Measure the world in metric units, and read the time on any clock.
Measure length in millimetres, centimetres, metres and kilometres, mass in grams and kilograms, and capacity in millilitres and litres. Read clocks, work out how long things take, and find perimeter and area.
You are ready for this book if
You can measure a pencil in centimetres with a ruler.
One step down M1.6 Longer, heavier, fuller, and o'clock
Written and drawn by attnom. Free to read, print and share.
M2.6.1 Chapter 1
Centimetres and metres
My table is 2 m long. Is that the same as 200 cm?
Your guess
Pick one before you read on. It is fine to be wrong.
By the end you can
Measure and draw lines to the nearest centimetre
Measure a room in metres and centimetres
Change 2 m 35 cm into 235 cm
Look at a ruler. It has a row of marks and numbers.
The gap between two numbers is one centimetre. We write cm.
To measure a pencil, line up one end with the 0 mark.
Draw it first
Measure a pencil
1 A ruler starts at 0. Find the 0 mark.
2 Put one end of the pencil on the 0 mark.
3 Read the number at the other end. It is 7 cm.
Do not start at the end of the ruler. Start at the 0 mark.
Sometimes the end falls between two marks.
The length to the nearest centimetre is the closest whole number.
The short tick is half way between two numbers. Before it, stay on the lower number. Past it, go up.
A ruler is too short for a room. For long things we use the metre.
100 cm make 1 m. We write m.
Worked example
A table is 2 m 35 cm long. Write this in centimetres.
1 m is 100 cm. So 2 m is 200 cm.
2 m 35 cm is 200 cm and 35 cm more.
200 + 35 = 235.
Answer: 235 cm
See it three ways
With things
Lay a 1 m string along a wall two times. Then measure 35 cm more with a ruler.
As a picture
In symbols
200 cm + 35 cm = 235 cm.
Try it
Make a metre string and measure a room
You need: a piece of string, longer than 1 m, a ruler, a pencil.
Put one end of the string on the 0 mark.
Pinch the string at the ruler's last number, such as 30. Put the 0 mark on your pinch and repeat.
Keep adding the centimetres. Stop when you reach 100 cm. Tie a knot there.
Lay your string along one wall of a room. Count how many strings fit.
Measure what is left with the ruler. Write the length as metres and centimetres.
What you will see: Your string is 1 m, which is 100 cm. You can change your answer to centimetres: each string is 100 cm.
If you cannot try it, this is what happens.
A wrong idea many people have
200 cm is longer than 2 m. After all, 200 is more than 2.
Why it feels right: We learn that a bigger number means a bigger amount.
The test that breaks it: Measure a wall 3 m long two ways. Use your 1 m string, then a 30 cm ruler. The string fits 3 times. The ruler fits 10 times.
What is true: The wall did not change. A small unit fits more times, so its number is bigger. 200 cm and 2 m are the same length.
Key words
centimetre
a small length. The gap between two numbers on a ruler. We write cm.
metre
a length of 100 cm. We write m.
nearest
closest. The nearest centimetre is the closest whole number of cm.
Back to your guess
The answer is C: Yes. 100 cm make 1 m, so 2 m is 200 cm.
Yes. 100 cm make 1 m, so 2 m is 200 cm. The same table, two ways to say its length.
Check yourself
Try each one before you look. A wrong answer tells you where to go next.
How long is the stick?
See the answer
8 cm
The stick starts at 0 and ends at the 8 mark. So it is 8 cm long.
If you chose A: You may have counted every mark, including 0. The 0 mark is the start, not a centimetre.
If you chose C: You read the end of the ruler. Read the number where the stick ends.
A leaf is longer than 9 cm. Its tip is past the half way tick to 10. How long is it to the nearest centimetre?
See the answer
10 cm
The tip is past the half way tick. It is closer to 10 than to 9.
If you chose A: The tip is past half way. It is nearer to 10 than to 9. Go up to 10.
Amina measures a wall. It is 4 m 5 cm long. How many centimetres is that?
See the answer
405 cm
4 m is 400 cm. 400 + 5 = 405.
If you chose A: You wrote 5 cm as 50 cm. 5 cm is only 5. 4 m is 400 cm, and 400 + 5 = 405.
If you chose B: You joined 4 and 5. 4 m is 400 cm, not 4 cm.
Change 3 m 20 cm into centimetres.
See the answer
320 cm
3 m is 300 cm. 300 + 20 = 320.
Which is longer, 150 cm or 2 m?
See the answer
2 m
2 m is 200 cm. 200 is more than 150.
If you chose A: You compared 150 with 2. Change to the same unit first. 2 m is 200 cm.
If you chose C: 2 m is 200 cm. 200 is not the same as 150.
Draw a line 8 cm long with a ruler. How do you do it?
See the answer
Put a dot at the 0 mark. Put another dot at the 8 mark. Join the dots with the ruler as a guide.
The line starts at 0 and ends at 8. So it is 8 cm long. Measure it again to check.
A stick lies on a ruler. Its left end is on the 2 mark. Its right end is on the 9 mark. How long is the stick?
See the answer
7 cm
The stick starts at 2 and ends at 9. The length is the gap between them. 9 − 2 = 7. You can also count the centimetres from 2 to 9: 7.
If you chose B: You read the right end only, as if it began at 0. The stick began at 2. The first 2 cm are not part of it.
If you chose C: You counted the numbers 2, 3, 4 and on to 9. That is 8 numbers. A length counts the centimetres between them. There are 7.
A rope is 3 m long. How many centimetres is that?
See the answer
300 cm
1 m is 100 cm. 3 m is 3 × 100 = 300 cm.
If you chose A: You used 10 cm for 1 m. A metre is 100 cm. So 3 m is 3 lots of 100 cm.
If you chose B: That is 1 000 cm for each metre. A metre is 100 cm. So 3 m is 300 cm.
Keep it
Copy this into your exercise book.
Put the 0 mark at one end. Read the other end. 100 cm make 1 m. 2 m 35 cm is 200 + 35 = 235 cm.
Draw: A ruler with a pencil from 0 to 7. Under it, write 100 cm = 1 m.
M2.6.2 Chapter 2
Millimetres and kilometres
Which unit is for an ant? Which is for a long road?
Your guess
Pick one before you read on. It is fine to be wrong.
By the end you can
Measure small things to the nearest millimetre
Say that 1 000 m make 1 km
Choose the right unit: mm, cm, m or km
A centimetre is too big for a grain of rice.
A metre is too small for the road to the next town.
A millimetre is very small. We write mm. Ten sheets of paper in a pile are about 1 mm thick.
Draw it first
Look closely at one centimetre
1 Look at the gap from 0 to 1 on the ruler. It is 1 cm.
2 Between 0 and 1 there are 10 small gaps. Each one is 1 mm.
3 Count the small gaps. 10 mm make 1 cm.
10 mm make 1 cm. 100 cm make 1 m. So 1 000 mm make 1 m.
To read mm, first read the whole cm. Then count the small marks after it.
If the end is between two small marks, pick the nearer one.
The strip ends 2 cm and 3 small marks from 0.
Worked example
A paper strip is 2 cm 3 mm long. Write this in mm.
1 cm is 10 mm. So 2 cm is 20 mm.
2 cm 3 mm is 20 mm and 3 mm more.
20 + 3 = 23.
Answer: 23 mm
For a long way we use the kilometre. We write km.
See it three ways
With things
Walk along a field that is 100 m long. Walk its length 10 times. You have walked 1 000 m, or 1 km.
As a picture
In symbols
10 × 100 m = 1 000 m = 1 km.
Most people walk 1 km in about 12 to 15 minutes.
Pick the unit that fits the thing you measure.
A good unit gives a number you can picture.
Try it
Measure small things in mm
You need: a ruler with mm marks, a bean, a seed or a button.
Lay the small thing next to the ruler. Put one end on the 0 mark.
Read the whole cm just before the other end.
Count the small marks after it. Each one is 1 mm.
Write the length in mm. A length of 1 cm 4 mm is 14 mm.
What you will see: You count small marks of 1 mm each. A grain of rice is only a few mm wide.
If you cannot try it, this is what happens.
A wrong idea many people have
1 km is 100 m, because 100 cm make 1 m.
Why it feels right: Going from cm to m uses 100. It seems that m to km will too.
The test that breaks it: Walk across a field 100 m long. It takes a bit more than a minute. Walking 1 km takes 12 to 15 minutes. That is about 10 times as long.
What is true: 1 km is 1 000 m. It is 10 fields of 100 m, end to end.
Key words
millimetre
a very small length. 10 mm make 1 cm. We write mm.
kilometre
a long length. 1 000 m make 1 km. We write km.
Back to your guess
The answer is B: Use mm for the ant and km for the road.
Use a small unit for a small thing. Use a big unit for a long way. So mm for the ant, and km for the road.
Check yourself
Try each one before you look. A wrong answer tells you where to go next.
Which unit is best for the distance between two towns?
See the answer
km
Towns are far apart. A kilometre is a long length, so it fits.
If you chose A: A millimetre is tiny. It is for things like a grain of rice.
If you chose B: A metre suits a room. Towns are thousands of metres apart. Use km.
The strip ends at 3 cm and 7 small marks. How many mm long is it?
See the answer
37 mm
3 cm is 30 mm. Then 7 small marks make 7 mm more. 30 + 7 = 37.
Change 4 km into metres.
See the answer
4 000 m
1 km is 1 000 m. So 4 km is 4 × 1 000 = 4 000 m.
From an earlier chapter
Kofi has a string 1 m 40 cm long. How many centimetres is that?
See the answer
140 cm
1 m is 100 cm. 100 + 40 = 140.
A road is 2 km 500 m long. How many metres is that?
See the answer
2 500 m
2 km is 2 000 m. 2 000 + 500 = 2 500.
How many mm make 1 m?
See the answer
1 000 mm
1 m is 100 cm. Each cm is 10 mm. So 100 × 10 = 1 000.
A seed ends 1 cm and 2 small marks from 0. How many mm long is it?
See the answer
12 mm
1 cm is 10 mm. Then 2 small marks make 2 mm more. 10 + 2 = 12.
If you chose A: You read 1 and 2 together as 12 cm. The seed is only 1 cm and 2 mm long.
If you chose C: 1 cm is 10 mm, not 100 mm. So 1 cm 2 mm is 10 + 2 = 12 mm.
Which is the longest: 900 m, 1 500 mm or 1 km?
See the answer
1 km
Use metres for all three. 1 000 mm is 1 m. So 1 500 mm is less than 2 m. 1 km is 1 000 m. The most is 1 km.
If you chose A: You may have used 100 m for 1 km. 1 km is 1 000 m. That is more than 900 m.
If you chose B: You picked the biggest number. 1 500 mm is 1 m 50 cm, which is short.
Ravi has a pencil 14 cm long. How many mm is that?
See the answer
140 mm
1 cm is 10 mm. So 14 cm is 14 × 10 = 140 mm.
If you chose B: You kept the same number. But 1 cm is 10 mm. So 14 cm is 14 lots of 10.
If you chose C: You used 100 mm for 1 cm. 1 cm is only 10 mm. So 14 cm is 140 mm.
Which length is about right for a pencil?
See the answer
18 cm
A pencil is about as long as a hand. That is about 18 cm. 18 mm is too short and 18 m is too long.
If you chose A: You may have mixed up mm and cm. 18 mm is less than 2 cm, about a thumb wide.
If you chose C: You may have mixed up m and mm. 18 m is longer than most classrooms. A pencil fits in your hand.
Keep it
Copy this into your exercise book.
10 mm make 1 cm. 1 000 mm make 1 m. 1 000 m make 1 km. Use mm for an ant. Use cm for a book. Use m for a room. Use km for a road.
Draw: A ruler with 1 cm split into 10 small gaps. Write 10 mm = 1 cm.
M2.6.3 Chapter 3
Tenths and the decimal point
My ruler says 1.5 m. Is that 1 m 5 cm?
Your guess
Pick one before you read on. It is fine to be wrong.
By the end you can
Read 0.1 as one tenth, the same as 1/10
Write 1 m 50 cm as 1.5 m
Read 1.5 and 1,5 as the same number, written two ways
Think of 1 m cut into 10 equal parts. Each part is 10 cm.
Draw it first
Cut a metre into tenths
1 This bar is 1 m long.
2 Cut it into 10 equal parts. Each part is 10 cm.
3 One part is one tenth of a metre. It is 0.1 m.
One part is one tenth of the metre.
1/10 and 0.1 are two ways to write one tenth.
The dot in 0.1 is the decimal point. Digits after it are tenths.
In 1.5 m, the 1 is one whole metre. The 5 is five tenths.
On the number line, 1.5 is 5 tenths past 1.
5 tenths of a metre is 50 cm. That is half a metre.
Worked example
Write 1 m 50 cm in metres, with a decimal point.
10 cm is one tenth of a metre.
50 cm is 5 lots of 10 cm. That is 5 tenths.
1 m and 5 tenths is 1.5 m.
Answer: 1.5 m
Many countries use a comma as the decimal mark.
So 1,5 and 1.5 are the same number. Use the mark your own books use.
Two ways to write the same length.
See it three ways
With things
Mark a 1 m string every 10 cm. Count 5 marks from the start. That is 50 cm.
As a picture
In symbols
5 tenths = 5/10 = 0.5. So 1 m 50 cm = 1.5 m.
Try it
Mark tenths on your metre string
You need: your metre string from chapter 1, a ruler, a pencil.
Lay your string beside a ruler. Make a pencil mark at 10 cm.
Make a mark at every 10 cm after that. You get 10 parts.
Count 5 parts from the start. Measure them. You find 50 cm.
Lay the string along a chair or a box. Count the parts.
Say the length in tenths of a metre, like this: 0.8 m.
What you will see: Each part is one tenth of 1 m. 3 parts is 0.3 m. 7 parts is 0.7 m.
If you cannot try it, this is what happens.
A wrong idea many people have
1 m 5 cm is 1.5 m.
Why it feels right: The digits 1 and 5 are there. It seems you just add a dot between them.
The test that breaks it: Mark 5 cm on your marked string. Then find the 5th tenth mark. They are far apart. The 5th tenth mark is at 50 cm.
What is true: 1.5 m is 1 m 50 cm. 1 m 5 cm is a little more than 1 m. It is much less than 1.5 m.
Key words
tenth
one of 10 equal parts. We write 1/10 or 0.1.
decimal point
the dot in a number like 1.5. In many countries it is a comma.
Back to your guess
The answer is B: No. 1.5 m is 1 m and 50 cm.
The 5 after the point means 5 tenths. 5 tenths of a metre is 50 cm. So 1.5 m is 1 m 50 cm.
Check yourself
Try each one before you look. A wrong answer tells you where to go next.
Write 1 m 20 cm in metres, with a decimal point.
See the answer
1.2 m
20 cm is 2 lots of 10 cm. That is 2 tenths. So 1 m 20 cm is 1.2 m.
What number is the dot on?
See the answer
0.7
Each step is one tenth. The dot is on the 7th step. That is 7 tenths, or 0.7.
If you chose A: That is far too small. The dot is on the 7th mark. That is 7 tenths.
If you chose C: The line only goes up to 1. The dot is 7 tenths of the way, so it is 0.7.
Which is the same as 0.1?
See the answer
one tenth
0.1 is one tenth, the same as 1/10.
If you chose A: Ten is a whole number. 0.1 is a small part of one.
If you chose B: One half is 0.5, which is five tenths. 0.1 is only one tenth.
Which is longer, 1.5 m or 1 m 5 cm?
See the answer
1.5 m
1.5 m is 1 m 50 cm. 50 cm is more than 5 cm.
If you chose A: The .5 may look small. It means 5 tenths of a metre, which is 50 cm. 50 cm is more than 5 cm.
If you chose C: You read 1.5 m as 1 m 5 cm. The 5 means 5 tenths, which is 50 cm.
Ana lives where a comma is the decimal mark. Her tape says 2,4 m. Write it with a point, and in m and cm.
See the answer
2.4 m, or 2 m 40 cm
A comma and a point mean the same. 4 tenths of a metre is 40 cm.
From an earlier chapter
Which is longer, 1 km or 900 m?
See the answer
1 km
1 km is 1 000 m. 1 000 is more than 900.
If you chose A: You compared 1 with 900. Change to the same unit first. 1 km is 1 000 m. Go to M2.6.2.
Kofi cuts a 1 m string into 10 equal parts. He keeps the 4 shaded parts. How many cm is that?
See the answer
40 cm
1 m is 100 cm. 10 parts, so each part is 10 cm. 4 parts are 4 × 10 = 40 cm.
If you chose B: You counted 4 parts and called each part 1 cm. Each part is 10 cm.
If you chose C: You used 100 cm for each part. 100 cm is the whole string, not one part.
A rope ends at the dot on the line. How long is the rope?
See the answer
2.3 m
The dot is 3 steps after 2. Each step is one tenth. So the rope is 2 m and 3 tenths, 2.3 m.
If you chose A: You counted the steps back from 3. Count the steps forward from 2. There are 3.
If you chose B: The line only runs from 2 m to 3 m. The dot is between them. So the rope is between 2 m and 3 m.
Keep it
Copy this into your exercise book.
One tenth is 1/10 and 0.1. 10 tenths make 1. 1 m 50 cm is 1.5 m. 1,5 and 1.5 are the same number.
Draw: A bar for 1 m cut into 10 parts. Shade 5 and write 0.5 m.
M2.6.4 Chapter 4
Grams and kilograms
Is a big thing always heavier than a small thing?
Your guess
Pick one before you read on. It is fine to be wrong.
By the end you can
Weigh things on a scale in grams and kilograms
Read a scale where the marks go up in 100 g
Change 2 kg 300 g into 2 300 g
We can weigh things on a scale. For light things we use the gram. We write g.
For heavier things we use the kilogram. We write kg.
1 000 g make 1 kg. The water in a 1 litre bottle weighs about 1 kg.
Look at this scale. The numbers on it are kilograms.
Draw it first
Read a scale
1 The numbers on this scale are kilograms.
2 Between two numbers there are 10 marks. Each mark is 100 g.
3 The arrow is 3 marks past 2. That is 2 kg 300 g.
To read a scale, find the last number the arrow passed.
Then count the small marks after it. Each one is 100 g.
Worked example
Write 2 kg 300 g in grams.
1 kg is 1 000 g. So 2 kg is 2 000 g.
2 kg 300 g is 2 000 g and 300 g more.
2 000 + 300 = 2 300.
Answer:2 300 g
See it three ways
With things
The water in a 1 litre bottle weighs about 1 kg. That is 1 000 g.
As a picture
In symbols
10 × 100 g = 1 000 g = 1 kg. So 2 kg 300 g = 2 300 g.
A balance shows which of two things is heavier.
Try it
Make a balance
You need: a stick or a coat hanger, string, two bags the same, a stone as big as your fist, and dry leaves.
Be safe: Hang the balance low. Keep your feet and face away from the stone. Wash your hands after you touch leaves or soil.
Tie a string to the middle of the stick. Hang it from a hook.
Slide the string until the stick hangs level.
Hang a bag from each end, the same distance from the middle.
Put the stone in one bag. Fill the other bag with dry leaves.
Watch which side goes down.
What you will see: The stone side goes down. The small stone is heavier than the bag of leaves.
If you cannot try it, this is what happens.
A wrong idea many people have
A bigger thing is always heavier.
Why it feels right: Big rocks and big boxes are often heavy.
The test that breaks it: Fill a bag with dry leaves. Put a stone as big as your fist in the other bag. The leaves take far more room. The stone side goes down.
What is true: Size is not weight. A bag of dry leaves is big but light. A small stone is heavy. Weigh them to find out.
Key words
gram
a small amount of weight. We write g.
kilogram
1 000 g. We write kg.
balance
two bags on a stick. The lower side is heavier.
Back to your guess
The answer is B: No. A small thing can be heavier than a big thing.
No. A small stone can be heavier than a big bag of leaves. The leaves still weigh something, only less. Size alone does not tell you.
Check yourself
Try each one before you look. A wrong answer tells you where to go next.
What does the arrow show?
See the answer
1 kg 400 g
The arrow passed 1 kg. It is 4 marks further. 4 × 100 g = 400 g.
If you chose A: You counted 4 marks, but each mark is 100 g. So 4 marks are 400 g.
If you chose C: You counted only the marks. First read the last number the arrow passed. That is 1 kg.
Change 4 kg 50 g into grams.
See the answer
4 050 g
4 kg is 4 000 g. 4 000 + 50 = 4 050.
If you chose A: You put 4 and 50 side by side. 4 kg is 4 000 g, not 400 g.
If you chose B: You wrote 50 g as 500 g. 4 000 + 50 is 4 050.
Change 5 000 g into kilograms.
See the answer
5 kg
1 000 g make 1 kg. 5 000 ÷ 1 000 = 5.
Tariq says a big pillow must be heavier than a small stone. Is he right?
See the answer
No. A bigger thing is not always heavier.
A pillow is big but light. A stone is small but heavy. A balance shows which is heavier.
If you chose A: Size is not weight. A big pillow is full of air, so it can be light.
If you chose C: Every thing has weight, soft things too. A pillow is light, but a scale shows some weight.
From an earlier chapter
Write 3 m 70 cm in metres, with a decimal point.
See the answer
3.7 m
70 cm is 7 lots of 10 cm. That is 7 tenths. So 3 m 70 cm is 3.7 m.
The arrow is 5 marks past 2 kg. Each mark is 100 g. Write the weight in grams.
See the answer
2 500 g
2 kg is 2 000 g. 5 marks are 5 × 100 = 500 g. 2 000 + 500 = 2 500.
What weight does the arrow show?
See the answer
2 kg 700 g
The arrow passed 2 kg. It is 7 marks further. 7 × 100 g = 700 g.
If you chose B: You started at 3 kg. The arrow has not reached 3 yet. Start at 2, the last number it passed. Count 7 marks on.
If you chose C: Each mark is 100 g, not 10 g. So 7 marks are 700 g.
The arrow points at 3 kg. How many grams is that?
See the answer
3 000 g
1 kg is 1 000 g. So 3 kg is 3 × 1 000 = 3 000 g.
If you chose B: You used 100 g for 1 kg. 1 kg is 1 000 g. So 3 kg is 3 000 g.
If you chose C: You kept the same number. But 1 kg is 1 000 g. So 3 kg is 3 lots of 1 000 g.
Keep it
Copy this into your exercise book.
1 000 g make 1 kg. 2 kg 300 g is 2 300 g. On a scale, count 100 g marks from the last number. Big is not always heavy.
Draw: A scale from 0 to 3 kg. Draw an arrow 3 marks past 2. Write 2 kg 300 g.
M2.6.5 Chapter 5
Millilitres and litres
How do I read how much water is in a jug?
Your guess
Pick one before you read on. It is fine to be wrong.
By the end you can
Read the water level on a measuring jug in millilitres
Say that 1 000 ml make 1 litre
Estimate how many cups fill a 1 litre bottle
A millilitre is a very small amount of water. We write ml for short. A teaspoon holds about 5 ml.
A measuring jug has marks up its side. Look at this jug. It holds up to 500 ml.
Draw it first
Read the water level
1 The long marks are 100 ml apart. The short marks are halfway, at 50 ml.
2 Pour in some water. The top of the water is flat.
3 The water is at the short mark after 300 ml. It is 350 ml.
Always put your eyes level with the water. Looking from above or below gives a wrong number.
The water stands halfway between 200 ml and 300 ml.
Worked example
The water is halfway between 200 ml and 300 ml. How much water is there?
The long mark before the water is 200 ml.
The long mark after the water is 300 ml.
Halfway between 200 and 300 is 250. So there is 250 ml.
Answer: 250 ml
A bigger unit is the litre. 1 000 ml make 1 litre. We write L for short.
The most a container can hold is its capacity. A 1 litre bottle has a capacity of 1 000 ml.
See it three ways
With things
Take a small cup that holds 100 ml. Pour 10 of these into one big jug.
As a picture
In symbols
10 × 100 ml = 1 000 ml. 1 000 ml = 1 L.
To change litres into ml, use × 1 000. 2 litres is 2 × 1 000 ml.
Each bottle holds 1 litre, which is 1 000 ml.
Worked example
Change 2 litres into ml.
1 litre is 1 000 ml.
2 litres is 2 × 1 000 ml.
2 × 1 000 = 2 000.
Answer:2 000 ml
A cup holds about 200 to 250 ml. How many cups fill a 1 litre bottle?
Worked example
A cup holds 250 ml. How many cups fill a 1 litre bottle?
1 litre is 1 000 ml.
Count on in 250s: 250, 500, 750, 1 000. That is 4 cups.
Check: 1 000 ÷ 250 = 4.
Answer: 4 cups
Four cups of 250 ml fill a 1 litre bottle.
Real cups differ. If your cup holds 200 ml, it takes 5 cups. So this is an estimate. Say 4 or 5 cups.
Try it
How many cups fill a litre?
You need: a bottle marked 1 litre, 1 L or 1 000 ml, one cup, a bowl of clean water, a tray to catch spills.
Be safe: Do not drink the water from this activity. Pour it on a plant after.
Fill the cup to the top. Pour it into the empty bottle.
Make a mark on paper for each cup.
Stop when the water is at the top of the bottle.
Count your marks. Count a part cup as a half.
What you will see: It takes about 4 or 5 cups. A bigger cup needs fewer cups.
If you cannot try it, this is what happens.The glass is poured into the bowl. The water looks low. It is the same water.
A wrong idea many people have
A tall thin glass holds more than a wide bowl.
Why it feels right: Tall things look big. In a thin glass, a little water stands high.
The test that breaks it: Fill a tall thin glass. Pour it into a wide bowl. The water covers only the bottom. The bowl has lots of room, so it holds more.
What is true: Height alone does not tell you how much a container holds. Measure the water in ml to compare.
Key words
millilitre
a very small amount of water. 1 000 ml make 1 litre.
litre
1 000 millilitres. Many water bottles hold 1 litre.
capacity
the most a container can hold.
Back to your guess
The answer is B: Read the mark at the flat top of the water.
Put your eyes level with the water. Read the mark at the flat top of the water. The top mark shows only how much the jug holds.
Check yourself
Try each one before you look. A wrong answer tells you where to go next.
How much water is in the jug?
See the answer
150 ml
The water is at the short mark halfway between 100 and 200. 100 + 50 = 150.
If you chose A: That is the long mark below the water. The water is past it, at the short mark halfway to 200.
If you chose C: That is the next long mark. The water has not reached it yet.
How many millilitres are in 3 litres?
See the answer
3 000 ml
1 litre is 1 000 ml. 3 × 1 000 = 3 000.
Mei has a cup that holds 250 ml. How many cups fill a 1 litre bottle?
Amina pours a full tall thin glass into a wide pan. The water looks low in the pan. Is there less water now?
See the answer
No. It is the same water.
Pouring water into a wider container does not change the amount. It only changes how high it stands.
If you chose A: The water spread out wide, so it stands lower. Nothing was lost. The amount is the same.
If you chose B: It spread out, so it seems like more. Nothing was added. The amount is the same.
A pot holds 4 000 ml of water. How many litres is that?
See the answer
4 litres
1 000 ml make 1 litre. 4 000 ÷ 1 000 = 4.
From an earlier chapter
A bag of rice weighs 2 kg 500 g. How many grams is that?
See the answer
2 500 g
1 kg is 1 000 g. 2 × 1 000 + 500 = 2 500.
How much water is in the jug?
See the answer
450 ml
The water is at the short mark halfway between 400 and 500. 400 + 50 = 450.
If you chose B: That is the top mark. It shows what the jug can hold. It is not the water.
If you chose C: That is the long mark below the water. The water is past it, at the short mark.
Which bottle holds more, 1 litre or 900 ml?
See the answer
1 litre
1 litre is 1 000 ml. 1 000 is more than 900. So the 1 litre bottle holds more.
If you chose A: You compared 900 with 1. Change to the same unit first. 1 litre is 1 000 ml.
If you chose C: You can compare them. Write both in ml. 1 litre is 1 000 ml. That is more than 900 ml.
Ravi has a cup that holds 100 ml. How many cups fill a 1 litre bottle?
See the answer
10 cups
1 litre is 1 000 ml. Count on in 100s: 100, 200, 300 and on to 1 000. That is 10 cups.
If you chose B: That is for a 250 ml cup. This cup holds 100 ml, much less. So more cups fill the bottle.
If you chose C: You took the cup size as the count. Count on in 100s: 100, 200, up to 1 000. That is 10 cups.
Keep it
Copy this into your exercise book.
Read the mark at the flat top of the water. 1 000 ml make 1 litre. A cup holds about 200 to 250 ml. A litre takes 4 or 5 cups.
Draw: A jug with marks every 100 ml. Draw water up to a mark and write the number.
M2.6.6 Chapter 6
Telling the time
A clock has two hands. How do I know which one tells the hour?
Your guess
Pick one before you read on. It is fine to be wrong.
By the end you can
Read a clock face to the nearest 5 minutes
Read a clock face to the nearest minute
Match a clock face to a 24 hour time like 15:40
Look at a clock. It has a short thick hand and a long thin hand.
The short hand is the hour hand. It shows the hour.
The long hand is the minute hand. It shows the minutes.
Draw it first
Read the clock in four steps
1 The short hand is past 7, but not at 8. The hour is 7.
2 The long hand points to 4.
3 Each number is 5 minutes. 4 × 5 = 20 minutes.
4 The time is 7:20.
The minute hand goes round once in 60 minutes. Each number is 5 minutes. Count in fives: 5, 10, 15, 20, and on.
Where the long hand points, and how many minutes that is.
Past 30 minutes, we can count to the next hour. 7:40 is 20 minutes to 8.
The small marks are single minutes. Between two numbers there are 4 small marks.
The long hand is 3 small marks past the 7.
Worked example
Read the clock above. The long hand is 3 small marks past the 7. The short hand is past 6.
The 7 is 7 × 5 = 35 minutes.
Add the 3 small marks. 35 + 3 = 38 minutes.
The short hand is past 6, but not at 7. The hour is 6.
Answer: 6:38
The hour hand moves slowly all the time. At half past 7 it is halfway between 7 and 8.
A day has 24 hours. The hour hand goes round the clock twice.
24 hour time counts the hours from midnight. It needs no morning or afternoon.
Midnight is 00:00. Midday is 12:00. From 1 o'clock after midday, add 12 to the hour.
See it three ways
With things
Use a paper clock. Put the short hand past 3. Put the long hand on 8. It is the afternoon.
As a picture
In symbols
3:40 in the afternoon. 12 + 3 = 15. So it is 15:40.
From 1 o'clock after midday until midnight, the hour is 12 more.
15:40 is also 20 minutes to 4.
Try it
Make a paper clock
You need: a sheet of paper, a plate to draw round, two strips of paper, one long and one short, a pencil.
Draw round a plate to make a circle. Write 1 to 12 round the edge.
Lay both strips with their ends at the middle of the circle.
Show 4:30. Point the long strip at 6. Point the short strip halfway between 4 and 5.
Now show 5:30. Look at where the short strip goes.
What you will see: At half past, the short hand is halfway between two numbers. It is not on a number.
If you cannot try it, this is what happens.In both clocks, the long hand is at 9. The short hand is nearly at the next number.
A wrong idea many people have
At 2:45 the short hand is nearly at 3. So the time is 3:45.
Why it feels right: We read the hour from the number the short hand is nearest.
The test that breaks it: Set a paper clock to 3:00. Count back 15 minutes. You reach 2:45. The short hand backs away from 3. The long hand points at 9.
What is true: Read the hour from the number the short hand has passed. At 2:45 it has passed 2, so the hour is 2.
Key words
hour hand
the short hand. It shows the hour.
minute hand
the long hand. It shows the minutes.
24 hour time
time that counts the hours from midnight, from 00:00 to 23:59.
Back to your guess
The answer is B: The short hand tells the hour. The long hand tells the minutes.
The short hand shows the hour. The long hand shows the minutes. The long hand goes round 24 times a day. The short hand goes round twice.
Check yourself
Try each one before you look. A wrong answer tells you where to go next.
What time does the clock show?
See the answer
4:25
The long hand points at 5. That is 5 × 5 = 25 minutes. The short hand has passed 4. So it is 4:25.
If you chose B: You read the 5 as 5 minutes. Each number is 5 minutes, so the 5 means 25 minutes.
If you chose C: The short hand has not reached 5. The hour is the number it has passed, which is 4.
What time does this clock show? Read it to the nearest minute.
See the answer
10:53
The 10 is 10 × 5 = 50 minutes. Add 3 small marks to get 53. The short hand has passed 10, so the hour is 10.
Which time is 18:30 in 24 hour time?
See the answer
half past 6 in the evening
18 is more than 12, so it is after midday. 18 − 12 = 6. So 18:30 is half past 6 in the evening.
If you chose A: In the morning, the 24 hour time is below 12. 18 is after midday.
If you chose C: You took away 10. Take away 12 instead: 18 − 12 = 6.
Write 8:15 in the evening in 24 hour time.
See the answer
20:15
In the evening, add 12 to the hour. 8 + 12 = 20. So it is 20:15.
It is half past 9. Where is the short hand?
See the answer
halfway between 9 and 10
The short hand moves all the time. Half an hour is half of the way from 9 to 10.
If you chose A: It is exactly on 9 only at 9 o'clock. Half an hour later it has moved on.
If you chose C: It reaches 10 only at 10 o'clock. At half past 9 it is on its way.
From an earlier chapter
A road is 3 km long. How many metres is that?
See the answer
3 000 m
1 km is 1 000 m. 3 × 1 000 = 3 000.
What time does the clock show?
See the answer
3:10
The long hand points at 2. That is 2 × 5 = 10 minutes. The short hand has passed 3. So it is 3:10.
If you chose A: You read the short hand as the minutes. The short hand shows the hour. The long hand shows the minutes.
If you chose B: You read the 2 as 2 minutes. Each number is 5 minutes, so the 2 means 10 minutes.
The clock shows a time in the evening. Which is its 24 hour time?
See the answer
19:45
The clock shows 7:45. In the evening, add 12 to the hour. 7 + 12 = 19. So it is 19:45.
If you chose B: You read the clock right. But in the evening, 24 hour time adds 12 to the hour.
If you chose C: You added 10 to the hour. Add 12 instead. 7 + 12 = 19.
Keep it
Copy this into your exercise book.
The short hand shows the hour. The long hand shows the minutes. Each number is 5 minutes. From 1 o'clock after midday, add 12 for 24 hour time.
Draw: A clock showing 7:20. Write 4 × 5 = 20 beside it.
M2.6.7 Chapter 7
How long it takes
A bus leaves at 09:40 and arrives at 11:15. How long is the journey?
Your guess
Pick one before you read on. It is fine to be wrong.
By the end you can
Use clock faces to find how long from 09:40 to 11:15
Change hours to minutes and minutes to seconds
Count days and weeks on a calendar
A bus leaves at 09:40. It arrives at 11:15. How long is the journey?
Jump to the next hour first. Then jump a whole hour. Then jump to the end time.
Draw it first
Jump from the start to the end
1 The bus leaves at 9:40. It arrives at 11:15.
2 Jump from 9:40 to 10:00. That is 20 minutes. Then jump to 11:00. That is 60 minutes.
3 Jump from 11:00 to 11:15. That is 15 minutes.
4 Add the jumps. 20 + 60 + 15 = 95 minutes. That is 1 hour 35 minutes.
An hour is 60 minutes. A minute is 60 seconds. A second is one tick of a clock.
Each hour has 60 minutes. Each minute has 60 seconds.
See it three ways
With things
Watch a clock. Wait until the long hand has gone once round. One hour has passed.