 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum  MENU          Session 3, Part B:
Undoing Algorithms (20 minutes)

An algorithm is a recipe or a description of a mechanical set of steps for performing some task. For example, you can have an algorithm for making a peanut butter and jelly sandwich.

Mathematical algorithms are increasingly important in the computer age. Computer programs are essentially algorithms written in a language that computers understand. Here's a mathematical algorithm (let's call it Algorithm A):
Note 3

 • Pick a number (that's the input) • Double it • Add 2 to the answer • Divide that answer by 2 • Subtract 7 from what you get • Multiply the result by 4 (that's the output)  Problem B1 Use Algorithm A for these problems.

 a. If the input is 9, what is the output? b. If the input is 10, what is the output? c. If the input is n, what is the output?  Try to run the algorithm's steps using the variable n rather than a particular value. After the first step, the result is 2n. After the second step, the result is 2n + 2.   Close Tip Try to run the algorithm's steps using the variable n rather than a particular value. After the first step, the result is 2n. After the second step, the result is 2n + 2.

 d. If the output is 28, what is the input? e. If the output is 32, what is the input? f. What input produces an output of 48? g. What input produces an output of 36?  Problem B2 What strategies did you use to answer parts (d)-(g) of Problem B1? Problem B3 Describe, in language similar to the way we described Algorithm A, an algorithm (call it Algorithm B) that undoes Algorithm A. This means that if you put a number into Algorithm A, then put that output into Algorithm B, you should end up with the original input.   Video Segment In this segment, Professor Cossey works with Lolita and Deanna to find the algorithm that undoes Algorithm A, then they discuss why such an algorithm would have its steps reversed. Watch the segment after you have completed Problem B3. If you get stuck on the problem, you can watch the video segment to help you. Professor Cossey refers to "inverse operations." Give some examples. Do all operations have inverse operations? You can find this segment on the session video, approximately 7 minutes and 29 seconds after the Annenberg Media logo.    Problem B4 Does Algorithm A undo Algorithm B? That is, if you put a number into Algorithm B and then put that output into Algorithm A, do you get back to your starting number?   Video Segment In this segment, Dr. Fujii of the Boston Medical Center describes the importance of doing and undoing in prescribing medication to newborns. Watch this segment after you have completed Part B: Undoing Algorithms. The segment is taken from the "real world" example at the end of the Session 3 video. What inverse operations does Dr. Fujii use? How are the questions he answers similar to those you answered in Problem B1? You can find this segment on the session video, approximately 21 minutes and 52 seconds after the Annenberg Media logo.      Session 3: Index | Notes | Solutions | Video

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