Developed in Partnership with Dr Frost Learning, these resources are suitable to 11-16 maths teaching (KS3 and KS4 in England), unless otherwise indicated.

Each lesson features a lesson PowerPoint as well as printable exercise and investigation sheets.

- Changing the Subject with Higher Powers, Roots Including Brackets and Fractions
- Change the Subject of a Linear Formula Involving Brackets and Fractions
- Substitution with the Four Operations and Integers
- Integer Substitution with Powers and Roots
- Substitution with Fractions and Decimals
- Form Simple Expressions
- Form and Use Simple Formulae
- Form and Solve Linear Equations from Simple Contexts
- Form and Solve Linear Equations for Problems Involving Perimeter and Area
- Changing the Subject – One Step

## Changing the Subject with Higher Powers, Roots Including Brackets and Fractions

**Climate change context**

Rearranging the formula for the power derived from a wind turbine, and substituting values into its rearranged form.

**Prior Learning**:

- Solve simple linear equations.
- Form simple expressions & formulae
- Use and interpret algebraic notation, including:

– ab in place of a×b,

– 3y in place of y+y+y and 3×y,

– a/b in place of a÷b,

– coefficients written as fractions rather than as decimals.

– brackets. - Distinguish between expressions, equations, inequalities, terms and factors
- Order of operations
- Change the subject of a linear formula requiring two steps (including simple divisions).
- Change the subject of a formula where the subject is multiplied or divided by more than one constant or variable.
- Change the subject of a formula where the subject appears on the denominator of a fraction.
- Change the subject of a linear formula where the coefficient of the subject is negative.
- Expanding single brackets.
- Change the subject of a linear formula involving multiplication using brackets.
- Change the subject of a linear formula requiring two steps resulting in a bracket.
- Change the subject of a formula with brackets and fractions.
- Change the subject of a formula where the subject is squared and with additional steps

## Change the Subject of a Linear Formula Involving Brackets and Fractions

**Climate change context**

2023 being confirmed as the hottest year on record

**Prior Learning**:

- Solve simple linear equations.
- Form simple expressions & formulae
- Use and interpret algebraic notation, including:
- 𝑎𝑏 in place of 𝑎×𝑏,
- 3𝑦 in place of 𝑦+𝑦+𝑦 and 3×𝑦,
- 𝑎/𝑏 in place of 𝑎÷𝑏,
- coefficients written as fractions rather than as decimals.
- Brackets

- Distinguish between expressions, equations, inequalities, terms and factors
- Order of operations
- Change the subject of a linear formula requiring a single step.
- Change the subject of a linear formula requiring two steps (including simple divisions).
- Change the subject of a formula where the subject is multiplied or divided by more than one constant or variable.
- Change the subject of a formula where the subject appears on the denominator of a fraction.
- Change the subject of a linear formula where the coefficient of the subject is negative.
- Expanding single brackets.
- Change the subject of a linear formula involving multiplication using brackets.

## Substitution with the Four Operations and Integers

Substitution is the process of replacing the variables in an algebraic expression, usually with a numerical value. We can then work out the total value of the expression.

**Climate change context**

Calculating household carbon dioxide emissions

**Prior Learning**:

- Negative numbers and arithmetic
- Decimals and arithmetic
- Fractions and arithmetic
- Powers and roots
- Basic algebraic notation
- Using function machines & their inverses

## Integer Substitution with Powers and Roots

**Climate change contexts**:

Substitution and the Sahara

Rainforest deforestation

**Prior Learning**

- Substitution with four operations and integers
- Using notation for powers and roots
- Knowing powers and roots with base 2, 3, 4, 5 and 10

## Substitution with Fractions and Decimals

**Prior Learning**

- Decimals and arithmetic
- Fractions and arithmetic
- Powers and roots
- Basic algebraic notation
- Substitution using integers with the four operations
- Substitution using integers with powers and roots

Investigation Sheet 1 – Wind Turbine

Investigation Sheet 2 – Wind Turbine

## Form Simple Expressions

**Climate Change Contexts**

Arctic warming

Building insulation

Carbon footprint of social media

Emissions reductions

**Prior Learning**

- Use and interpret algebraic notation, including:

–ab in place of a×b,

–3y in place of y+y+y and 3×y,

–a/b in place of a÷b,

–coefficients written as fractions rather than as decimals.

–brackets

- Simplify expressions with sums, products and powers including index laws
- Distinguish between expressions, equations, inequalities, terms and factors
- Algebraic substitution
- Recognise & create equivalent expressions
- Order of operations

## Form and Use Simple Formulae

**Climate Change Contexts**

Tree planting

Vehicle emission reductions

Solar panel output

**Prior Knowledge**

- Use and interpret algebraic notation, including:

–ab in place of a×b,

–3y in place of y+y+y and 3×y,

–a/b in place of a÷b,

–coefficients written as fractions rather than as decimals.

–brackets

- Simplify expressions with sums, products and powers including index laws
- Distinguish between expressions, equations, inequalities, terms and factors
- Algebraic substitution
- Recognise & create equivalent expressions
- Order of operations
- Form simple expressions

## Form and Solve Linear Equations from Simple Contexts

**Climate Change Context**

Emission reductions and net zero

**Prior Knowledge**

- Solve simple linear equations.
- Solve linear equations with brackets.
- Solve linear equations where the variable appears on both sides of the equation.
- Solve linear equations involving brackets.
- Expanding single brackets.
- Form simple expressions & formulae.
- Use and interpret algebraic notation, including:

–ab in place of a×b,

–3y in place of y+y+y and 3×y,

–a/b in place of a÷b,

–coefficients written as fractions rather than as decimals.

–Brackets.

## Form and Solve Linear Equations for Problems Involving Perimeter and Area

**Climate Change Context**

Carbon footprint/ growing food

Tree planting

**Prior Knowledge**

- Find the area and perimeter of simple shapes.
- Solve simple linear equations.
- Solve linear equations where the variable appears on both sides of the equation.
- Expanding single brackets.
- Form simple expressions & formulae
- Use and interpret algebraic notation, including:

–ab in place of a×b,

–3y in place of y+y+y and 3×y,

–a/b in place of a÷b,

–coefficients written as fractions rather than as decimals.

–Brackets

- Simplify expressions with sums, products and powers including index laws
- Distinguish between expressions, equations, inequalities, terms and factors
- Algebraic substitution
- Recognise & create equivalent expressions
- Order of operations

## Changing the Subject – One Step

**Climate Change Context**

Ocean Warming

**Prior Knowledge**

- Solve simple linear equations.
- Expanding single brackets.
- Form simple expressions & formulae
- Use and interpret algebraic notation, including:

–ab in place of a×b,

–3y in place of y+y+y and 3×y,

–a/b in place of a÷b,

–coefficients written as fractions rather than as decimals.

–Brackets

- Simplify expressions with sums, products and powers including index laws
- Distinguish between expressions, equations, inequalities, terms and factors
- Algebraic substitution
- Order of operations

Dr Frost Learning is a UK registered charity with goal of delivering high quality education for all individuals and institutions regardless of income, centred around the philosophy that education is a fundamental right of all and central to addressing social inequality on a global level. The charity was founded by Dr Jamie Frost and he received the Covid Hero Award in the Global Teacher Prize 2020.