# Core Representations

## Primary

### Tens frames ### Number Line ### Gattegno chart ### Partitioning diagrams including bar models ### Groups of units in addition to ones such as Dienes, Place Value counters ## Secondary

### Counters and algebra tiles (zero pairs) Making sense of the number system

Working with integers

Linking the structure of number to algebra

Manipulating algebraic expressions

### Arrays and area models Multiplicative relationships

Area

Multiplication of integers, decimals, fractions …

Expand and factorise

Commutativity property of multiplication

Distributive property of multiplication

Multiplying and dividing algebraic expressions

### Cuisenaire Rods Proportional reasoning

Additive and multiplicative relationships

Linking the structure of number to algebra

Sequences

Area and perimeter

Proportional reasoning

Additive and multiplicative relationships

Manipulating algebraic expressions

### Gattegno chart Structure of the number system

Multiplying and dividing by powers of 10

Standard index form

Percentages

### Place Value Charts Base 10 system

Understanding of the structure of the standard algorithms for the 4 operations on number

Standard index form

### Partitioning diagrams including bar models Additive and multiplicative relationships

Part part whole

Equal parts

Comparison

Additive and multiplicative relationships

### Dienes, Base blocks, Place Value counters  Base 10 system

Understand the geometrical structure common to all bases including base x with base blocks (links to algebra tiles)

Understanding of the structure of the standard algorithms for the 4 operations on number (make connections with place value charts)

Perimeter, area and volume

Standard index form

Indices including negative indices.

Make links to the 4 operations on number to algebra.

### Number lines Understanding the number system

Number operations

Positioning and ordering

Negative numbers

Fractions and decimals

Rounding

Graphs

Bounds

### Double number lines and ratio tables Multiplicative relationships

Scaling

Ratio and proportion

Compound measures