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Key words
Place value
digit
units
tens
hundreds
thousands
place value
zero place holder
Read and write numbers using digits or words
Know the value of each digit in a whole number
The position of each digit in a number shows its value:
3 6 7 2
2 units
7 tens
6 hundreds
3 thousands
You can use headings to show the place value of each digit: Th
3
H
T
U
6
7
2
This number can be written in words:
Three thousand, six hundred and seventy two
3672 is a 4-digit number
Example 1
What is the value of the underlined digit in the following numbers:
a) 95
b) 6307
a) 90
9 tens
b) 300
3 hundreds
c) 5
Example 2
c) 125
5 units
Write 8 300 5000:
a) as a single number
b) in words
There are no tens. The 0 in the tens
column is called a zero place holder.
a) 5308
b) Five thousand, three hundred and eight
Example 3
What is the value of each position on this number line?
(c)
(a)
4000
a) 4320
14
b) 4750
Maths Connect 1G
(e)
(b)
4500
c) 4140
d) 4890
(d)
5000
e) 4640
The large
divisions
mark
hundreds.
The small
divisions
mark tens.
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Exercise 2.1
What is the value of the underlined digit in the following numbers:
a) 64
b) 435
c) 2917
d) 7832
e) 5420
e) 3117
Write these numbers using digits:
a)
b)
c)
d)
e)
f)
Ninety five
Six hundred and eighty seven
Four thousand, three hundred and twenty six
Five thousand, one hundred and eight
Seven thousand and twenty three
Twenty six thousand, three hundred and forty one
You need to use a zero place
holder for parts d) and e).
Write these numbers in words:
a) 35
b) 267
c) 4591
d) 3605
e) 27 346
For each of a), b) and c), put these place value cards together to create one number and
write down that number:
a)
6
0
b)
0
0
7
5
3
0
c)
0
8
6
4
0
7
0
0
0
0
5
0
Write each of the following as a single number:
a) 400 50 8
d) 70 4000 5
0
8
0
b) 2000 100 60 7
e) 200 7 6000
c) 500 9 3000 20
f) 25 000 40 600 9
What is the value of each position on these number lines:
(a)
300
(f )
(b)
(c)
(g)
(d)
(h)
(e)
(i)
(j)
5000
400
6000
Write out the following:
a) 100 more than 456
d) £1000 less than £4479
b) 10 less than 6582
e) 10 kg more than 1690 kg
c) 1 more than 4508
f) 10 m less than 3200 m
Investigation
You need these four digit cards:
Investigate how many 4-digit
numbers you can make which are
greater than 7000.
5
2
7
4
You could start with numbers beginning with 72 ,
then 74 , then 75 How many 4-digit numbers can you make which are less than 5000?
Place value 15
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Key words
Tenths
tenth
decimal number
decimal point
Understand the meaning of a tenth
Write tenths as fractions and decimals
When a unit is divided into ten equal parts, each part is called a tenth .
one tenth
5
6
You can write tenths using decimal numbers . A decimal point separates the
whole numbers from the tenths:
13 . 7
1 ten
3 units
decimal point
A decimal number is
sometimes just called
a decimal.
7 tenths or 170
You can show this on a number line or using place value headings:
13.7
13
Example 1
7
10
b) 0.7
Example 2
tenths
column
Write the shaded part of this shape as:
a) a fraction
a)
TU . t
1 3 . 7
14
b) a decimal
The shape is divided into 10 equal parts.
Each part is one tenth. 7 parts are shaded.
What is the value of each position on this number line:
(a)
(b) (c)
(d)
(e)
6 units and
4 tenths.
6
a) 6.4
7
b) 6.9
c) 7.0 or 7
8
d) 7.4
e) 7.7
7 units and 0 tenths.
You can write 7.0 or 7
Example 3
Write ‘two units and one tenth’ as a) a fraction b) a decimal.
1
a) 210
16
Maths Connect 1G
b) 2.1
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Exercise 2.2
Write the shaded part of each shape as: i) a fraction
a)
b)
c)
Write these fractions as decimal numbers:
a)
3
10
b)
ii) a decimal
7
10
c) 1120
d)
d) 2110
e) 3150
d) 11.7
e) 2.5
Write these decimal numbers as fractions:
a) 0.1
b) 0.9
c) 3.6
Write each number as: i) a fraction
a)
b)
c)
d)
ii) a decimal
Look at Example 3.
six tenths
four units and nine tenths
two hundreds, eight tens, one unit and five tenths
three tens and one tenth
What is the value of each position on these number lines:
(a)
(b)
(c)
(d)
(e)
(i)
(j)
2
3
(f )
(g)
3
(h)
4
5
Write each of the following answers as a decimal:
a) 70 3 0.2
b) 0.5 60 4
c) 7 0.2 20
Write these numbers as decimals:
a) 110 more than 5.3
d) 1 less than 8.5
g) 0.1 more than 15.6
b) 110 less than 6.5
e) 0.1 more than 15.6
h) 0.1 less than 7
c) 1 more than 2.7
f) 0.1 less than 2.9
What needs to be added or subtracted to change 17.8 to:
a) 17.9
b) 18.8
c) 7.8
d) 17.7
e) 27.9?
Who am I? I am a decimal number. I am between 3 and 4. My digits add up to 8.
Investigation
You need a counter to use as a decimal point and these 3 digit cards:
3
5
6
a) How many decimal numbers
You could start with numbers beginning with 6 tenths . 6,
can you make of the form .?
then 5 tenths . 5 and so on.
b) Write the numbers, in order,
from smallest to largest.
c) How many of them are more than 50?
d) How many are between 30 and 40?
Tenths 17
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Key words
Hundredths
tenth
hundredth
decimal
Understand the meaning of a hundredth
Write tenths and hundredths as fractions and as decimals
When a unit is divided into one hundred equal parts, each part is called a hundredth .
There are ten hundredths in one tenth .
5
5.1
5.2
5.3
5.4
5.5
one tenth
5.6
5.7
5.8
6
5.9
one hundredth
You can write hundredths using decimals :
25.69
2 tens
5 units
6 tenths or 160
9 hundredths or 1900
You can show this on a number line or using place value headings:
25.69
25.6
Example 1
hundredths
column
What is the value of the underlined digit in the following numbers:
a) 3.87
b) 25.49
a) 7 hundredths
b) 4 tenths
c) 6 units
d) 8 tens
Example 2
TU . t h
2 5 . 6 9
25.7
c) 6.73
d) 183.19
H
T
2
1
8
U
3
5
6
3
.
.
.
.
.
t
8
4
7
1
h
7
9
3
9
Write the following as decimals:
a) Four units, nine tenths and six hundredths
b) 60 130 1400
a) 4.96
Example 3
c) 8 0.1 0.07
b) 60.34
60 130 1400 60 0.3 0.04
c) 8.17
Work out the value of £0.10 more than £5.81.
£5.81 £0.10 £5.91
Add one tenth to the eight tenths
Exercise 2.3
What is the value of the underlined digit in the following numbers:
a) 4.25
b) 17.36
c) 3.78
d) 5.38
e) 145.06
f) 7.01
g) 2107.44
h) 322.59
i) 17.08
j) 0.09
18
Maths Connect 1G
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Write the following as decimals:
a) Five units, nine tenths and three hundredths
b) Four tens, seven units, one tenth and six hundredths
c) Nine hundreds, three units, two tenths and six hundredths
d) One unit and one hundredth
Write the following as decimals:
a) 7 0.8 0.02
b) 0.3 10 0.05 6
d) 0.04 0.6 30
e) 1700 130 9
g) 2000 6 1800 190
h) 1400 3
c) 5 0.09 20
f) 10 1500 110
Write these fractions as decimal numbers:
a) 12030
b) 14050
c) 111070
d) 21700
What is the value of
each position on
these number lines:
(a)
10 hundredths 1 tenth
100 hundredths 1 unit
(b)
(c)
(d)
(e)
2
3
(f )
(g)
(h)
(i)
10
(j)
11
Work out the following:
1
a) 100 more than 4.72
d) 0.01 less than 4
b) 1 less than 5.59
e) 0.1 more than 5.68
Work out the value of:
a) £1.00 less than £4.71
c) £0.10 less than £0.89
e) £0.01 less than £12.60
b) £0.10 more than £1.50
d) £0.01 more than £2.99
f) £0.10 more than £5.95
What needs to be added or subtracted to change 3.67 to:
a) 3.68
b) 3.57
c) 4.67
d) 3.69
c) 0.01 more than 6.36
f) 0.1 less than 5.07
Look at Example 3.
e) 2.66?
Jamie has collected fifteen £1 coins, seven 10p coins, and eight 1p coins. Write how much
he has left after spending £0.42.
The builders are building a wall that is 1.32 metres long at the moment. After working on it
the next day it is 4 tenths of a metre longer, and the day after it is 14060 of a metre longer still.
How long is the wall now?
Investigation
You need a counter to use as a decimal point and these four digit cards:
8
7
4
2
a) What is the biggest number you can make?
b) What is the smallest number you can make of the form . ?
c) How many of numbers can you make between 50 and 100?
Hundredths 19
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Key words
Multiplying and dividing by 10, 100
and 1000
multiply
divide
convert
place value grid
Know how to multiply numbers by 10, 100 and 1000
Know how to divide numbers by 10, 100 and 1000
To multiply a number by 10, 100 or 1000 you move the digits one, two or three
places to the left on a place value grid .
To divide a number by 10, 100 or 1000 you move the digits one, two or three places
to the right on a place value grid.
Th H
T
U
.
t
9
.
3 5
9
3
.
5
9
3
5
7010 100 3
5
0
7010 1000 9.35 10 9.35 100 9.35 1000 Example 1
9
a) 59 10 590
b) 166 100
T
U
7
0
1
0
7
0
1
7
7010 10 c) 3.8 100
b) 166 100 1.66
Find in each of the following:
a) 870 8.7
a) 870 100 8.7
Example 3
Th H
Work out:
a) 59 10
Example 2
h
c) 3.8 100 380
b) 35 350
b) 35 10 350
.
t
h
0
.
1
7
.
0 1
The digits move one
place to the left. You
need to add a zero
place holder.
c) 4.1 4100
c) 4.1 1000 4100
To get from 870 to 8.7
you move two places
to the right on a place
value grid.
Convert 42 m into cm.
42 100 420
1 m 100 cm. To convert m into cm multiply by 100.
Exercise 2.4
Copy and complete this place value grid:
Th H
67 10 67 100 67 10 67 100 20
Maths Connect 1G
6
T
U
6
7
.
t
h
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Work out:
a) 7 10
b) 43 10
c) 152 100
d) 95 100
e) 5.6 100
f) 31.1 10
g) 1.7 1000
h) 3.8 100
i) 9180 1000
j) 0.03 1000
Find in each of the following:
a) 76 7600
d) 4.7 4700
c) 85 8.5
h) 147 14.7
i)
e) 6.49 64.9
g) 1475 14 750
j)
b) 1500 15
1000 4610
f) 372 3.72
10 37.1
Find the matching letter from the box for the answer to each of the following:
a) 32 10
b) 32 10
c) 320 10
d) 0.32 100
e) 3200 10
f) 3.2 100
g) 320 1000
h) 0.32 1000
i) 3200 100
j) 100 3.2
A 32
B 3.2
C 0.32
D 320
Convert:
a) 600 cm into m
b) 80 cm into mm
c) 350 m into cm
d) 75 mm into cm
e) 0.5 m into cm
f) 3.5 m into mm
100 cm 1 m
10 mm 1 cm
Write these amounts in pounds:
a) 356p
b) 470p
c) 24p
d) 60p
e) 2800p
f) 1385p
Write these amounts in pence:
a) £1.50
b) £4
c) £3.26
d) £6.40
e) £7.05
f) £16
Work out:
a) 3 10 10
b) 47 100 10
c) 5600 10 10
d) 2.3 100 10
e) 100 10 3.4
f) 470 100 10
The Seashore Store buys 100 buckets at £2.52 each, and then sells them at £3 each.
How much profit has it made?
Investigation
Use the digits 2 and 4, and as many zeros as you like, together with any of these
operations:
1
1
10
10
100
100
Can you write eight different true statements like this:
24 100 24 10
1000
1000
You could try statements
that contain two signs,
then two signs, then one
of each sign.
Multiplying and dividing by 10, 100 and 1000 21
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Key words
Positive and negative numbers
positive number
negative number
integer
Recognise positive and negative numbers
Know how to put positive and negative numbers in order
You can count back past zero on a number line:`
The numbers below zero are called
negative numbers . You write
The numbers above zero are called
positive numbers . You can write
negative numbers with a sign in
front of them.
positive numbers with a sign in
front of them.
5
4
3
2
1
1
0
2
3
4
5
The set of positive and negative whole numbers, including zero, are called integers .
This temperature scale shows positive and negative temperatures:
Vienna
Palma
Barbados
Seoul
London
Orlando
ⴚ10
ⴙ10
0
ⴙ20
ⴙ30°C
Thermometer
Example 1
The temperature in Seoul is 6 °C. This is
6 °C below zero.
Write down the next four numbers in the sequence 10, 7, 4, …
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
The temperature in Orlando is 19 °C.
This is 19 °C above zero.
0
+1 +2 +3 +4 +5 +6 +7 +8 +9 +10
Counting back in
threes.
1, 2, 5, 8
Example 2
–5
Write these numbers in order, smallest first: 5, 1, 3, 4, 2
–3
–5
+ 1 +2
0
Marking the numbers on a number line.
+4
+5
The order is: 5, 3, 1, 2, 4
Example 3
Decide whether the
temperature has risen or
fallen, and by how much:
(b)
ⴚ10
0
(a)
ⴙ10
a) from 9 °C to 4 °C
b) from 4 °C to 3 °C
22
Maths Connect 1G
a) Fallen by 5 °C
b) Risen by 7 °C
ⴙ20 °C
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Exercise 2.5
Write down the next five numbers in each sequence:
a) 10, 8, 6, 4, …
b) 25, 20, 15, 10, …
c) 7, 5, 3, …
d) 8, 6, 4, …
Positive numbers are sometimes
written without the sign. 10 is
the same as 10.
What is the value of each position on this number line:
(c)
(e)
(a)
10
(d)
(b)
(f )
10
0
Draw a number line from 5 to 5. Label the positions of these points on the line.
a) 2
b) 4
c) 312
d) 2.5
e) 0.5
Write the temperatures in each cloud in order, lowest first:
a)
c)
e)
b)
3°C, 2°C, 1°C, 4°C, 1°C
d)
0°C, 4°C, 1°C, 3°C, 2°C
f)
5°C, 1°C, 2°C, 6°C, 3°C
5°C, 3°C, 6°C, 2°C,
0°C
6°C, 6°C, 3°C, 3°C, 1°C
0°C, 2°C, 1°C, 1°C, 2°C
Write ‘True’ or ‘False’ for each statement:
b) 2 is more than 6
a) 3 is less than 4
c) 5 is more than 2
d) 3 is less than 1
e) 3 is more than 7
f) 4 is less than 6
Use a number line
to help you.
Write each pair of numbers, with either a or sign between them.
a) 2 and 4
b) 3 and 5
c) 3 and 5
d) 3 and 2
e) 5 and 1
f) 1 and 3
g) 0 and 5
h) 4 and 0
i) 6 and 2
means ‘less than’
means ‘more than
Decide if the temperature has risen or fallen, and by how much:
a) from 11 °C to 2 °C
b) from 5 °C to 4 °C
c) from 9 °C to 3 °C
d) from 2 °C to 1 °C
e) from 4 °C to 15 °C
f) from 1 °C to 9 °C
Work out the following:
a) 5 more than 2
b) 3 less than 2
c) 6 less than 7
d) 4 less than 1
The temperature is shown on this thermometer.
ⴚ10
0
ⴙ10
ⴙ20 °C
What would the temperature be after the following changes:
a) rises by 3 °C
b) falls by 2 °C
c) falls by 8 °C
d) rises by 6 °C
e) rises by 7 °C, and then falls by 4 °C
The temperature in Shipton is 6 °C at midday. It decreases by 2 degreees every hour for
the next five hours. What is the temperature at 5 o’clock in the afternoon?
Positive and negative numbers 23
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Key words
Adding
add
carry
Add whole numbers using written methods
Estimate answers to addition by rounding
You can add whole numbers using a pencil and paper in two different ways.
Always start with an estimate.
To use the long method you add the units, tens, hundreds and thousands separately:
To calculate 4573 1652:
Estimate 6000
4573
+ 1652
32
5
70 50
120
500 600
1100
4000 1000
5000
6225
4573
+ 1652
4000 1000
5000
500 600
1100
70 50
120
32
5
6225
You can start with the units
or with the thousands.
Always write your numbers
in the correct place value
column.
To use the short method you can start adding from the right. If a column adds up to
10 or more you carry the tens into the next column on the left:
4573
+ 1652
6225
7 5 12, so you need to carry 1
into the next column.
11
Example 1
Work out 3906 2291 using the long method.
You can add the units first, then the tens, then the hundreds, then
the thousands.
3906
229 1
7
90
1 1 00
5000
6 1 97
Example 2
Work out 2867 673 3685 using the short method.
2867
673
3685
7225
22 1
24
Maths Connect 1G
Estimate 7000.
7 3 5 15, so you need to carry 1 ten into the next column.
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Exercise 2.6
Work out:
a) 472 356
c) 226 702 441
e) 810 758 365
g) 268 391 654
b)
d)
f)
h)
Work out:
a) 1007 3691 4010
d) 8216 3170 15
g) 2795 1368 2895
b) 456 3724
e) 9306 2997
h) 812 3625 7085 973
c) 5846 326
f) 5407 3062 1793
i) 7584 2648 584 1309
Copy and complete these addition pyramids.
a)
The number in each brick is found
by adding the two directly below it.
b)
45
731
25
You can use either the
long method or the
short method.
685 249
907 366
837 546 792
137 238 456 732
439
854
176
398
235
This electrical store is having a sale.
SALE
Calculate the cost of:
a) a computer and a stereo
b) a DVD player and a video camera
c) a widescreen TV and a computer
d) a video camera, a computer and a stereo
e) two computers and a DVD player
f) one of each item.
Computer
Widescreen TV
Stereo
Video Camera
DVD Player
This is the map of a fun run.
START
The run has been divided into four stages.
a) How long is the whole run?
b) How far will I have run if I stop after Stage 3?
£1576
£764
£1236
£859
£685
Stage 1: 2709 m
Stage 2: 2920 m
Stage 3:
875 m
FIN
IS
H
Stage 4: 1088 m
Investigation
You need digit cards from 0 to 9. Use the cards to create correct additions:
For example,
5
7
1
This arrangement creates a
4-card addition.
2
2
7
8
3
5
This arrangement creates a 5-card
addition.
Can you create a 6-card addition, 7-card addition, and so on …
Adding 25