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 …

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