Addi on Progression towards a formal wri en method:
47+25 = 47 25 60 + 12
Addi on starts very prac cally using straws then dienes. Children use knowledge of place value to make the numbers and then add them togeth-­‐
er before exchanging when there are 10 1’s.
Leading to exchanging:
72
Children par on their numbers horizontally and add each place value column (star ng with the ones) con nuing to use resources for support (straws, dienes and then place value counters). Children then use the expanded ver cal method con nuing to focus on place value and adding their ones first. Children con nue to use prac -­‐
cal resources alongside this to support under-­‐
standing. Finally children use the formal wri en method for addi on lining their numbers up ver cally and exchanging underneath when required.
Subtrac on
Progression towards a formal wri en method:
Subtrac on starts prac cally using straws then dienes. Children learn that they only need to make the top num-­‐
ber and that they have to subtract the bo om number from this. They learn to write this expanded horizon-­‐
tally using place value columns.
This progresses to ques ons where children will need to exchange. Again, children start by doing this prac cally to reinforce the understanding that a 10 is the same as 10 1’s. They learn how to record this by crossing out and exchanging to the 10.
When children are secure with their place value they no longer need to expand the method horizontally by par -­‐
oning and use the formal wri en method for subtrac-­‐
on. Numbers are lined up ver cally in the correct col-­‐
umns and exchanging is marked without place value.
Mul plica on
Progression towards a formal wri en method:
Children use arrays as a visual to represent mul plica on. These can be done prac cally as well as wri en. Children understand that mul plica on is the same as repeated addi on and that 3 mul plied by 4 and 4 mul plied by 3 give the same answers.
The array is used to represent mul plica on with larger numbers so children understand the place value involved.
This leads clearly into the grid method where children par on each of the numbers they are mul plying and write the answers to each calcula on within their grid.
The grid method con nues to be used with larger num-­‐
bers and when children are confident and secure they are moved onto the formal wri en method for mul pli-­‐
ca on. Children are encouraged to see the connec ons between the grid and formal methods. As this gets more difficult, the children show their exchanging above and below the numbers.
Division
Progression towards a formal wri en method:
Children look at division as sharing and grouping. When children share they use objects to share prac cally. When grouping, children apply their coun ng skills using prac -­‐
cal resources, their fingers or a number line.
15 ÷ 3 = 5
Children make links between mul plica on and division using arrays. E.g. 15 ÷ 3 = 5 there are 5 groups of 3
15 ÷ 5 = 3 there are 3 groups of 5
Children con nue to develop grouping on a number line using their mes tables facts to work with larger numbers. They learn to look for groups of the divisor e.g. 10 groups of, 100 groups of. Calcula ons may have remainders.
Children learn to use the formal method alongside place value counters or dienes. They con nue to use grouping within this method e.g. How many groups of 3 can I make in the hun-­‐
dreds?
Children con nue to develop their use of the formal method where ques ons involve exchange.