for each container. Then see which one holds more.
- Count the cups for A. Each cup is one unit.A: 4 cups
- Count the cups for B. Each cup is one unit.B: 6 cups
- Compare the two numbers. The bigger number holds more.6 > 4
- Write the answer. B
Check. 4 cups is less than 6 cups. ✓
Watch out. Count the cups. Do not guess from the shape of the container.
Method. Count the cubes on each scale. Then choose the one that needs fewer cubes.
- Count the cubes for A. Each cube is one unit.A: 7 cubes
- Count the cubes for B. Each cube is one unit.B: 2 cubes
- Compare the two numbers. The bigger number is more cubes.7 > 2
- Write the answer. B (the apple)
Check. 2 is smaller than 7, so the answer is right. ✓
Watch out. Count the cubes on both scales. Do not guess from the size of the objects.
Method. Count the cups already in the jug. Then count how many more fill the empty spaces.
- Count the cups already in the jug. Count the full spaces.6 cups
- Count the empty spaces left. Each empty space needs one more cup.8 − 6 = 2
- Write the answer. 2 more cups
Check. 6 + 2 = 8. ✓
Watch out. Count the empty spaces, not the full ones.
Method. Compare the two objects, then decide if the sentence is true.
- Find the two objects. Read the sentence carefully.book and bag
- Say which one is heavier. The heavier one makes its side go down.The bag is heavier
- Write the answer. Does the sentence match what we found?False
Check. Read the sentence the other way round to check. ✓
Watch out. Heavier and lighter mean opposite things. Read them carefully.
Method. Look at how full each one is. Start with the emptiest.
- Look at each container. Check how high the water reaches.A: half full; B: empty; C: quarter full
- Put them in order. Start with the one that has the least water.B, C, A
- Write the answer. B, C, A
Check. There are 3 containers in the question and 3 in the answer. ✓
Watch out. Empty comes first, then quarter full, then half full, then full.
Method. Compare the two jugs. Look at how high the water reaches.
- Compare the two fractions. Half is bigger than a quarter.1/2 is bigger than 1/4
- Look at the water levels. The half full jug has water higher up.Half full is higher than quarter full
- Write the answer. No. Half full has more water than quarter full.
Check. Half of a jug is more than a quarter of it. ✓
Watch out. Two fractions can look alike, but the bigger one has more water.