A weaker class pattern in symbolic number understanding may affect place value, notation and later written methods. Pupils may follow a procedure while losing sight of what each digit, symbol or step represents.

Plan a clear connection between the mathematical structure and its written form.

Choose one representation with a purpose

Use objects, images, number lines, place-value counters or diagrams when they expose the structure being taught. Select one main representation rather than displaying several competing models at once.

Ask:

• What does each part represent?

• Where can we see the value or relationship?

• How does this connect to the symbol or calculation?

• What changes and what stays the same?

For example, represent 3.4 with place-value counters and on a number line before writing it as 3 + 0.4. Then connect the representation to the operation pupils will perform.

Move deliberately towards notation

A useful sequence is:

1. build or inspect the representation;

2. describe the quantities and relationships;

3. record the matching notation;

4. complete a calculation;

5. explain how each written step relates to the model.

Do not leave the representation as decoration beside an unexplained method.

Where symbolic understanding is slightly weaker, showing what one new symbol represents may be enough. Where it is lower, use explicit modelling and guided practice before pupils work independently.

Vary representations after the connection is secure

Once pupils understand the relationship, show the same idea in another form and ask what remains equivalent. At Secondary level, this may involve fractions, decimals, percentages, algebraic notation or standard form.

When some pupils need more

This is whole-class representation planning. Pupils who cannot connect the model and notation may need a personal starting structure or focused checking.

Further guidance

• NCETM: Representation and structure at Primary

• NCETM: Using mathematical representations at KS3