Patterns from function graphs in GeoGebra
Functions are an important topic in mathematics. In Estonia, the study of functions begins in Grade 7, when students learn about linear functions and inverse proportionality. Quadratic functions are introduced in Grade 9. The topic of functions is often challenging for students, especially at the beginning, because developing a conceptual understanding requires familiarity with different representations of a function, such as equations and graphs, and an understanding of how these representations are connected.
Research has shown that using dynamic geometry software can be beneficial when learning this topic. Such programs allow students to see in real time how the graph of a function changes as the coefficients in its equation change.
Below, I present an idea for creating a visually appealing pattern in GeoGebra while simultaneously working with different representations of functions. Studies indicate that this kind of activity brings students joy and helps them feel that they understand functions more deeply.
Instruction for workshop
Open GeoGebra.
provide an opportunity to discuss whether the relation represents a function or not.
- Insert a Slider in the Graphics view. Fill in the cells (Min, Max, Increment). Open the Animation tab and choose Speed and Repeat.
- Insert some more Sliders.
- To make a pattern, type in an equation of a line in the Input bar. When doing this, you should use the slider names in the equation. For example, if you want to insert a line y = ax + b, you should have sliders named a and b. If you want to plot a graph of y = c/x, you should have a slider named c. You can plot several lines, hyperbolas and parabolas.
- Make a right-click in Graphics view and untick Axes and Grid.
- Make a right-click on one of the graphs, choose Object Properties and follow the next steps: (a) Open the Basic tab, untick Show Label and tick Show Trace. (b) Open the Style tab and choose a Line Thickness and Style. (c) To get a nice pattern, you can make changes in the dynamic colours. To do this, open the Advanced tab and add Dynamic Colours. You can use the slider names you already have or insert new sliders. Make changes until you are happy with your picture.
- Repeat the steps (see point 5) with other graphs you have created.
- To animate the slider, right-click the slider and click Animation On. That way, you can also turn off the animation if you want.
- When creating a pattern, you can use several functions, and their graphs can be displayed or hidden by clicking on the small circle in front of the function equation in the Algebra view.
- Pause the animation when you have a picture that you like. To export your picture, open the menu File -> Export ->Graphics View as Picture or take a screenshot.
provide an opportunity to discuss whether the relation represents a function or not.
