Leagrave Primary School CALCULATIONS FRAMEWORK
Year 4
Progressing to 4-digits
Expanded column addition modelled with place value
counters, progressing to calculations with 4-digit
numbers.
Year 5
Mental methods should continue to develop, supported by a range of models and images,
including the number line. The bar model should continue to be used to help with
problem solving. Children should practise with increasingly large numbers to aid fluency
e.g. 12462 + 2300 = 14762
Written methods (progressing to more than 4-digits)
As year 4, progressing when understanding of the expanded method is secure, children
will move on to the formal columnar method for whole numbers and decimal numbers as
an efficient written algorithm.
Addition
172.83
+ 54.68
227.51
1 11
Place value counters can be used alongside the columnar method to develop
understanding of addition with decimal numbers.
As year 5, progressing to larger numbers, aiming for both conceptual
understanding and procedural fluency with columnar method to be secured.
Continue calculating with decimals, including those with different numbers of
decimal places
Compact addition using carrying for thousands, hundreds, tens and units and
decimals.
Short Column addition up to 3 decimal places
16.528
+ 17.348
33.876
1
1
Also cover partitioning for mental
Addition and to 2 decimal places
e.g.
185.74+126.25
100+100=200
80+20=100
5+6=11
0.70+0.20=0.90
0.04+0.05=0.09
200+100+11+0.90+0.09=311.99
(Encourage jottings to record answers)
Problem Solving
Teachers should ensure that pupils have the opportunity to apply their
knowledge in a variety of contexts and problems (exploring cross curricular
links) to deepen their understanding.
Extend to up to two places of decimals (same number of
decimals places) and adding several numbers (with
different numbers of digits).
72.8
+ 54.6
127.4
1 1
Progressing to 4-digits
Expanded column subtraction with
decomposition, modelled with place value
counters, progressing to calculations with 4digit numbers.
Year 6
Progressing to more than 4-digits
Continue written methods taught in year 5-
Short Column subtraction
1095-876
Subtraction
8
1 10 9 15
- 8 7 6
2 1 9
Short Column subtraction with decimal places
e.g. 24.95—16.87
Move on to short formal methods -
Progress to calculating with decimals, including those with different numbers
of decimal places.
1
2 14 .
-1 6 .
8 .
8
9 15
8 7
0 8
1
3
3
dig
it
by
2
dig
it
Year 4
Continue to practise formal written method
introduced in year 3, extend using larger
numbers.
Year 5
Year6
Multipliy numbers up to 4 digits by a one or two digit numbe using formal Continue to refine and deepen understanding of written methods
including fluency for using long multiplication and short
written methods, including long multiplication for two digit numbers:
multiplication.
Multiplication
Long multiplication
TUxU, , HTU xU
14
x 3
12
30
42
***Some children may still use the grid method
to support their understanding, then move onto
formal written methods.
2 digit by 2 digit short
multiplication
3 digit by 2 digit
3 4
1 3
1 3 4
5 3
x
Long Multiplication
2
27
x 6
42
120
162
24
x 16
240
144
384
1
1
1
4 0 2
1 0 2
3 4 0
4 4 2
1
2
67 0 0
7, 1 0 2
3 digit by 2 digit
1 3 4
5 3
1
1
4 0 2
1
2
67 0 0
7, 1 0 2
Formal short division should only be introduced
once children have a good understanding of
division, its links with multiplication and the
idea of ‘chunking up’ to find a target number.
Short division to be modelled for understanding
using place value counters as shown below.
Continued as shown in Year 4, leading to the efficient use of a formal method.
The language of grouping to be used
By the end of year 5 children should learn to write formal written
methods – Short division.
Sharing and Grouping and using a number line
Children will continue to explore division as sharing and grouping,
and to represent calculations on a number line as appropriate.
Quotients should be expressed as decimals and fractions
Formal Written Methods – long and short division moving onto
decimals.
Short division
75 r2
5 3 7 27
Division
75 r2
5 3 7 27
Long division:
96 ÷ 6 = 16
6 9
6
3
3
6
0 (10 x 6)
6
6 (6 x 6)
Children begin to practically develop their understanding of how express the
remainder as a decimal or a fraction. Ensure practical understanding allows
children to work through this (e.g. what could I do with this remaining 1?
How could I share this between 6 as well?