Additive Number Facts
Fluency
Key number facts should be learned to the point of automaticity, with other important mathematical facts explored deeply and practised regularly. Developing procedural fluency and conceptual understanding together is essential, as each strengthens the other.
Learning mathematical facts typically progresses through three stages:
1. Figuring out facts using procedural knowledge.
2. Using strategies based on relationships between numbers to support recall.
3. Achieving automaticity, where facts can be recalled effortlessly.
Automaticity is crucial because it frees working memory, allowing pupils to focus on higher-order thinking and new learning. Establishing secure additive relationships provides the foundation for later work with multiplicative relationships. By ensuring pupils have fluent recall, teachers help prevent cognitive overload and enable children to engage confidently with increasingly complex ideas.
Key Understanding Children Should Develop:
1. Addends can be swapped
Children must know that:
a + b = b + a
The whole stays the same even when the part order changes.
2. The equals sign means ‘is equal to’, not ‘makes’
Misunderstanding the equals sign is common. Children should understand it as a balance, not an operator.
E.g. 3 + 4 = 4 + 3 is a valid and important statement.
3. Commutativity helps with efficiency
Once children recognise that they already know a fact in a different order, addition becomes quicker and more fluent.
E.g. if they know 2 + 7, then they instantly know 7 + 2.
4. Commutativity applies to addition and multiplication, but not subtraction or division
Additive Number Facts Covered in KS1
Key
Adding zero
Developing fluency within 10
Composition of 11-20
Doubles
Near doubles
Bridging through 10