Mathematics
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Mathematics Framework
This set of learning objectives and outcomes can be adapted to engage and challenge pupils throughout Key Stages 3 and 4.

APP in mathematics
Examples of marked work (standards files) that uses assessment focuses to help you make level judgements when Assessing Pupils' Progress (APP).

Developing pedagogy in mathematics
Study units and focused materials to help you gain a deeper understanding of mathematical pedagogy and enhance children's knowledge of key mathematical concepts.

Intervention and personalisation in mathematics
Lesson ideas to help you organise and monitor progression. This includes approaches you can use to reduce gaps in pupils’ performance through personalised support.

Study Plus
A twoyear programme aimed at helping Key Stage 4 pupils achieve their potential in GCSE mathematics and English.

Algebra Study Units
Learning objectives provide the focus for these activities, examples and resources, which you can use to create and connect classroom approaches.

Core plus in mathematics
Focused materials that help subject leaders of mathematics raise pupil attainment levels as part of the crosscurricular programme.

A parent's guide to secondary mathematics
These reallife contexts and teaching summaries can help you involve parents and carers with their children’s education.
Mathematics topics

Step 4 Objective
This objective focuses on understanding and using the relationships between the four operations, principles of the arithmetic laws, and using brackets. Relevant questioning and downloads help teachers to identify the skills which pupils should already have at this stage of their learning, along with probing questions relating to this knowledge. For pupils who find this objective a barrier, simpler scenarios and activities are proposed, together with suggested resources. The objective is part of the Equations, formulae and identities substrand in the mathematics progression maps for Algebra.

Step 5 Objective 1
This objective focuses on using letter symbols to represent unknown numbers or variables. Relevant questioning and downloads help teachers to identify the skills which pupils should already have at this stage of their learning, along with probing questions relating to this knowledge. For pupils who find this objective a barrier, simpler scenarios and activities are proposed, together with suggested resources. The objective is part of the Equations, formulae and identities substrand in the mathematics progression maps for Algebra.

Step 5 Objective 3
This objective focuses on constructing and solving linear equations with positive integer coefficients (unknown on one side only) using appropriate methods. Relevant questioning and downloads help teachers to identify the skills which pupils should already have at this stage of their learning, along with probing questions relating to this knowledge. For pupils who find this objective a barrier, simpler scenarios and activities are proposed, together with suggested resources. The objective is part of the Equations, formulae and identities substrand in the mathematics progression maps for Algebra.

Step 6 Objective 1
This objective focuses on constructing and solving linear equations with integer coefficients using appropriate methods (e.g. inverse operations, transforming both sides in same way). Relevant questioning and downloads help teachers to identify the skills which pupils should already have at this stage of their learning, along with probing questions relating to this knowledge. For pupils who find this objective a barrier, simpler scenarios and activities are proposed, together with suggested resources. The objective is part of the Equations, formulae and identities substrand in the mathematics progression maps for Algebra.

Step 6 Objective 2
This objective focuses on simplifying or transforming linear expressions by collecting like terms, and multiplying a single term over a bracket. Relevant questioning and downloads help teachers to identify the skills which pupils should already have at this stage of their learning, along with probing questions relating to this knowledge. For pupils who find this objective a barrier, simpler scenarios and activities are proposed, together with suggested resources. The objective is part of the Equations, formulae and identities substrand in the mathematics progression maps for Algebra.

Step 7 Objective
This objective focuses on constructing and solving linear equations with integer coefficients (with and without brackets, negative signs anywhere in the equation, positive or negative solution), using an appropriate method. Relevant questioning and downloads help teachers to identify the skills which pupils should already have at this stage of their learning, along with probing questions relating to this knowledge. For pupils who find this objective a barrier, simpler scenarios and activities are proposed, together with suggested resources. The objective is part of the Equations, formulae and identities substrand in the mathematics progression maps for Algebra.

Step 8 Objective 1
This objective focuses on using systematic trial and improvement methods and ICT tools to find approximate solutions to equations such as x³ & x = 20. Relevant questioning and downloads help teachers to identify the skills which pupils should already have at this stage of their learning, along with probing questions relating to this knowledge. For pupils who find this objective a barrier, simpler scenarios and activities are proposed, together with suggested resources. The objective is part of the Equations, formulae and identities substrand in the mathematics progression maps for Algebra.

Step 8 Objective 2
This objective focuses on transforming algebraic expressions by factorising to produce a single term multiplied by terms in a bracket. Relevant questioning and downloads help teachers to identify the skills which pupils should already have at this stage of their learning, along with probing questions relating to this knowledge. For pupils who find this objective a barrier, simpler scenarios and activities are proposed, together with suggested resources. The objective is part of the Equations, formulae and identities substrand in the mathematics progression maps for Algebra.

Step 9 Objective
This objective focuses on squaring a linear expression, expanding the product of two linear expressions of the form x ± n and simplifying the corresponding quadratic expression. Relevant questioning and downloads help teachers to identify the skills which pupils should already have at this stage of their learning, along with probing questions relating to this knowledge. For pupils who find this objective a barrier, simpler scenarios and activities are proposed, together with suggested resources. The objective is part of the Equations, formulae and identities substrand in the mathematics progression maps for Algebra.

Step 10 Objective
This objective focuses on solving a pair of simultaneous linear equations by eliminating one variable, and linking a graphical representation of an equation or pair of equations to the algebraic solution. Relevant questioning and downloads help teachers to identify the skills which pupils should already have at this stage of their learning, along with probing questions relating to this knowledge. For pupils who find this objective a barrier, simpler scenarios and activities are proposed, together with suggested resources. The objective is part of the Equations, formulae and identities substrand in the mathematics progression maps for Algebra.