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 |
| Graphs and transformations (AS) | Functions - Transformations |
| 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 |
| 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
