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Secondary Maths Lessons

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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.

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

    • 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

Lesson

Exercise 1

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.

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