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 6 October 23 rd, 2010

3. Slide 3 ESSENTIAL QUESTIONS How can we assist students in conceptually understanding the Pythagorean Theorem? How can we introduce the Pythagorean Theorem in a tangible, fun, and conceptual? How can the relationship between the legs and hypotenuse of a right triangle become more visual and concrete?

4. Slide 4 ESSENTIAL STANDARDS Seventh Grade & Algebra Readiness Seventh Grade and Algebra Readiness Standard Measurement and Geometry 3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement.

5. Slide 5 Frontloading Everyday Vocabulary Leg Hypotenuse Area SquareSquare Root Right Triangle Units SquaringConjecture

6. Slide 6 Preparing the Learner: Connecting to Prior Knowledge- Frayer Model Frayer Model for Square and square root.

7. Slide 7 Preparing the Learner: Finding the Side of a Square Look at the table provided. Draw the square given the area and identify the side length. Make sure to put the information into the table.

8. Slide 8 Using the lengths of your group’s assigned triangle make a Collaborative Poster that includes the following: Draw the triangles with the given leg lengths. Draw out the squares on the side of each side of the triangle. Find the areas of the squares and record the results in the table. Interacting with the Text: Squaring the Sided of the Triangle

9. Slide 9 Complete the table based on group reports. For each triangle, look for a relationship among the areas of the three squares. What conjectures or predictions can be made bout the areas of the squares drawn on the sides of the right triangles? My conjecture on __________ is… If I use … then I predict … will happen. Based on the past results, I predict…. Interacting with the Text: Squaring the Sided of the Triangle

10. Slide 10 There are several arithmetic, geometric and graphical proofs for the Pythagorean Theorem. The following is one: A Pythagorean Proof Using the triangles and squares provided physically generate this proof. Interacting with the Text: Pythagorean Theorem Proof

11. Slide 11 Having students synthesize their learning is an essential component of learning. Any tools we can provide that scaffold this process will aid students develop their understanding. Fold and create your little book. Extending the Learning: My Little Pythagorean Theorem Book

12. Slide 12 Where does this task fit?

13. Slide 13 Modeling The Pythagorean Theorem Proof 1 Proof 2 Proof 3 Proof 4

14. Slide 14 Task Analysis/ Debrief How did the activities develop conceptual understanding of the Pythagorean Theorem? How did it foster problem solving skills? What are the benefits to tasks of this type and what are some drawbacks or precautions to consider?

15. Slide 15 Break 15 Minutes