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

4. Slide 4 ESSENTIAL STANDARDS Seventh Grade & Algebra Readiness 7NS1.2: 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 FlatRodUnit Cube Digit Ones Tenths Hundredths Decimal Place Value

6. Slide 6 It All Adds Up Look at the Place Value Mats provided. Partner A please represent 3.45 using the base 10 manipulatives on the mat. Partner B please represent 2.34 using the base 10 manipulatives on the same mat. Discuss with your partner how you could add these two numbers. What is your strategy? Write a brief summary of your strategy.

7. Slide 7 Please take some time to fill your appointment record sheet. Ensure that you clarify the time and location where you will meet. Make note of these on your appointment record sheet. It All Adds Up

8. Slide 8 You will have two problems to solve for each appointment. Please make sure that in each problem each person builds one of the numbers using the base ten blocks. On your record sheet please make a drawing or diagram representing your physical model and represent it numerically as well. It All Adds Up

9. Slide 9 Copy the problem on your sheet. Create a model for each number using the base 10 blocks, draw the diagram of your numbers on your sheet, show the numerical representation. 7.65 + 4.87 = 2.67 +35.8 = Appointment 1:

10. Slide 10 Copy the problem on your sheet. Create a model for each number using the base 10 blocks, draw the diagram of your numbers on your sheet, show the numerical representation. 28.6 + 3.88 = 7.65 – 2.31 = Appointment 2:

11. Slide 11 Copy the problem on your sheet. Create a model for each number using the base 10 blocks, draw the diagram of your numbers on your sheet, show the numerical representation. 4.21 - 2.71 = 9.5 – 8. 73 = Appointment 3:

12. Slide 12 How did your strategy for using the base ten blocks change as the problems changed? What was your strategy for using the base ten blocks to represent subtraction? How did you tackle problems that had a different number of digits in one number versus the other, i.e., 39.7 + 4.83? It All Adds Up

13. Slide 13 Write your names on the top of column A or B. You will take turns working out problems. As you work out your problem make sure you rewrite your problem aligning the decimal to respect place value. As you work out your problem explain to your partner what you are thinking and how you are solving the problem. The partner listening; your job is to ask questions, coach and praise and check off the vocabulary you are using. Go back and forth until time is called. Mathematically Speaking Pairs Check Sums and Differences

14. Slide 14 In adding decimals it is important to ________because _________________. Adding decimals are similar to subtracting decimals in that ____________________. Adding decimals are different from subtracting decimals in that ____________________. I feel that decimals are________________ for me. It All Adds Up

15. Slide 15 Where does this task fit?

16. Slide 16 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?

17. Slide 17 Break 15 Minutes