Project: Explore, design and predict sequences

The objective of this project is to analyze sequences and create by design using GeoGebra and your knowledge of arithmetic sequences.

The task

The task has three parts:

Part 1: Explore. Go to Explore Sequences of points, circles, line segments and polygons. Follow the instructions on that webpage.

Part 2: Design.

Based on what you learned from part 1,

  1. Design and explain a sequence of circles using at least one arithmetic sequence for the center coordinates and/or the radius.
  2. Design and explain a sequence of line segments using at least one arithmetic sequence for one or both of the end points.
  3. Design and explain a third sequence diagram of your choice.

Part 3: Predict and verify/correct.

  • Collect a sequence command from the teacher.
  • Draw the picture on paper that you think will be created with the command.
  • Use the sequence command on GeoGebra to generate the sequence.
  • Explain what you got correct and any errors you might have made.

Suggested Page Structure

Page 1 Title page. Your name, the course, the date, a title for your project, a sentence describing the objective of the project and perhaps a relevant image.
Page 2 Part 1, Exploration. Reflect on the exploration in part 1. Screenshot a sequence you made on the ‘explore sequences‘ page. Explain something you noticed and something you discovered while you were exploring sequences.
Page 3 Part 2, Explain your design intention. Include an image of your circle design and the sequence command used to generate it. Explain the purpose of each component of your sequence command.
Page 4 Part 2, Explain your design intention. Include an image of your line segment design and the sequence command used to generate it. Explain the purpose of each component of your sequence command.
Page 5 Part 2, Explain your design intention. Include an image of your own design and the sequence command used to generate it. Explain the purpose of each component of your sequence command.
Page 6 Part 3. Your pencil and paper prediction (drawing) of the image generated by the sequence command given to you by the teacher.
Page 7 Part 3. The GeoGebra diagram and your reflection regarding how you correctly or incorrectly understood the sequence command.

Grading