# analyzing patterns from an input/output machine to find a pattern and function rule.

**Student Name:**

One of the best ways to deepen mathematical understanding is by *writing*. When you try to articulate the process, your mind connects the concepts at a higher level.

For many of the projects or assignments in this class, you will submit a write-up based on discussion questions and your mathematical thinking process. Because this write-up includes writing and math, it is called a WAM. Your WAM can be fun and creative, and must be in complete sentences.

**What To Do:**

In this project, you will be analyzing patterns from an input/output machine to find a pattern and function rule.

**Instructions**

View the rubric below to see how this Assignment will be graded. Then follow the instructions below to complete and submit this Assignment.

1. Open the “Function Machine” game __at this website__ .

2. Click on “Advanced”. Start at Activity Level 1. You will enter your input by clicking on “You Decide the Input” and the machine will provide an output.

3. Enter five inputs and share your table below:

Input (x) | Output (y) |

2 | 1 |

4 | 3 |

6 | 5 |

8 | 7 |

10 | 70 |

4. Share the rule for your function above:

5. Start a new function! Change the Activity Level to 2.

6. Enter five inputs and share your table below:

Input (x) | Output (y) |

2 | -1 |

4 | 3 |

6 | 7 |

8 | 11 |

10 | 15 |

7. Share the rule for your function above:

8. Start a new function! Change the Activity Level to 3.

9. Enter five inputs and share your table below:

Input (x) | Output (y) |

2 | 72 |

4 | 82 |

6 | 92 |

8 | 102 |

10 | 112 |

10. Share the rule for your function above:

11. WAM Write-up: In your slides, write a paragraph describing your mathematical thinking. Please use the following questions as prompts to guide your answer:

a. What strategies did you use in your mathematical thought process?

b. What new knowledge did you gain?

c. What caused you to think about mathematics at a deeper level?

d. How was your curiosity sparked by this assignment?

e. How does this connect to what we’ve learned in class/before?

f. How did you determine the answer?

g. What mathematical questions are you still curious about?