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 place value? How can we introduce decimals in a tangible, fun, and conceptual? How can decimal alignment become more visual and concrete?

4. Slide 4 ESSENTIAL STANDARDS Seventh Grade & Algebra Readiness Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole number powers

5. Slide 5 Frontloading Everyday Vocabulary Leg Square Square Root Right Triangle Units Area Squaring

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 fill the information out 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 Interacting with the Text: Pythagorean Theorem Proof

11. Slide 11 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

12. Slide 12 Having student 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

13. Slide 13 Where does this task fit?

14. Slide 14 Modeling The Pythagorean Theorem Proof 1 Proof 2 Proof 3 Proof 4

15. Slide 15 Task Analysis/ Debrief How did “It All Adds Up ” 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