## Objectives

Students program Fable in order to study parabolas and obtain knowledge about the significance of variables for the leading coefficient of a parabola.

Students will examine how they can influence the trajectory of the ball and hence the shape of a parabola by making changes to the programming or the robot.

## Planning

It is a prerequisite for the project that students have worked with quadratic polynomials, including the leading coefficient, the slope of the tangent line, and vertex. It is also an advantage if students are able to graph functions in Geogebra.

## Materials

• Fable
• Ball – not too heavy, e.g. a ping pong ball
• LEGO bricks for building a throwing arm
• PC
• Smartphone or tablet with a slow motion camera (can be downloaded as an app)
• Measuring instruments
• Pen and paper (possibly Geogebra or similar program)

Duration: 6 lessons

## Learning activities

Students work in groups of 2-3. Each group receives a copy of the assignment sheet. In order to ensure that students understand the assignment, the sheet should be reviewed in class so students have time to ask questions.

The class should discuss non-linear functions with particular focus on parabolas. It is important that the students have knowledge of the leading coefficient of parabolas, the slope of the tangent line, and vertex.

Students construct the robot so that it is suitable for making throws.

Note: It is challenging to make the robot throw very far using LEGO. Instead, you may build a throwing arm using fiberglass, a much more flexible material, allowing you to   catapult the ball further away. Contact us to get at prototype.

It is important that they test their setup thoroughly and document it so they can continue their work in subsequent classes with the same setup.

Students also develop a setup that allows them to measure the height and length of the ball’s trajectory when it is filmed in slow motion on a phone. One option is to draw a grid in a given size on a surface that is used as a backdrop when filming the robot as it performs the throw. The aim here is that students find a viable method for collecting data for processing.

When students have developed a functioning setup and have plotted in a parabola, they must find a relationship between their setup and the variables in the leading coefficient of a function.

Students can either change the programming or the robot to achieve a higher vertex or longer throw. Changes to the hardware could be a longer or shorter throwing arm. Changes to the software could be a quicker execution of the throw.

## Evaluation

Class evaluation where students present their results.

In addition, students complete a self-evaluation form. This evaluation is intended for the students’ own use but can also be used by the teacher in connection with future lessons.