Number Bonds

Number bonds are a way of showing how numbers can be combined or split up. They are used to reflect the ‘part-part-whole’ relationship of numbers.

Number bonds teach children how numbers join together and how they can be broken down into their component parts. From year 1, children use number bonds to build up their number sense before learning about addition and subtraction.


Where Do Number Bonds Come From?

Number bonds are a core element of teaching maths for mastery using Singapore Maths and have been part of Singapore’s primary curriculum since the early 1970s. However, the phrase ‘number bonds’ has been around since the 1920s and became widespread in the UK in the late 1990s as a way of developing mental arithmetic strategies.

How Do Number Bonds Look?

Number bonds are often represented by circles that are connected by lines as illustrated below. The ‘whole’ is written in the first circle and its ‘parts’ are written in the adjoining circles.

What are number bonds?

How Do Children Learn About Number Bonds?

Children are introduced to number bonds through the concrete, pictorial and abstract approach.


  • Concrete – Young children learn by counting real objects. Then they’ll use counters to represent the objects and start grouping them into two groups.


(For example, by putting five counters into two groups, they will learn the different ways that five can be made. For example, 3 and 2 as illustrated below. With further exploration they’ll work out other ways to break the number up into two groups.)


  • Pictorial – Having understood the concept with hands-on experiences children will now represent what they are doing by writing on whiteboards or other resources to create a number bond.
  • Abstract – At this stage, children are capable of representing problems by using mathematical notation, i.e 3 + 2 = 5


More about Number Bonds

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Taking Number Bonds Further

Number bonds are also used to develop strategies such as ‘making ten’ using ten frames, multilink or unifix cubes.

By mastering number bonds early on, pupils build the foundations they need for subsequent learning and are better equipped to develop mental strategies and mathematical fluency. By building a strong number sense, pupils can also decide what action to take when trying to solve problems in their head.

This example shows how a pupil would develop their number sense, or mathematical fluency, by using number bonds to perform a mental calculation.

Maths No Problem - Number Bonds