In this unit, students use algebraic notation to express the multiples of integers and see collecting like terms as a development of the distributive property. Students first use a range of representations and contexts including Cuisenaire rods, bar models, number pyramids to manipulate expressions into their simplest form as well as representing equality statements. Seen alongside ‘tracking calculations’, students will develop flexibility in expressing relationships algebraically as well as being comfortable substituting constant values for variables. Once familiarity with this notation system has been developed, students will explore representations of equality, and understand the preservation of equality in written equations. This will then lead to exploration of inequalities utilising bar models and algebraic coding of perimeter as a problem-solving context. Finally, students will explore tracking calculations for counting strategies in growing dot patterns as another context for generalisation, introducing the foundation for later study of sequences.

Substitute variables to evaluate simple expressions. Understand the algebraic notation of multiplication.

Collecting together like terms using tracking arithmetic and algebra.                                                     Manipulating linear expressions involving multiple variables.                                                                       

Using the distributive property to ‘expand brackets’ with linear expressions.     

An introduction to factorising basic linear expressions.                                                                    Introducing the concept of an equation.                          Using Cuisenaire Rods or bar models to form equations.  Form equations related to a known equation.                                                                                                   Explore how equality is preserved. (i.e. balancing) Using Cuisenaire Rods or bar models to form inequalities.                                                                                   Form inequalities related to a known equation. Forming expressions using algebraic lengths specified on a grid                                                                    Drawing shape given expressions for the perimeter Forming expressions using algebraic lengths specified on a grid.                                                             Establishing inequalities from perimeter expressions.                                                                           Generalising counting strategies algebraically for repeating patterns.                                                     Generalising counting strategies algebraically for different repeating patterns.

Representing numbers with variables. 

Understanding the order of operation

Understanding and using distributivity 

Familiarity with basic algebraic notation               

Using brackets and the order of operations 

Simple algebraic notation                                                     

Simple manipulation of linear algebraic expressions                                                                     

Identifying factors and multiples

Representing variables using letters

Simple algebraic manipulation 

Forming simple equations with appropriate models 

Simple algebraic manipulation                               

Forming simple equations with appropriate models

Preserving equality in simple linear equations

Inequality and simple algebraic notation                          Modelling inequality and equality statements

Basic algebraic manipulation                                                      Understanding of perimeter as a length                              Reading and writing algebraic inequalities           

Understanding of perimeter as a length                            Reading and writing the order of operations in written expressions                                                                   

Using letters as variables                                                  Reading and writing the order of operations in written expressions

Understand that algebra is used to express mathematical structures, and
that algebraic terms represent numbers that are unknown or variable

Be able to substitute (into), simplify, expand, and factorize algebraic
Expressions
Understand what is meant by an equation and an inequality

Be able to manipulate equations and inequalities to form new equations
and inequalities.

Be able to form expressions and inequalities in a new context

Be able to simplify and manipulate algebra in a new context

Experience generalizing patterns and how algebra can be used to represent them 

Factorize Expand Variable

 Key questions that students should be able to answer at the end of the 'Topic'

Can I use the inequality symbols to express an inequality.

Can I express perimeter of a polygon shape into an expression which has unknown values?

Can I express perimeter of a polygon shape into an inequality which has unknown values?