Student Tasks: GeoGebra
These tasks are designed to help students in understanding mathematical relationships better through exploring dynamic constructions. They can be accessed using the computer-based version of GeoGebra or the tablet/smartphone app. They have been designed with the following structure:
- Construction: step-by-step guidance of how to construct the objects in GeoGebra.
- Questions for discussion: The emphasis is on students being able to observe mathematical relationships by changing objects on their screen and being able to describe what happens, and explain why.
- Problem: The purpose is for them to formalise what they have learnt through exploration and discussion and apply this to a “standard” style question.
- Further tasks: Extension activities with less structure for students who have successfully completed the first three sections.
GCSE Mathematics
AS/A level Mathematics: Pure Mathematics (AS)
| Topic | Classroom tasks |
|---|---|
| Surds and indices (AS) | |
| Quadratic functions (AS) | Plot y=ax2+bx+c in and vary a, b and c. Graphs of quadratic functions |
| Equations and inequalities (AS) | Intersection of a line and a curve Quadratic inequalities |
| Coordinate geometry (AS) | Perpendicular lines |
| Trigonometry (AS) | Solution of trig equations |
| Polynomials (AS) | The Factor Theorem (GeoGebra Classic) The Factor Theorem (GeoGebra graphing app) |
| Graphs and transformations (AS) | Functions - Transformations Functions - Transformations of y=1/x curves |
| The binomial expansion (AS) | |
| Differentiation (AS) | Exploring the gradient on a curve Introduction to Stationary Points |
| Integration (AS) | Area under a curve |
| Vectors (AS) | Introduction to vectors |
| Exponentials and logarithms (AS) | Graph of y=kax Derivate of exponential functions y=ekx |
Between April and July 2019 MEI trialled the use of GeoGebra exam mode with a selection of schools and colleges. The materials included practice questions and guidance based on the pure content of AS Mathematics. These materials can be used by students to learn how to use GeoGebra to support their studies.
| Topic | Classroom tasks |
|---|---|
| Trigonometry | Trig equations in radians |
| Sequences and series | Sum of an AP Sum of a GP |
| Functions | The Modulus Function Inverse functions |
| Differentiation | Points of inflection |
| Trigonometric functions | |
| Algebra | Partial Fractions |
| Trigonometry identities | Double Angle formulae Rcos(θ−α) |
| Further Differentiation | Differentiating trigonometric functions |
| Integration | Gradient of tangent to y=lnx |
| Parametric equations | Tangents to parametric curves |
| Vectors | |
| Differential equations | |
| Numerical methods | Change of sign Fixed point iterations Newton-Raphson |
AS/A level Further Mathematics
| Topic | Classroom tasks |
|---|---|
| Complex numbers |
Roots of quadratic equations Addition and subtraction in the Argand diagram |
| Roots of polynomial equations | Roots of polynomial equations |
| Matrices |
Transformation matrices Determinants and inverse matrices 3x3 matrices and transformations |
| Polar curves | Polar curves |
| Vectors | Intersection of three planes |
| Conic sections | Parabolas, hyperbolas and ellipses |
| Rational functions | Sketching the curves of rational functions |
Problem solving activities using GeoGebra
These problem solving activities are constructions that test students' understanding of connections between representations and reinforce generalisation
