Pupils must learn to use the mathematical symbols + , – and = .
Expressions or equations involving these symbols should be introduced as a way to represent numerical situations and mathematical stories.
An expression such as 3 + 5 should not be interpreted as asking “What is 3 + 5 ?” but, rather, as a way to represent the additive structures discussed below, either within a real-life context or within an abstract numerical situation. It is important that pupils do not think of the equals symbol as meaning ‘and the answer is’.
They should instead understand that the expressions on each side of an equals symbol have the same value.
All examples used to teach this criterion should use quantities within 10, and be supported by manipulatives or images, to ensure that pupils are able to focus on the mathematical structures and to avoid the cognitive load of having to work out the solutions.
There are 4 additive structures (aggregation, partitioning, augmentation and reduction)
Pupils should learn to link expressions (for example, 5 + 2 and 6 – 2 ) to contexts before they learn to link equations (for example, 5 + 2 = and 6 – 2 = 4 ) to contexts.
For each case, pupils’ understanding should be built up in steps:
Pupils should first learn to describe the context using precise language (see the language focus box).
Pupils should then learn to write the associated expression or equation.
Pupils should then use precise language to describe what each number in the expression or equation represents.
In the course of learning to read, write and interpret addition and subtractions equations, pupils should also learn that equations can be written in different ways, including:
- varying the position of the equals symbol (for example, 5 –2 =3 and 3 = 5 – 2)
- for addition, the addends can be written in either order and the sum remains the same (commutativity)
Pupils must also learn to relate addition and subtraction contexts and equations to mathematical diagrams such as bar models, number lines, tens frames with counters, and partitioning diagrams.