Equations and functions

Discover our collection of GCSE maths algebra - equations and functions lessons, activities, powerpoints and notes. These resources are hand-picked by the Tes Maths Panel for their relevance to the 9-1 specifications - use them for planning, homework and revision.

This page contains the very best resources for teaching sections A7 and A17 to A21 from the GCSE maths specification (first examined in 2017), combining structured lessons and engaging activities. With the old staple of solving equations, together with the brand new topic of functions, this collection of resources should help refine and develop algebraic competence in these key areas.

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Solving linear equations

Mathonopoly - Solving Equations

Based on Manoj Mistry (manojm03)'s excellent Mathonopoly idea, this is an adapted version I've made. The questions are designed for Year 7 students being introduced to solving equations. I&'ve also created some humerous chance and community chest cards (although some references may need to change to suit your school).
By Daniel Burke

Solving equations bingo game.

A nice bingo game to add some spice to solving simple linear equations.

By MrBartonMaths

Solving Equations powerpoint

A powerpoint showing how to solve linear equations, it encourages students to read the equations and work backwards. There are some questions with answers at the end.
By bcooper87

Solving Equations using the Balance Method

Algebra level 6 Powerpoint: An introduction to solving equations using the balance method
By MrBartonMaths

Solving quadratic equations

Solving Quadratic Equations W/S

This A4 worksheet (exercise mat) has a selection questions which involve solving quadratic equations grouped by methods of how to solve. Factorisation (non calc), using the quadratic formula and completing the square.
By climbingjack

Quadratic equations

Powerpoint including examples and worksheets on forming and solving quadratic equations using factorising, completing the square and the quadratic formula. Includes some problem solving tasks adapted from Don Steward's Median blog and a few resources I found via resourceaholic.com (sorry I can't remember exactly who these should be credited to).
By danwalker

GSCE Maths: Solving Quadratics Worksheet

Solve the quadratic equations, colour in the grid and reveal a problem to solve!
By alutwyche

Quadratic Equation

This is a good resource of introducing quadratic equation to help students building up the formula.
Suitable to higher tier KS4 and for AS-level C1.
By ak1978

Solving simultaneous equations

Simultaneous Equations Introduction

This lesson is intended as an introduction to Simultaneous Equations, where students solve picture-based puzzles without using formal Algebra. The idea is that the following lesson they can see equations given algebraically and see how it is effectively the same thing! If you liked this resource then please check out my other stuff on TES!

By Owen134866

Arithmagon 14 - Simultaneous Equations

This a rich, Arithmagon activity on solving simultaneous equations.

I love Arithmagons as they allow consolidation of key topics when going Forwards, and then opportunities for extension, creativity and discovery when working Backwards. They are also really easy to modify to suit the particular needs of your class.

For all the Arithmagon activities in this series, together with teaching notes and extra information, please visit http://www.mrbartonmaths.com/arithmagon.htm
By MrBartonMaths

Simultaneous Equations Graphically

This lesson will show students how plotting two linear equations in x and y allows them to solve simultaneous equations. The powerpoint has a full explanation as the starter and there is a sheet of questions for students to practice. Before doing this task they should have covered algebraic versions of simultaneous equations, as well as linear graph plotting. If you liked this resource then please check out my other stuff on TES!

By Owen134866

Trial and improvement and iteration

Trial and Improvement

How to solve an equation using trial and improvement.
By Daniel Burke

Iteration and Square Roots

In this lesson, students learn what iteration is and see an example of how it was used to calculate square roots of non-square numbers. There is an explanation of the notation involved and students get to try the process out for themselves. Could be used as an introduction to the topic. If you liked this resource, please check out my other stuff on TES!

By Owen134866

Tarsia - Iteration

A brilliant Tarsia activity by Gill Hillitt on iteration and iterative functions. These type of activities can be used to consolidate understanding of a given topic, and foster positive group work and co-operative learning. For more ideas on how to use these types of activities (including twists!) and to download the latest version of the wonderful free software to open this resource (and create your own), just click on the web-link. If you have any comments or feedback for Gill, please share them below.
By MrBartonMaths

Substitution into formulae

Who wins the Heptathlon?

Lesson on the official formulae used to calculate the amount of points athletes get for different events of the Heptathlon. An important part is the discussion afterwards as to whether the scoring system is fair or not (an article is linked in the powerpoint) If you like this resource then please check out my other stuff on here!
By Owen134866

Algebraic Substitution

My thanks to an earlier contributor for the core idea. An activity to allow students in KS3 & 4 to test their substitution skills. Each substitution gives a numerical answer, which is then translated into a letter using the code grid. 4 sets of substitutions proivde clues to the identity of a famous person.
By whistleblower1

Which gives the biggest answer?

Students have to try and work out which expression will give the biggest answer when a value for x is substituted in. Of course, it isn't that simple and they find that the answer varies depending on the value used. It is a good opportunity for them to consider how drawing graphs can help find whereabouts solutions might lie. I have also included some blank autograph axes which can be used to plot the graphs more dynamically and find what regions are highest for each. Extension questions could include finding expressions where one is always bigger, one which is higher above a specific value for x etc. Lots of opportunity for extension - students could also use Autograph themselves to experiment! If you liked this resource, then please check out my other stuff on TES! :) https://www.tes.com/resources/search/?authorId=2095097
By Owen134866

Venn Diagrams 7 - Algebraic Substitution

This is a rich Venn Diagram activity on algebraic substitution and formula.

To access all the Venn Diagram activities in this collection, as well as teaching notes, please visit: http://www.mrbartonmaths.com/venn.htm

Here is why I love Venn Diagram activities so much:

1) Students can always make a start. If they can think of a number/expression/object or whatever it might be, it has to go in one of the regions on the diagram, so they are up and running
2) The more regions student find, the more challenging the task gets, which adds a nice element of differentiation
3) They are incredibly versatile, and can be used for almost all maths topics for all ages and abilities
4) They are easy to tweak by simply changing one of the circle labels if you find they are too difficult/easy
5) Students can create their own as an extension task

I hope you and your students enjoy them.
By MrBartonMaths

Rearranging formulae

Rearranging Explosions

I am about to tackle rearranging formulae (a topic so many find difficult) with my Year 10 class so came up with this in an attempt to make them more comfortable with playing with algebra; it should also encourage discussion about different ways of doing it.
By alutwyche

Changing the subject

These two powerpoints go through the basics of changing the subject of an equation or formula. The first includes just simple linear rearrangement, and the second includes example of factorising and dealing with roots and fractions. Nothing especially exciting, just trying to be as clear as possible!

If you liked this resource, then please check out my other stuff on TES!

By Owen134866

Rearranging formulae / changing the subject

If these are given to students pre-cut, they can then group them according to equivalent equations. Suggested groupings on the second page.
By MarysMaths

Functions (notation, inverse, composite)


These 4 powerpoints have been made for the Cambridge IGCSE course and cover the section on functions. Pupils learn about function notation and what it means, and see how to approach problems involving composite and inverse functions. The textbook has the relevant exercises! If you like this resource then please check out my other stuff on here! :)
By Owen134866

Functions (New GCSE 2015)

A PowerPoint I made to take my Year 10s through the new GCSE topic on Functions. Starts with simple function notation and substitution, before moving on to composite functions - both numeric and algebraic - and finishing with inverse functions.

Also included are two codebreakers for the substitution elements that lead to a funny joke. I also created a Tarsia for the inverse functions element, but sadly can't upload that to TES. Instead, you can download it here: https://drive.google.com/file/d/0B_raar3XGLkMVVhRdFZvUDJQNk0/view?usp=sharing (ignore the weird preview it gives you - just download it and it's fine).
By Daniel Burke

Functions multiple choice starter

IGCSE has some functions work on it. This is mainly consolidation of what I have taught them so far but I am about to move onto composite functions hence the last few slides look a bit different to what they will need to get used to as I want them to figure out what's going on. When I teach with this I will show them the proper notation for composite functions on the board after they have answered the questions. If you have time, you may want to add in some animations to replace the f(g(x) with fg(x) etc.
By Tristanjones