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| XY Encounter |
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Teacher's Guide: Part 3: Conclusion
Watch Video Clips @ XY Encounter Streaming Video Page
Related Activities and Extensions:
Guess My Rule
Help students grasp rules and sequences with the game of Guess My Rule. Make it as easy or as challenging as you want. For example, in Table 1 if the input is 4, the output is 13. If the input is 6, the output is 19. If the input is 2, the output is 7. In this example, the rule is to multiply 3 by 3 then increase that product by 1. Draw students in by letting them suggest numbers to input (x). Tell them the output (y). Continue until a student, or group of students, can come up with the correct rule.
In Table 1a, the data is not organized. Show how to organize the data (Table 1b) so that students see the value in helping to determine a pattern. You might want to show how Table 1b is organized from the least to greatest in the X column. This helps lead to pattern recognition.
Develop strategies to help the students ask better questions. For example, why are zero and one good numbers to input?
To solve the problem, organize information in a table and look for a pattern. For thinking about problems, create a table similar to the one shown below. Ask students to make observations about the patterns and record them. The entries in the far left column are the values for x, or the input values. The entries in the middle column are the values for y, or the output values. The entries in the far right are possible explanations students may give to explain the patterns they may notice to get from one value to the next. These explanations will vary, however, they become a valuable tool in analyzing what students are thinking.
| x | y | Explanations |
| 0 | 1 | Add 1 to the x-value. This y-value is the first y-value. |
| 1 | 4 | Take the first y-value, 1, and add three. |
| 2 | 7 | Take the first y-value, 1, and add six (which is 2 x 3). |
| 3 | 10 | Take the first y-value, 1, and add nine (which is 3 x 3). |
| 4 | 13 | Take the first y-value, 1, and add twelve (which is 4 x 3). |
| x | y | Explanations |
| 0 | 1 | Multiply x by 3, add 1. |
| 1 | 4 | Multiply x by 3, add 1. |
| 2 | 7 | Multiply x by 3, add 1. |
This student will quickly see the rule: y=3x + 1
Other Activities
- Identify and extend whole number and geometric patterns to make predic-
tions and solve problems.
- Extend the idea of patterns by investigating figurate numbers, i.e. square,
pentagon, hexagon, etc.
Conclusion to Part 3:
Three cheers for Max and Keisha! They solved the sequence: 1-3-6-10-15. Next, the alien delivers a print out of another set of clues and uses a distortion of Keisha’s voice through the computer to say: “Hurry up, Max, I have to go.” The alien is trying any means to communicate, and the kids are more convinced than ever that they can find it.
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