Secondary Maths – Topic Special: Algebra: Quadratic Expressions and Graphs
Collection Author: Owen Elton - Maths Secondary Panel Member
Students’ first encounters with quadratic expressions are important. The underlying mathematics is full of ideas that they may well be considering for the first time: zeros and factors of polynomials; many-to-one functions; graphs that are curved; stationary points; complex numbers; models for projectile paths. Quadratic expressions are the key to unlocking a world of non-linear mathematics and they offer a rich vein of maths for exploration. The TES website contains many excellent quadratic-related resources. Here are ten that each offer something a little extra.
Top 10 Resources:
- This is an absolutely stunning idea. It combines artwork from a popular smartphone app and the idea that quadratic equations may be used to model the path of projectiles. Students are challenged to enter an equation that fits certain conditions, then fire the catapult to see if they are correct.
- This Excel file offers a comprehensive overview of graphs of quadratic functions. Enable macros and use the slider bars to alter the graphical and numerical output. Make sure that you explore all five sheets; each covers a different aspect of the Cartesian form of a parabola.
- Here is another graph based activity. This one is aimed at KS4 students and is the penultimate in a series of four Sketching Quadratics activities available here. Students are invited to predict points that will lie on a given parabola before checking their calculations by using the software.
- This fun activity will encourage students to practise quadratic factorisation accurately and at pace. The Excel file generates bingo cards and contains the smart board display required during the game.
- Here’s a quadratics worksheet with a twist. Students find the roots of several quadratics and colour in the corresponding cells in a grid; this reveals a further question to solve.
- This jigsaw activity will help students who are seeing the quadratic formula for the first time. To successfully complete it, they will need to correctly identify values of a, b, and c from a quadratic equation. There are two levels of difficulty provided.
- Another splendid jigsaw activity; this time, students have to identify the solutions of quadratic inequalities. A tarsia activity is particularly valuable here since students frequently correctly solve the quadratic equation of critical values but fail to produce a correct expression for the range of values; this activity will re-emphasize how the solutions should appear.
- This worksheet emphasizes the information that can easily be inferred from each of three different methods of writing a quadratic expression. A useful summary or revision activity for GCSE and C1 candidates.
- This neat Excel file will help students put graphs of quadratic equations in context. Using slider bars, they can see the effect of making the quadratic term of a polynomial non-zero. They can also investigate what happens when cubic and quartic terms are introduced.
- Finally, here’s something that’s quite fun to play with. Investigate how changing a quadratic and a quartic equation can change the expression on a cartoon character’s face.