Top resources and advice to help you to get to grips with quadratic graphs as part of the new GCSE specification
Everyone is talking about functions and frequency trees, but what else has changed with the advent of the new specification? And what resources are available to help? Throughout this series, TES Maths aims to find out.
What does the specification say?
The expectation is that:
- All students will develop confidence and competence with the content identified by standard type
- All students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content
- Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.
A11: Identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square.
What's the same?
Much to the displeasure of Year 11s up and down the country, quadratic graphs continue to feature as part of the new GCSE specification. Both foundation and higher tier students will need to be able to plot quadratic graphs from a table of values, as well as recognise the general shape of a quadratic function.
What has changed?
In short, candidates sitting both tiers are expected to do a bit more with the quadratic function.
Foundation tier students will need to be able to make deductions from a graph they've been given, or one they have drawn themselves from a table of values. They should be able to work out the roots of the graph (a result of also being expected to factorise quadratic equations - more on this later in the series!), the y-intercept and also the turning point. Thankfully, students will not be expected to complete the square in order to deduce the turning point. Instead, they will be expected to use the symmetry of a quadratic function and their knowledge of roots.
Higher tier candidates won't miss out on the fun. They willbe expected to complete the square in order to find the turning point of a quadratic graph. While many teachers will have covered this skill over the last few years, it is worth going over it again as it is now mentioned explicitly in the new specification. Additionally, students may be expected to complete the square for expressions in the form ax2+ bx + c, where the coefficient of x2 is greater than 1. It is unclear whether students will also be expected to find the turning points of such graphs. Watch this space!
How can TES Maths can help?
As ever, the wonderfully talented authors of the TES Maths community have stepped up to the mark to lend a hand. Here is a selection of my favourite resources to help support the teaching of this topic:
- Introduction to quadratic graphs
Take students through the process of plotting a quadratic graph with this well-structured presentation and accompanying worksheet.
- Plotting practice worksheets
Use these simple worksheets to give students the chance to practise plotting quadratics from a table of values.
- Themed plotting activity
Engage students with this Angry Birds-themed task, in which they must plot quadratic functions in order to destroy The Pigs.
- Sketching quadratics lesson
TES Author, Pixi_17, takes the basics one step further with this fully differentiated lesson, including opportunities for students to expand brackets and develop their sketching skills.
- Quadratic graph sketching practice
Challenge students to factorise and solve equations to find roots, identify the intercept, complete the square to find the turning point and decide whether it is minimum or maximum.
- Time Rider activity
Encourage students to make the link between plotting quadratics and the completing the square form of the equation using this engrossing task.
- Quadratic graph match-up
Reinforce knowledge of all forms of quadratic graph with this tricky, original exercise in which students match pre-sketched graphs to equations.
- Completing the square cards
Differentiated by colour, these well-designed cards require students to complete the square to sketch quadratic graphs, including those where the coefficient on x2 is greater than 1.
- Properties and forms of quadratic functions lesson
Extend learning with this demanding lesson, which allows students to make connections between the different forms of quadratic equation, as well as dabble in calculus.
Craig Barton, TES Maths adviser
Craig is a secondary maths teacher in the North of England.
Find more resources to support the changes to the GCSE maths specification by taking a look at the rest of the series.