Years 1, 2, 3
25 September 2012
1
Aims
To explain how we teach your child the main operations
+, -, x and ÷ in KS1 and in Year 3.
To give you some ideas of how you can help and support
your child at home.
2
Maths – when do we use it?
3
Conserving number
4
Addition vocabulary
o altogether
o more than
o count on
o plus
o add
o total
o and
+
5
Addition
Adding practically using objects or pictures.
+
Encourage your child to put the larger number in
their head and count on. They can use their fingers to
do the counting on if they need to.
7 + 5 = 12
6
Addition
6+5=?
Number Track
Counting on
7
Addition
Counting on using a number line
Counting on 4 from zero
0
Counting on 4 from 5. Make
sure you emphasise counting
the jumps. (Not the numbers.)
8
Addition
Using an empty number line to count on in 1s.
0
5
9
10
9
10
5 + 4 Start at zero, jump on 5 then jump on 4.
0
5
5 + 4 Start on 5 then jump on 4.
9
Addition
Using a hundred
square to count on
and back in 1s and
10s.
We encourage
children to do this
practically with the
hundred square and
then using a mental
image.
10
Same number
Place value
2units
2 tens
2 4
4
4 units
2
4 tens
Different value
11
Place value
This is a ten stick – it is made up of 10 cubes
joined together.
This is a unit or one. It is
one cube on its own.
12
Place value
What number
do these
make?
3 tens and 4
units = 34
13
Addition
Start on any
number
32 + 6 = 38
25 + 40 = 65
Need to understand
place value – the 4 in 40
means 4 tens. So you
move down 4 squares in
the column to add 40.
14
Number bonds
Knowing pairs of numbers that make 10 and then 20
is really important.
Year 1 children need to know number bonds for 10
by the end of the year. Then move onto bonds for
20.
10 + 0, 9 + 1, 8 + 2, 7 + 3, 6 + 4, 5 + 5, 4 + 6, 3 + 7, 2 + 8, 1 + 9, 0 + 10
Game – Ping pong.
15
Partitioning
Partitioning is splitting a number into different parts.
So we teach children to partition into tens and ones (units).
18 = 10 + 8
12 = 10 + 2
27 = 20 + 7
This is the beginning of understanding place value –
The 1 in 18 means 1 ten, the 2 in 27 means 2 tens.
16
Addition
Once children can partition, they can use this knowledge to add
using an empty number line.
Step 1
24 + 5 = 29
29
24
Step 2
24 + 15 = 39
+ 10
24
34
39
17
Your turn!
Use an empty number line to do this calculation
36 + 23 = 59
+10
+10
36
46
56
59
18
Next step is to become more efficient by adding the
units in one jump.
And then add the tens in one jump
34 + 23 = 57
+20
34
+3
54
57
19
Bridging through 10 or a multiple of 10 can help children
become more efficient.
20
Your turn!
37 + 56 =
Remember to start from the larger
number.
21
Your turn!
37 + 56 = 93
Remember to start from the larger number.
+ 30
+4
56
86
+3
90
93
22
Addition in Year 3
Year 3 children continue to use empty number lines to support addition. They will
start to add 2 digit numbers that bridge 100, and then 3 digit numbers.
They also are taught to use an empty number line to help them compensate for
numbers that are near multiples of 10
49 + 73 =
49 is 1 less than 50. 50 is a much easier number to
add than 49. So first add 50. Then subtract 1.
+50
73
122 -1 123
23
Your turn!
59 + 123 = 182
+ 60
-1
123
182
183
24
Year 3 Addition
•Adding the least significant digits first. (Units in these calculations). In
Year 2 tens were added first.
•Vertical (column) addition is a change from Year 2 where calculations
were horizontal.
•Mental strategies still more important – add hundreds or tens first.
•No ‘carrying’ in this method – children need to understand what they are
adding; units, tens or hundreds and this method makes it explicit.
+
67
24
11 ( 7 + 4)
80 (60 + 20)
91
267
+ 85
12 ( 7 + 5)
140 (60 + 80)
200
352
25
Your turn!
89
+ 64
13
140
153
( 9 + 4)
(80 + 60)
256
+ 78
14
120
200
__334
( 8 + 6)
( 70 + 50)
26
Subtraction vocabulary
o
o
o
o
o
o
o
o
o
take away
minus
count back
less than
subtract
difference between
decrease
how many left
take from
27
Subtraction
As with addition, start by using objects or pictures.
6–3=3
Cross out 3.
Count what is left.
28
Subtraction
20 – 7 = 13
Subtract by counting back. Remember to count the jumps.
29
Using a number line to count back.
10 – 5 =
5
To subtract multiples
of 10 count up the
columns.
To subtract small
numbers count back
along the rows.
30
Difference
What is the difference between 3 and 6?
6–3=3
(count back)
or count on from 3 to 6.
31
Counting back:
•First partitioning and counting back in tens and ones.
•Then helping children to become more efficient by subtracting the
units in one jump (by using the known fact 7 – 3 = 4).
32
•Subtracting the tens in one jump and the units in one jump.
•Bridging through ten can help children become more efficient.
33
Your turn!
78 – 45 = 33
- 40
-5
33
38
78
34
Subtraction in Year 3
• Continue to use empty number lines with increasingly larger
numbers.
• Partitioning demonstrated using arrow cards (started in Year 2).
4 05 060
35
Subtraction – Year 3
Partitioning before subtracting
89
- 57
=
-
80 + 9
50 + 7
30 + 2
= 32
36
Beginning to exchange
Your turn!
83
- 47
37
Your turn!
38
Multiplication vocabulary
x
o groups of
o lots of
o times table
o times
o multiplied by
o multiply
o double
39
Multiplication
Counting in 10s
40
Multiplication
Counting in 2s
41
Multiplication
Counting in 5s
42
Multiplication
• Children
need to learn multiplication tables and multiplication
facts.
• Yes – learn to recite tables but also need to know table facts at
random.
• e.g. 8 lots of ten are?
• And answer questions like “ How many tens in 80?”
• Not secure in times tables until able to do this quickly.
Should be working on 10x, 2x and 5x tables in Year 1, continue and
work on 3x and 4x in Year 2. Secure in Year 3.
43
•
Multiplication
Problem solving
There are 10 pencils in a pack.
How many pencils are there in 4 packs?
Repeated addition
10 + 10 + 10 + 10 = 40
44
Multiplication
3 times 5 is the same as 5 + 5 + 5 = 15 or 3 lots of 5 or 3 x 5
On a number line
5
5
0
5
5
10
15
45
Multiplication
As an array
3 x 5 = 15
5 x 3 = 15
46
Problem solving
Ella’s dad washes some cars. He
uses 12 buckets of water. Each
bucket has 5 litres of water. How
many litres of water does he use
altogether?
There are 15 apples in a tray. Ling
has 4 trays of apples.
How many apples does Ling have
altogether? Show how you work
it out.
Your turn! Can you draw pictures or make jottings to show how you could
work one or both of these out?
47
Ella’s dad washes some cars. He uses 12 buckets of water.
Each bucket has 5 litres of water. How many litres of water
does he use altogether?
5 10 15 20 25 30
35
40 45
50 55
60
Or 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 60
Or count in 5s 12 times.
Or 12 x 5 =60
48
There are 15 apples in a tray. Ling has 4 trays of apples.
How many apples does Ling have altogether? Show how you
work it out.
151415
15
10 + 5
151415
15
10 + 5
4 lots of 10
4 lots of 5
40
+ 20
151415
15
151415
15
10 + 5
10
20
30
5
10
15
10 + 5
40
20
= 60
49
Multiplication – Year 3
•Partitioning
38 x 5 = (30 x 5) + (8 x 5)
= 150 + 40
= 190
50
Division vocabulary
share
o share equally
o divide
o divided by
o groups
o halve
o half
o
51
Division
• Children start by understanding equal groups and sharing items out in
play and problem solving. Count in 2s, 10s and 5s.
•Sharing equally.
There are 6 sweets. How many sweets can 3
children have each?
52
Division
Grouping
There are 6 sweets.
How many children can have 2 each?
53
So how can you work out a division sum
using times tables?
Count in 2s until you get to 16.
2 4 6 8 10 12 14
16
54
Division using an empty number line
How many groups of 5 are there in 25?
25 ÷ 5 = 5
5
0
5
5
5
10
5
15
5
20
25
55
Your turn!
There are 30 children in the class. They need to be
in teams of 5. How many teams will there be? Use
an empty number line to work it out.
5
0
5
5
5
10
5
15
6 groups of 5 make 30.
5
20
5
25
30
So 6 teams.
56
How you can support your child at home
Look for and talk about numbers in the environment
Play games
Shopping
Counting on/back
Number bonds
Doubles/Halves
Times tables
Multiplication facts
Division facts
57
Useful websites
http://www.familylearning.org.uk/multiplication_games.html
http://www.ictgames.com/resources.html
http://www.bbc.co.uk/bitesize/ks1/maths/
http://www.comberps.newtownards.ni.sch.uk/maths_games_for_ks1.htm
http://www.maths-games.org/time-games.html
http://www.bbc.co.uk/schools/websites/4_11/site/numeracy.shtml
http://www.woodlands-junior.kent.sch.uk/maths/index.html
58