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We've just played "telephone" with the tiles problem. This problem can be represented, and communicated about, in another way, as a table of values.
Complete this table of values, (which represents the relationships between terms and number of tiles shown in the previous problem).
| terms |
values |
| 1 |
2 |
| 2 |
5 |
| 3 |
10 |
| 4 |
17 |
| n |
n2 + 1 |
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- Describe what you notice about this table of values.
- What is similar about your descriptions of the table of values and the pictures of tiles? What is different?
- What does each representation communicate? What does each representation lack?
- Explain how the function rule relates to the tiles activity. How does it relate to the table of values?
- If you were to play "telephone" starting with the table rather than the tiles, how would you do it?
As emphasized in another session of this course, the ability to understand representations in mathematics and move fluently among them is a goal for teachers and students alike. Fostering that understanding and ability depends greatly on how teachers communicate about mathematics and help their students develop communication skills. One point to remember is that every representation highlights some mathematical features and hides others, prompting different kinds of communication with different results.
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