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
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
Lesson ppt
Mixed Exercise pdf
Mini Exercises.pdf
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.
Lesson ppt
Exercise pdf
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
Lesson ppt
Exercise pdf
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
Lesson ppt
Exercise pdf
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
Lesson ppt
Exercise pdf
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
Lesson ppt
Exercise pdf
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
Lesson ppt
Exercise pdf
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.
Lesson ppt
Exercise pdf
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
Lesson
Exercise 1
Exercise 2
Mixed Exercise
Changing the Subject – One Step
Climate Change Context
Ocean Warming
Prior Knowledge
Lesson
Exercise 1
Solving Linear Simultaneous Equations Using Graphical Methods
Climate Change Context
Determining the cost to plant trees following deforestation in the Amazon
Prior Knowledge
- Coordinates
- Recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in 𝑥 and 𝑦 and the Cartesian plane (KS3)
- y=mx+c
Lesson
Exercise 1
