Forgot your password?
Number Sequences
Introduction
This activity focuses on gerenating and analyzing numeric sequences. It is a foundation activity, in the sense that it establishes tools, practices and base knowledge useful for a wide range of activities such as Convergence and Divergence, Coding and Fibonacci.When investigating sequences, students will create mechanisms to generate sequences, and then observe the real-time execution of the process. The advantage of ToonTalk is that the sequences can be viewed not only as a product (a series of terms), but also as a process that can be observed and altered. This is in contrast with traditional algebraic representations that are 'static'. These alternative representations may lead to different understandings, for example, the sequence {0, 2, 5, 7, 10, 12…} has a relatively simple rule (+2, +3) that is easily programmed in ToonTalk, but not easily described by conventional algebra.
When generating more complex sequences, students will 'chain' (connect using bird-nests) a number of robots together. By altering the parameters and number of chained robots, any polynomial sequence can in theory be generated. Students will explore the relationships between the number of robots and the complexity of the corresponding sequence (the order of the polynomial). They will also investigate how rules for sequences are determined, and build robots to help them with this task.
Aims
- To develop a non-algebraic language for describing, discussing and reasoning about polynomial (and maybe some non-polynomial) sequences.
- To develop an understanding of the generation of number sequences, the rules that sequences rely on and how sequence generation relates to the ToonTalk environment (robots, birds, etc).
- To gain some insight into the relationship between the number of chained robots and the type and complexity of the corresponding sequence.
- To develop students' ability to make conjectures, suggest more than one solution to a problem, evaluate arguments and reason.
Prerequisites
This activity is fairly self-contained, both in terms of mathematical content and programming skills. It has been tried successfully with ToonTalk beginners, after a few sessions playing the puzzle game.Activity plan and resources
Motivation
A possible way to start the activity is by playing Guess my Sequence in a group discussion.
- Researchers: Use the pre task assesment (GuessMyRobotPreTask.doc) as initial motivation for the discussion.
Programming challenges
Other resources
- Tutorial on chaining robots
Assesment and data collection
Related activities
Things to look out for
Past experience with this activity has shown several classes of canonical sequences to be popular among students. Read about the mathematical structure of these sequence types.
References and further reading
-
Sequences, differences of terms, applications : General mathematical background.
- Pedagogical advice on number sequences