I found today's class about patterns and instances very interesting. Some of you think recursively while the rest of you think explicitly. In algebra, a little bit of both works best.

Let's review. Recursion is the process of describing the next term in a sequence in relation to preceding terms. If you refer to the first example that we used in class today (the shapes that look like the letter L), you should notice that the first design contains three tiles, the second design contains five tiles, and the third design contains seven tiles. The question posed in class was, "How many tiles are in the 10th design?"A recursion formula tells how the current value for number of tiles, i.e. number of tiles in the tenth design, is related to the previous value, i.e. the number of tiles in the ninth design. Since two tiles are added to the NOW design to obtain the number of tiles in the NEXT design, another way of stating this is to say: NEXT = NOW + 2

Students who looked at the number of the design and realized that the number of tiles could be determined by doubling the number of the design and then adding one were thinking about the explicit relation. If x = the number of the design and y = the number of tiles in the design, then y = 2x + 1.

This would be a good opportunity for you to comment.

Today's Assignments:
1. Finish Lesson 1-7.
2. Use the handout from class today to complete the In-Class Activity at the beginning of Lesson 1-8. Be sure you glue both into your Math Journal. (Does it seem funny that I assigned an in-class activity to be done outside of class?)
3. Study for the quiz on Lessons 1-4 through 1-6. This should be an easy one, if you prepare.
4. If you have no idea what the Pythagorean Theorem is about, you need to read pp. 46-47. You can also visit this website.
5. Practice reciting the first ten perfect squares. Friday is the deadline.