# Dynamic worksheet for counting chords and diagonals

Here is a dynamic worksheet you can use in problems involving chords of circles and diagonals of polygons. The figure produced by the worksheet not only models solution to the problem ‘What is the maximum number of chords you can form with six points on the circle?”. It also illustrates the solution to problems like “If six people will shake hands with one another once, how many handshakes can they do in all?” or “How many games will six basketball teams play of they are to play each other once?”

Suggested teaching sequence:

1. Let the students explore the applet.
2. Ask them to make problems/questions based on the diagram. (E.g. If a circle has six points along its circumference, how many chords can be formed?)
3. Ask them to show different ways of answering the question or solving the problem.
4. Extend the problems to n points.

Don’t forget to extend the lesson to polygons with n vertices as this lead to a quadratic expression. You can therefore use this activity to introduce quadratic function.

To use the worksheet, drag the slider in the applet below. You can hide the circle, change the position of points and use other tools by pointing on the object and then ‘right click’ to choose the tools/ command.

You can also extend the use of this worksheet to counting diagonals, points of intersections, and number of regions.

This material may be downloaded upon sending a request e-mail to jacq.agimat@gmail.com.

### Erlina Ronda

I love to develop mathematical tasks and activities that involve basic mathematics concepts but have the potential to engage both teachers and students in higher level thinking. I am particularly interested in students’ learning trajectories of big ideas in number, algebra, geometry, and in the use of GeoGebra in learning mathematics. More. Email: linesronda@gmail.com