A collection of resources on solving simultaneous equations…
We could start with the White Rose Year 10 materials. An Autumn term block is on simultaneous equations; excellent free publications from White Rose include the scheme of learning with small steps, exemplar questions & answers, and Foundation and Higher End of Block assessments with answers.
Staying with the idea of small steps, check Building Blocks on Simultaneous Equations, a collection of 14 problems from Andy Lutwyche; I do like this Building Blocks series – a useful reminder of the skills students need and the question types they can encounter. As Andy states – “This takes students through all the skills required to solve simultaneous equations graphically (only linear graphs), by elimination and by substitution including one linear and one non-linear up to GCSE level. Work from the bottom building the skills up to the most complex style of question.”
I have often used the Building Blocks resources as revision resources with GCSE students.
From Andy, we have several resources on simultaneous equations including Clumsy Clive who is making mistakes on his homework again!
From Dr Austin Maths we have a lovely collection including some very recent additions on Simultaneous Equations. The collection includes a favourite format of mine – fill in the blanks.
Note also a new type of activity, sort it out – see Simultaneous Equations sort it out where students must decide which of 4 categories the pair of equations belongs to, which is the most efficient method for solving the equations by elimination?
On Transum Mathematics, several resources on Simultaneous Equations are available. This really is a lovely collection with a great variety of resources. See also the topic list for teachers.
For a great introduction to simultaneous equations, try Simultaneous Shopping, a reminder of just how helpful diagrams can be. Level 1 is illustrated.
Level 5 uses coupons to introduce the idea of negative coefficients.
From Don Steward, see his many (34) Simultaneous Equations posts including an article with some suggested steps for teaching the topic and a series of 6 on generalising which you will see were written in February 2019, a PowerPoint is available for this series.
From PixiMaths, her Simultaneous Equations collection starts with a lovely introduction using bar models. This collection includes four lessons, including equations where one is linear and the other quadratic.
On Matt Woodfine’s Maths White Board, search for Simultaneous Equations, illustrated above is a retrieval board on linear simultaneous equations.
Colin Foster’s wonderful Mathematical Etudes Project includes simultaneous equations; the article describes a complete lesson, to quote Colin Foster:
In this lesson, students explore a set of two-variable linear equations, constructed so that when you solve any pair of them simultaneously you get solutions which are all nonnegative integers.
From Craig Barton – see Simultaneous Equations Staircase, rather like Colin Foster’s lesson this will provide practise of solving simultaneous equations, whilst at the same time sparking students’ curiosity. Starting with linear sequences, students form a pair of simultaneous equations and solve them. What happens if they start with 2 different sequences?
We could use the excellent Mobile Puzzles from The Transition to Algebra (TTA) project, an initiative of the Learning and Teaching Division at Education Development Center, Inc. (EDC).
Here’s a lovely problem from Open Middle to really get your students thinking, this post includes a Desmos page and a Graspable Maths canvas for the problem.
From Teachit Maths, we have a collection on Simultaneous equations.
For practising problems with words try Simultaneous scenarios, the free pdf includes the questions and solutions. Subscribers can access a PowerPoint version.
We should of course illustrate solutions graphically, when working on simultaneous equations using algebra, it is so easy to show a graphical illustration. For exploring graphical solutions, we could use David Smith’s Simultaneous Equations Graphical Solution on Geogebra which includes questions for students to try.
From Ishak Hassan, this Simultaneous Equations GeoGebra resource allows you to create pairs of simultaneous equations.
You can change 3 points on the screen including the intersection of the two lines.
We are so fortunate in Maths to have so many resources available to us, just a sample of some further resources:
- Minimally Different Problems, from Jess Prior includes Simultaneous Equations
- Increasingly Difficult Questions from Dave Taylor, under Algebra you will find Simultaneous Equations
- Maths HKO, Miss Konstantine, Simultaneous Equations
- Diagnostic Questions, see from the Eedi Ultimate Scheme of Work – Simultaneous Equations – Linear, Simultaneous Equations – non-linear, and Simultaneous Equations – solving linear equations graphically. You can also find Simultaneous Equations in the exam board collections.
- Corbett Maths:
Simultaneous equations (elimination) Video 295 Practice Questions Textbook Exercise Simultaneous equations (substitution, both linear) Video 296 Practice Questions
Simultaneous equations (graphical) Video 297 Textbook Exercise
Simultaneous equations (advanced) Video 298 Practice Questions Textbook Exercise
The answers are all here, look for the video numbers.
- Maths4Everyone GCSE questions by topic (select Algebra from the menu)
- DrFrost Exam Questions by topic includes Full Coverage: Simultaneous Equations
- From CIMT, the GCSE materials include Equations, this chapter from the GCSE text includes simultaneous equations in section 10.8 and provides plenty of practice examples including wordy problems.
- Nrich resources connected to Simultaneous Equations. Arithmagons are an ideal resource for solving simultaneous equations.