MATHEMATICS
Y4 Counting and Understanding Number
5210
Use decimal notation.
Order decimal fractions.
Equipment
Paper, pencil, ruler
Calculator
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Use decimal notation.
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Order decimal fractions.
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Concepts
In Year 5 children are expected to be able to read and write decimal fractions
to two decimal places and understand the importance of the decimal point.
This is a revision module following from the similar Year 4 module.
Number lines where children can count up and down in tenths and hundredths
are still important.
Part of this work is recognising in money, for example, that the first digit after
the point is tenths, which can be thought of as the number of 10p, and the
second digit after the point is hundredths, or the number of one pence.
Practical work on this, using real coins, is always very helpful.
Avoid only using one figure after the decimal point in the context of money
and length because £4.5 means four pounds fifty and not four pounds and five
pence (£4.05).
In a similar way 5.5 m means 5 metres and 50 cm ( not 5 m and 5 cm).
Calculators may be used, but only as a tool to display the results of mental
arithmetic e.g. in one step change 5.32 to 5.39 . In questions such as this the
calculator is of no help if the child does not understand place value.
Some of the hardest work involves adding or subtracting using mixed units
e.g. 1.4 litres + 300 millilitres. Children will need a secure grasp of the
decimal system in order to answer these correctly.
Much of this work will also re-inforce the language of mathematics - less
than, more than, count on, count back etc.
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Decimal fractions
The number 4.67 is pronounced 'four point six seven'.
Note: you do not say 'four point sixty seven'.
It means 4 whole ones, 6 tenths of a whole one and 7 hundredths of a whole
one.
In the chart below write down how you say each of these decimal fractions.
The first is done for you.
1. 6.63
Six point six three
2. 7.24
3. 6.55
4. 8.96
5. 6.02
6. 8.02
What does 4.65 mean?
The four means four whole ones and the six means six tenths, so 4.6 is a
number between 4 and 5. Then the five means five hundredths, which means
it is a number between 4.6 and 4.7 Look at the number line below to see
where it comes:
4.60 4.61 4.62
4.63 4.64
4.65 4.66 4.67
4.68 4.69 4.70
Fill in the missing numbers on the number line below. Practice counting up
and down each time.
7.
6.10 6.11
6.13
6.15 6.16
6.18 6.19 6.20
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Decimal fractions
8.10 8.11 8.12
8.13
8.14 8.15 8.16
The arrow is pointing at 8.17
8.17 8.18 8.19 8.20
We say this, 'eight point one seven'.
Fill in the missing numbers on the number lines below. Practise counting up
and down each time.
1.
7.20 7.21
7.23
7.25 7.26
7.28 7.29 7.30
2.
2.60
2.62 2.63
2.65
2.67
2.68
2.70
9.38
9.40
3.
9.30 9.31
9.35
4.
5.10
5.15
5.20
Write these in numbers:
e.g. four point six two = 4.62
5. Three point two three
6. One point nought five
7. Nine point three eight
8. Six point nought two
9. Three point four seven
10. Five point one six
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Decimal fractions
In the number 6.82 the digit 6 represents 6 whole ones, or six units.
In the number 6.82 the digit 8 represents eight tenths or
8
10
In the number 6.82 the digit 2 represents two hundredths or
2
100
The decimal point separates the whole number part from the less than one whole
part.
Draw out the chart and write down the value of the digits underlined in the numbers
below. The first has been completed for you.
1. 3.51
Five tenths
2. 6.39
3. 7.21
4. 3.45
5. 9.62
6. 0.80
Notice how if there are no whole units we still place a nought at the start:
eg 0.1 in words is nought point one.
(It would be easy to mistake .1 as 1 whole one!)
Put these sets of numbers in order, starting with the smallest:
7.
5.39
7.39
1.39
4.39
3.39
8.
2.75
2.51
2.58
2.50
2.27
9.
9.70
0.79
5.79
6.70
9.75
10.
6.26
6.27
6.25
6.20
0.26
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Decimal fractions
In the number 4.73 the digit 4 represents 4 whole ones, or four units.
In the number 4.73 the digit 7 represents seven tenths or
7
10
In the number 4.73 the digit 3 represents three hundredths or
3
100
The decimal point separates the whole numbers from the less than one whole part.
Draw out the chart and write down the value of the digits underlined in the numbers
below. The first has been completed for you.
1. 5.51
One hundredth
2. 4.36
3. 8.21
4. 4.68
5. 6.05
6. 0.08
Notice how if there are no whole units we still place a nought at the start: eg
0.4 in words is nought point four.
(It would be easy to mistake .4 as 4 whole ones!)
Put these sets of numbers in order, starting with the smallest:
7.
7.31
7.01
7.04
7.08
7.02
8.
0.30
0.60
0.20
0.40
0.80
9.
9.12
9.51
9.52
9.50
9.02
10.
6.25
6.27
6.26
5.28
5.26
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Decimal fractions - money
£1
One pound is written £1
10 p
Ten pence is written £0.10
1p
One penny is written £0.01
£4 .9 8
four units
nine tenths
eight hundredths
Write down the value of the digit underlined in the table below. The first has
been done for you.
1. £3.75
Seven tenths
or
2. £2.36
or
3. £1.95
or
4. £0.12
or
5. £6.29
or
6. £3.14
or
seventy pence
If the amounts below were all in one pence pieces how many would you
have:
7. £2.02
8. £3.30
9. £5.55
10. £6.06
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Decimals
Place these decimals on a line from 0 to 1:
1. 0.5
2. 0.7
3. 0.8
4. 0.1
5. 0.4
0
1
Place these numbers on a 2.10 to 2.20 number line:
6. 2.14
7. 2.12
8. 2.19
9. 2.17
10. 2.15
2.10
2.20
Estimate the number that the arrow is pointing to on these questions:
11.
12.
13.
3.40
3.50
Estimate the number that the arrow is pointing to on these questions:
14.
15.
7.20
17. Write down a number between 8 and 9.
18. Write down a number between 0 and 1.
16.
7.30
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Decimals - mixed problems
Use a calculator to solve these problems. You are only to make one step or
operation to solve them.
E.g. change 6.23 to 6.29
type in 6.23
press the + sign
press 0.06 and the equals sign.
Write down: Add 0.06
If you get the wrong answer, don't worry - TRY AGAIN!
1. Change 4.12 to 4.15
2. Change 4.06 to 4.09
3. Change 3.10 to 3.17
4. Change 4.20 to 4.60
5. Change 8.71 to 8.61
6. Change 5.27 to 5.21
7. Change 9.12 to 9.10
8. Change 7.64 to 7.74
9. Change 4.26 to 6.26
10. Change 2.42 to 6.42
11. Change 8.07 to 8.27
12. Change 6.06 to 2.06
Write these measurements in km:
Remember 1 000 m = 1 km
eg
1 234 m = 1.234 km
13. 3 469 m
14. 2 358 m
15. 2 246 m
16. 566 m
17. 4 020 m
18. 5 004 m
19. 167 m
20. 86 m
Write these measurements in litres:
Remember 1 000 ml = 1 litre
eg 8 765 ml = 8.765 litres
21. 9 641 ml 22. 7 486 ml 23. 2 903 ml 24. 5 580 ml
25. 455 ml
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9 . 5 24 km
nine units five tenths two hundredths four thousandths
(9 kilometres) (500 metres) (20 metres)
(4 metres)
Remember: 9 kilometres = 9 000 metres
9.524 km = 9 kilometres and 524 metres = 9 524 metres
Change these measurements from kilometres to metres:
( Remember, there are 1000 m in a kilometre. )
1. 3.456 km =
2. 7.966 km =
3. 8.727 km =
4. 5.003 km =
5. 6.006 km =
6. 0.404 km =
Change these measurements from centimetres to metres:
7. 4 604 cm =
8. 8 098 cm =
9. 6 036 cm =
10. 3 093 cm =
11. 6 006 cm =
12. 7 000 cm =
Work out the following problems:
13. Paul poured 1.5 litres of water into a jug and then added a
further 400 ml. How much did he pour in altogether?
14. Joe was making a huge cake. He put in 1.4 kg of flour and then added
500g of sugar. How much did these ingredients weigh?
15. Jason ran 1.6 km in ten minutes. Jack then took over and ran a further 700
metres. How far did they run altogether?
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Decimals
Estimate the numbers that the arrows are pointing to:
1.
2.
3.
8.20
8.30
Estimate the numbers that the arrows are pointing to:
4.
5.
6.
0.20
0.30
Change these measurements from kilometres to metres:
7. 4.530 km =
8. 3.270 km =
9. 7.800 km =
10. 2.060 km =
11. 3.010 km =
12. 9.120 km =
Change these measurements from metres to kilometres:
13. 5 748 m =
14. 6 402 m =
15. 7 709 m =
16. 4 100 m =
17. 9 001 m =
18. 7 001 m =
19. Write 5 centimetres in metres.
20. Write 6 metres in kilometres.
21. Write 7 millilitres in litres.
22. Write 8 grams in kilograms.
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Answers
Page 3
1. six point six three 2. seven point two four 3. six point five five
4. eight point nine six 5. six point nought two 6. eight point nought two
7. 6.12, 6.14, 6.17
Page 4
1. 7.22, 7.24, 7.27 2. 2.61, 2.64, 2.66, 2.69 3. 9.32, 9.33, 9.34, 9.36, 9.37, 9.39
4. 5.11, 5.12, 5.13, 5.14, 5.16, 5.17, 5.18, 5.19
5. 3.23 6. 1.05
7. 9.38
8. 6.02
9. 3.47
10. 5.16
Page 5
1. five tenths 2. six units 3. one hundredth 4. four tenths 5. nine units 6. eight
tenths 7. 1.39, 3.39, 4.39, 5.39, 7.39
8. 2.27, 2.50, 2.51, 2.58, 2.75
9. 0.79, 5.79, 6.70, 9.70, 9.75
10. 0.26, 6.20, 6.25, 6.26, 6.27
Page 6
1. one hundredth 2. four units 3. one hundredth 4. six tenths 5. five hundredths
6. eight hundredths 7. 7.01, 7.02, 7.04, 7.08, 7.31 8. 0.20, 0.30, 0.40, 0.60, 0.80
9. 9.02, 9.12, 9.50, 9.51, 9.52
10. 5.26, 5.28, 6.25, 6.26, 6.27
Page 7
1. seven tenths or seventy pence
2. six hundredths or six pence
3. nine tenths or ninety pence
4. Two hundredths or two pence
5. six units or six pounds
6. One tenth or ten pence
7. 202 p
8. 330 p
9. 555 p
10. 606 p
Page 8
11. 3.41 12. 3.44 13. 3.47 14. 7.22 15. 7.24 16. 7.28
17. any number between 8.0 and 9.0 18. any number between 0 and 1
Page 9
1. add 0.03 2. add 0.03 3. add 0.07 4. add 0.40 5. subtract 0.10 6. subtract 0.06
7. subtract 0.02 8. add 0.10 9. add 2 10. add 4 11. add 0.2 12. subtract 4
13. 3.469 km 14. 2.358 km 15. 2.246 km 16. 0.566 km 17. 4.020 km 18. 5.004 km
19. 0.167 km 20. 0.086km 21. 9.641 l 22. 7.486 l 23. 2.903 l 24. 5.580 l 25. 0.455 l
Page 10
1. 3 456 m
2. 7 966 m
3. 8 727 m
4. 5 003 m
5. 6 006 m
6. 404 m
7. 46.04 m
8. 80.98 m
9. 60.36 m 10. 30.93 m 11. 60.06 m 12. 70 m
13. 1.9 litres or 1 900ml
14. 1.9 kg or 1 900 g 15. 2.3 km or 2 300 m
Page 11
1. 8.24 2. 8.26 3. 8.28 4. 0.23 5. 0.26 6. 0.29
7. 4 530m 8. 3 270 m 9. 7 800 m 10. 2 060 m 11. 3 010 m 12. 9 120 m
13. 5.748 km 14. 6.402 km 15. 7.709 km 16. 4.1 km 17. 9.001 km 18. 7.001 km
19. 0.05 m 20. 0.006 km 21. 0.007 ml 22. 0.008 kg