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.
Pupils must understand that, in partitioning situations, the subtraction symbol represents a splitting up or differentiating of the whole.
The problem “There are 6 children altogether. 2 children are wearing coats. How many are not wearing coats?” is represented by 6–2 =4 .
Here, the subtraction symbol represents the separation of the 2 children wearing coats, and so, the number of children not wearing coats is exposed
“There are 6 children altogether. 2 children are wearing coats. 4 children are not wearing coats.”
“We can write this as 6 minus 2 is equal to 4.”
“The 6 represents the total number of children.”
“The 2 represents the number of children that are wearing coats.”
“The 4 represents the number of children that are not wearing coats.”