Unit 2, Lesson 1 – Identifying patterns in shapes and numbers

1. Unit 2, Lesson 1 – Identifying patterns in shapes and numbers September _____, 2009

2. This year we’ll explore variables used in several ways: • As an unknown amount Like our last unit… 5 + x = 7 2. To show a relationship between 2 values An example of this is graphing 3. To show a pattern in a sequence of numbers This is what we are doing in this unit. We’ll use the variable to find the pattern in numbers and shapes.

3. Finding the Pattern in a Sequence A sequence is any list of numbers or geometric objects. Example of a sequence of numbers: 2 , 3 , 4 , 5 , 6 , 7 , … Can you predict the next number? ________ You’ll also learn to find a rule for the nth term In the above example it is n + 1

4. A geometric sequence What would the next figure look like? How could we develop a rule to decide the number of diamonds in the next term and all following terms (the nth term)

5. A geometric sequence The next figure has 3 diamonds on top&bottom. How would you describe the pattern? 3 tiles are added to one side continually Make a table to find the nth rule:

6. Describe the pattern: Make a table to find the nth rule:

7. Describe the pattern: Make a table to find the nth rule:

8. Describe the pattern: Make a table to find the nth rule:

9. We can do the same with numbers:

12. HOMEWORK PW 4-8 #1-7