Teaching for mastery in primary maths

In this chapter, pupils build on their work on place value up to 10. In order to understand addition and subtraction, they should be able to compare and appreciate the size of numbers, as well as represent them using a variety of objects, such as counters and cubes.

Pupils start to read, write and interpret mathematical statements involving addition (+), subtraction (-) and the equals sign (=). They begin to understand what it means to add and subtract two numbers and use concrete objects and simple part-whole diagrams to represent this. They write related calculation statements using these representations. 

Throughout this chapter, pupils explore how numbers within 10 can be partitioned and, as such, are able to represent and use number bonds of any number up to 10. They also add and subtract one-digit numbers (including 0) within 10.

Using concrete objects and pictorial representations, pupils solve simple one-step and missing number problems. They also start to understand the different uses of the subtraction symbol, such as to “take away” and “find the difference”.

In this chapter, pupils extend their learning from the previous chapter, and from the relevant chapter on number and place value, by working with numbers within 20. They represent numbers using a variety of concrete and pictorial representations.

Pupils continue to read, write and interpret mathematical statements involving addition (+), subtraction (-) and the equals sign (=). They secure their understanding of the concepts of addition and subtraction and use concrete objects and simple part-whole diagrams to add and subtract one and two-digit numbers (including 0) within 20.

As such, pupils become increasingly confident in writing the related calculation statements, showing the connection between addition and subtraction. They start to use these calculations to check their answers.

Throughout this chapter, pupils explore how numbers within 20 can be partitioned and, as such, are able to represent and use number bonds of any number up to 20. They see the connection to number facts within 10. 

Using concrete objects, pictorial representations and their knowledge of addition and subtraction, pupils solve simple one-step and missing number problems.

In this chapter, pupils further secure their understanding of addition and subtraction by working with numbers within 40 or 50.

Pupils continue to read, write and interpret mathematical statements involving addition (+), subtraction (-) and the equals sign (=). They represent and use number bonds and related subtraction facts, while building on their previous knowledge of adding and subtracting one and two-digit numbers (including 0), within 40 or 50. 

At this stage, pupils do not use formal methods without concrete or pictorial representation. They continue to use representations to explore the concepts of addition and subtraction, to see the connection between the two and to write down the related calculations. They also use them to solve simple one-step and missing number problems.

In this chapter, pupils extend their understanding of addition and subtraction by working with numbers within 100.

As in previous chapters, it is important that pupils represent addition and subtraction problems using concrete and pictorial representations.

Pupils continue to read, write and interpret mathematical statements involving addition (+), subtraction (-) and the equals sign (=). They represent and use number bonds and related subtraction facts, while building on their previous knowledge of adding and subtracting one and two-digit numbers (including 0), within 100. 

At this stage, pupils do not use formal methods without concrete or pictorial representation. They continue to use representations to explore the concepts of addition and subtraction, to see the connection between the two and to write down the related calculations. They also use them to solve simple one-step and missing number problems, which involve using numbers of increasing size.

In this chapter, pupils become increasingly confident with adding and subtracting numbers of increasing size. 

Pupils have secured an understanding of addition and subtraction within 100 and can partition three-digit numbers. They start working with two-digit numbers of any size by recalling and using addition, and related subtraction, facts to 20 and deriving and using related facts to 100. 

At this stage, pupils do not necessarily move onto formal column methods, although steps can be taken to introduce this. For example, pupils may use place value grids and counters to see how numbers can be partitioned and further explore what it means to add and subtract. 

Pupils add and subtract numbers mentally, in addition to using concrete objects and pictorial representations. They add and subtract ones and tens to or from a two-digit number, as well as adding and subtracting two two-digit numbers and adding three one-digit numbers. 

Although pupils have already been writing down the family of related addition and subtraction facts, they can now show that addition of two numbers can be done in any order (commutative), but that subtraction of one number from another cannot. They should also recognise the inverse relationship between addition and subtraction and use this to check calculations of increasing size and solve missing number problems.

In this chapter, pupils start to use formal column methods for addition and subtraction, using approaches introduced in previous chapters.  

These approaches may, for example, include the use of place value grids and counters to understand the concept of addition and subtraction and the language associated with it. They should be linked explicitly to each step of the formal methods. 

Once formal methods have been introduced, they can easily become the go-to method pupils use to solve any addition or subtraction problem. However, they are not always the most efficient. Often simple mental methods are more appropriate and pupils should be encouraged to identify the best option.

Pupils mentally add and subtract ones, tens and hundreds to or from a three-digit number. They also begin to solve increasingly complex problems with more than one step, using their knowledge of number facts, place value and addition and subtraction. They estimate the answer to a problem and make use of inverse calculations to check it.

In this chapter, pupils use estimation and inverse operations to check answers to calculations.

Building on learning from the relevant place value chapter, pupils consolidate their recognition of four-digit numbers (ie, in thousands, hundreds, tens and ones), as well as the connection between concrete, pictorial and formal methods. Accordingly, pupils add and subtract numbers with up to four-digits using formal written methods, such as columnar addition and subtraction, where appropriate. 

Pupils solve increasingly complex problems with more than one step. Many of the problems are set in authentic, real-life contexts and require pupils to use representations (eg, bar modelling) to decide which operations and methods to use. They should be able to explain why they chose a particular method.

In this chapter, pupils extend their understanding of addition and subtraction to include larger integers.

Building on learning from previous chapters, pupils add and subtract whole numbers with more than four digits, including using formal written methods such as columnar addition and subtraction. They also mentally add and subtract increasingly large numbers.

Pupils use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy.

They also solve increasingly complex problems with more than one step. Many of the problems are set in authentic, real-life contexts and require pupils to use representations (eg, bar modelling) to decide which operations and methods to use. They should be able to explain why they chose a particular method.

In this chapter, pupils continue to solve addition and subtraction problems with numbers of any size. 

Problems are set in authentic, real-life contexts and involve multiple steps. They draw on pupils’ knowledge of other topics and may involve decimals.