Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 2, Part A:
What Do You See?

In This Part: Finding a Pattern | Descriptions of a Pattern

Problem A4

Here is a recipe to perform on a number:

What does this recipe do to the numbers from 1 to 10? Record your answers in a table. Can you explain how this is related to the patterns you saw in the table from Problem A1 (below)?

 Input Output 1 6 2 10 3 14 4 18 5 22 6 26

Problem A5

Comment on each of the following descriptions of the table given in Problem A1. Do all of these descriptions produce the same list of outputs? Are all of these descriptions valid for the table?
Note 4

 a. As the input increases by 1, the output increases by 4. b. If you add 2 to 1 and double it, you get 6. If you add 3 to 2 and double it, you get 10. If you add 4 to 3 and double it, you get 14. Or, if you add the input to the next input, double that, you get the output. c. The units digits are in the sequence 6, 0, 4, 8, 2, so the next number would be 26, then 30, 34, 38, and 42, and then 46, 50, 54, 58, 62, etc. d. To get the output, multiply the input by 4 and add 2. e. To get the output, triple the input, then add 2 more than the input. f. After 6 as an input, the output numbers repeat over again: 6, 10, 14, 18, 22, 26, etc. g. After 6, the output numbers remain constant: 26, 26, 26, etc.

 Problem A6 Which number comes next in this sequence: 1, 2, 3, ... ? Find as many different answers and explanations as you can.

Problem A7

Let's take a closer look at the four skills for thinking about patterns.

 • Finding patterns involves looking for regular features of a situation that repeats. • Describing patterns involves communicating this regularity in words or in a mathematically concise way that other people can understand. • Explaining patterns involves thinking about why the pattern continues forever, even down the line in cases you haven't looked at. • Predicting with patterns involves using your description to predict pieces of the situation that aren't given.

Look back at Problems A1-A6. Describe how you use these skills in each problem. In other words:

 • Finding is observing the pattern you see • Describing is putting what you see into words or symbols • Explaining is figuring out why the pattern continues • Predicting is using your description or rule for a new value

 Session 2: Index | Notes | Solutions | Video