1. Gradient as a tangent to a graph at a point
At GCSE, students are introduced to the concept of finding the gradient of a curve at given point by drawing a tangent to the curve at the point, then finding the gradient of the tangent. They are then expected to be able to interpret the gradient as a rate of change.
This activity reinforces the concept using GeoGebra in preparation for students developing a graphical understanding of the gradient function.
Click below to download the PowerPoint slides with embedded GeoGebra links. Then watch the video for instructions on using GeoGebra and an explanation of the intended learning.
2. Sketching the gradient function of a curve
Sketching the gradient function and identifying key features is crucial for developing an understanding of differentiation.
Here, GeoGebra is used to automatically plot the gradient function as a point is dragged along the curve, to help reinforce students’ graphical understanding of the gradient function.
Click below to download the PowerPoint slides with embedded GeoGebra links. Then watch the video for instructions on using GeoGebra and an explanation of the intended learning.
3. Exploring the effect of the y-intercept on the gradient function
Sometimes students feel that constant terms just ‘disappear’ when a function is differentiated. Here, GeoGebra is used to explore the gradient function for a number of functions, which are identical apart from their intercept. After examining what happens graphically, they then explore the effect of the y-intercept on the gradient function of a curve more formally.
Click below to download the PowerPoint slides with embedded GeoGebra links. Then watch the video for instructions on using GeoGebra and an explanation of the intended learning.
4. Determining where a function is increasing and decreasing
Students are required to be able to determine where a function is increasing and decreasing, but many find it hard, particularly when trying to determine these algebraically. In this activity, colour coding within GeoGebra is used to identify where functions are increasing and decreasing more clearly.
Click below to download the PowerPoint slides with embedded GeoGebra links. Then watch the video for instructions on using GeoGebra and and explanation of the intended learning.
5. Classifying stationary points
Here, two different approaches to classifying stationary points, both of which involve the use of GeoGebra are explored.
Click below to download the PowerPoint slides with embedded GeoGebra links. Then watch the video for instructions on using GeoGebra and an explanation of the intended learning.
6. Summarising learning to sketch the gradient function for a given function
This activity can be used to explicitly identify features of a function to support students in sketching a gradient function for a given function.
Click below to download the PowerPoint slides with embedded GeoGebra links. Then watch the video for instructions on using GeoGebra and an explanation of the intended learning.
7. Modelling with differentiation
Students frequently find this the most challenging element of Year 12 differentiation. However, using GeoGebra can make both the links between the information they are given, and the process of optimisation much clearer.
Click below to download the PowerPoint slides with embedded GeoGebra links. Then watch the video for instructions on using GeoGebra and an explanation of the intended learning.
Sinéad Vaughan PhD Study 