+ Addition +
This shows the progression of teaching addition at Parrett and Axe. Each method is designed to lead on to the next gradually building up children’s understanding of number.
Remember, children should think about whether a calculation can be done mentally first.
STEP
Tips for mental /
Concept & images
Comments
oral session
1
Counting
Early addition
Combining groups of objects to find the
total
using fingers to make number sentences eg4 (on one
hand) and 1 (on the other) + counting on from any number
eg. Start at 7 onto 20
Put all objects together and count…
Find total of 2 groups using objects in hoops…
Then total of 2 groups using objects and numerals in
hoops…
Then… total of 2 groups using objects and hoops and
recording as a number sentence…
Then without hoops, with objects and record as a number
sentence
counting on and back on a number line, pointing as you go
2
Finding numbers
Relating
‘Informal number line’ / number
sentences
groups of
As above, alongside a calculation
3
Counting to ten and Add one onto a number
Locating
back
numbers on a Locating numbers
more.
Then… Look at number sentences – use objects provided
Look at number sentences: what do we have to do? Use
number line
& adding one
answer
to find the answer
objects to
number line
Look at number sentences. Use objects on sheets to find
objects to find an answer
Find 5 on number track, then add one
Encourage children to locate the first number and count on
from there, rather than starting at zero.
4
Number
bonds up to
10.
play “pingpong” for
bonds to 10
Pegs on a coat
hanger (turn round
to show inverse)
Write all the ways
to make
2,3,4,5,6,7,8,9,10
How many ways of splitting up a
number?
rapid recall
Using number
Adding to a ten
bonds to add
mentally
on the
(10 + 2 = 12,
number line.
on the number line rather than count.
10 = ? + ?
9 = ?+?
20 = ? +?
8 = ? + ? 100 = 20+80 100 = 24 + 76
Using counters and 2 plates + show me ways to make 9
Bridge 10 (e.g. 8 + 5 =13)
Include use of bead bar
10 + 3 = 13
10 + 4 = 14…)
In order to calculate effectively children must know all the
bonds for numbers up to ten. This will enable them to jump
etc. Domino pairs
5
Model with numicon
Doubling and repeated addition
Using a bead bar is also an effective way to showing how
to split smaller numbers up
KS1 children to also model this using jumps on a number
line in order to lead to step 5.
Emphasise JUMP on number line, NOT counting!
Use number bonds to jump to the next ten on the number
line. Then add what is left in one jump.
Vocab – add, sum, total etc
Link to subtraction – sum families
8+5=13 13-5=8
5+8=13 13-8 =5
6
Counting on and
Adding multiples of 10
Using number
back in steps of
Addin near multiples of 10 – (9 19 29)
line to jump
ten.
rounding and readjusting
jump in steps of ten.
Focus on what happens to the tens and units as you count.
Focus on tricky parts: counting over 100, counting back
past 20 in the teen numbers.
in tens from
any 2-digit
number.
Starting from any 2-digit number children must be able to
Adding multiples of 100 using number grids as well as
number lines
7
Adding on the
number line.
Counting on in tens
Adding to a ten
mentally
This puts together the two previous ways of adding on a
TU + TU
number line.
THE NUMBER LINE REPRESENTS THE JUMPS IN YOUR
Adding by partitioning
HEAD!
If adding near multiples of ten, more confident pupils can
38+26=64
do adding a ten and adjusting:
30+20=50
8+6=14 50+14=64
8
Practice partitioning
Column
Number bonds up
addition for
to ten (to avoid
adding pairs
counting in ones when
of 3 digit
43 + 19, =
43 + 20 = 63 -1 = 62
HTU + HTU using partitioning
Start by partitioning the numbers so the children understand
347 + 122 =
what each column represents.
300
+100
40
20
400
60
7
347
2
122
9 = 469
Children should only use this when adding together 3-digit
9
numbers and preferably when the units add to more than
60
adding up columns)
ten. (Although to introduce concept using simpler numbers
400
numbers.
is a good idea)
469
THEN, GO BEYOND 10 in U column etc.
159 + 264 =
100
50
9
+200
60
4
300
9
Practice partitioning
Compact
Number bonds up
Column
to ten (to avoid
addition
counting in ones when
adding up columns)
110
13 = 423
As the children become more confident in column addition
347 + 122
347
+122
Then
347
Then, with carrying
+122
9
469
60
they can gradually start to use the compact method for
159
speed.
+ 264
423
1
It is vital that they still understand that the small ‘1’
represents tens or hundreds.
400
469
10
‘Moving digits’ ITP
Same number of decimal places
As with the compact column addition strategy it is vital that
Compact
to investigate
Column
decimals.
+54.6 km
addition with
Practice partitioning
133.1 km
decimals
Number bonds up
to ten (to avoid
78.5 km
always taking care with columns
keep carried numbers half size
1 1
Then, different number of decimal places
counting in ones when
124.9
adding up columns)
+
7.25
132.15
11
children understand what each column represents in terms
of value.