# Core Representations

## Primary

### Rekenrek

### 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 â€¦

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

https://www.ncetm.org.uk/media/8d84e791bafa491/ncetm_ks3_representations_bar_models.pdf

http://thewessens.net/ClassroomApps/subindex.html?id=wordproblems&topic=models&path=Models

http://thewessens.net/ClassroomApps/subindex.html?id=fractions&topic=models&path=Models

Part part whole interactive model - Desmos

### 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