1. A Collaboration between: Los Angeles Unified School District University of California, San Diego San Diego State University University of California, Irvine San Diego Mathematics Project Preparing for Success in Algebra English Language Learners in Mathematics

2. Slide 2 Welcome California Mathematics and Science Partnership (CaMSP) Year 2, Day 4 July 15, 2010

3. Slide 3 ESSENTIAL QUESTIONS How can we model exponential growth? How can we introduce exponential growth tangle, fun, and conceptual? How can we explain and justify that ?

4. Slide 4 ESSENTIAL STANDARDS Seventh Grade & Algebra Readiness AF 2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents Alg 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.

5. Slide 5 The Power of Two

6. Slide 6 Grab your piece of paper and actually try to fold it in half as many times as possible. Please no footprints or teeth marks on the paper (those are stomps and chomps but not folds). The Power of Two

7. Slide 7 How many times where you actually able to fold your paper in half? How did the actual result fare with your prediction? If there was a discrepancy, why do you feel you were not able to fulfill your predicted number of folds? The Power of Two

8. Slide 8 What we have just experienced is exponential growth. On the table provided, go back and record the number of folds in comparison to the number of layers. The Power of Two

9. Slide 9 The Power of Two

10. Slide 10 Essential Content Vocabulary ExponentBase PowerResult Exponential Growth Repeated Multiplication

11. Slide 11 How many folds and layers would there have been in the initial predictions? How many layers would there be if the paper was folded 10 times? 20 times? If we now place in the blank space of your table; what does that mean and what is your answer? The Power of Two

12. Slide 12 Pick one of the following to answer in writing: How could you increase the number of folds you could achieve? Why is = 1? How does compare to ? Be prepared to share what you have written. The Power of Two

13. Slide 13 In means________ by _______, which is_________. means____________________________ _____________,which is________. Another way to think of exponents is _______ ____________________ so it is a shortcut for writing ______________. The Power of Exponents

14. Slide 14 Where does this task fit?

15. Slide 15 Task Analysis/ Debrief How did “The Power of Two” develop conceptual understanding? How did it foster problem solving skills? What are the benefits to a task of this type and what are some drawbacks or precautions to consider?

16. Slide 16 Break 15 Minutes