1. Unpacking the Standards for Mathematical Practice Professional Development September 16, 2013

2. Outcomes Participants will: Unpack the Standards for Mathematical Practice Apply English Learner strategies to make meaning of the Standards for Mathematical practice (i.e. Think-Pair-Write-Share, Academic Vocabulary Instruction, Identifying Text Structures) Engage in strategies for problem solving for all students, including English Learners

3. COMMON CORE MATH STANDARDS MATH PRACTICES CONTENT STANDARDS USE APPROPRIATE TOOLS STRATEGICALLY MODEL WITH MATHEMATICS CONSTRUCT VIABLE ARGUMENTS AND CRITIQUE THE REASONING OF OTHERS REASON ABRSTRACTLY AND QUANTITATIVELY MAKE SENSE OF PROBLEMS AND PERSEVERE IN FOLLOWING THEM ATTEND TO PRECISION LOOK FOR AND MAKE USE OF STRUCTURE LOOK FOR AND EXPRESS REGULARITY IN REPEATED REASONING

4. Common Core While promoting literacy is explicitly specified across the curricula, the mathematical practices imply the same need for mathematics across the curricula. Science Language Arts Social Studies

5. Thinking About Math Practices Each group will be Assigned one informational Text about a math Practice. Create a tree map connecting The math practice to all Content areas. Choose one Tier 2 Word to define. Read the passage the 2 nd Time and take notes based On the text structure. Read the passage once and Identify the Tier 2 and Tier 3 Vocabulary words

6. Thinking About Math Practices Each group will be Assigned one informational Text about a math Practice. Create a tree map connecting The math practice to all Content areas. Choose one Tier 2 Word to define. Read the passage the 2 nd Time and take notes based On the text structure. Read the passage once and Identify the Tier 2 and Tier 3 Vocabulary words

7. Read for Vocabulary Mathematical Practice #3 Construct Viable Arguments Tier 2 Tier 3 Words that are not content specific, but necessary for understanding complex text. Words that are content specific and are normally defined within the context of the text. How can I make this accessible for my English Learners?

8. Thinking About Math Practices Each group will be Assigned one informational Text about a math Practice. Create a tree map connecting The math practice to all Content areas. Choose one Tier 2 Word to define. Read the passage the 2 nd Time and take notes based On the text structure. Read the passage once and Identify the Tier 2 and Tier 3 Vocabulary words

9. ILLUSTRATION EXAMPLES CHARACTERISTICS, PROPERTIES DEFINITION IN YOUR OWN WORDS

10. Thinking About Math Practices Each group will be Assigned one informational Text about a math Practice. Create a tree map connecting The math practice to all Content areas. Choose one Tier 2 Word to define. Read the passage the 2 nd Time and take notes based On the text structure. Read the passage once and Identify the Tier 2 and Tier 3 Vocabulary words

11. Thinking About Math Practices Each group will be Assigned one informational Text about a math Practice. Create a tree map connecting The math practice to all Content areas. Choose one Tier 2 Word to define. Read the passage the 2 nd Time and take notes based On the text structure. Read the passage once and Identify the Tier 2 and Tier 3 Vocabulary words

12. Connecting Math Practice Standard #____ with critical thinking in all content areas Science Language Arts Social Studies When do you construct viable arguments in science, language arts etc.?

13. Let ’ s Share! Each group needs to post their chart/charts in a designated area of the room. Each group will present their standard to the rest of the group. Each member in each group, must present one piece.

14. Reflecting on my learning/Think- Pair-Write-Share... What I now understand about the Common Core Standards for Math Practice is.... This understanding is important because....

15. Problem Solving in Mathematics Part 2

16. Spend It! You will need two handouts. Price sheet Recording sheet

17. The objective of the game is similar to “The Price is Right!” I will give you an amount of money that you can spend. You will choose your items, total them and try to spend all of the money in your budget. The closer you get to spending all of the money, the closer you get to winning. So if I give you a budget of $35.00 and you spend $34.59 you did a pretty good job. If you spend exactly $35.00, you WIN. If you spend $35.01, you LOSE. Ready? Here are the rules.

18. Here are the rules of the game. 1. You must choose five different items. Write these items in the first branch of your Tree Map. 2. Write the price for each of those items in the second branch of your Tree Map. For Example:

19. Here are the rules of the game. 3.You may buy as many of each item as you want. 4.Record the number of units and calculate the total for those items. 5.Add this information to your Tree Map You may use a calculator! For Example:

20. Finally total all of your costs. Feel free to continue to work toward winning the game. Give yourself no more than 6 minutes to play. Good Luck.

21. So how did you do? Now that you have finished the game, I want you to think about the thinking behind your strategy. Analyzing how you approached this problem is your Frame of Reference. So let’s add to your Frame of Reference.

22. When students solve a problem, they should answer these three questions.

23. So let’s add the answers to all 3 of these Frame Questions to your Spend It Tree Map.

24. First, think about the strategy you used to make your decisions about what to buy and how many of each item you chose. Think about WHY you chose the items you chose. Did you 1. Start with prices that were large and then use the lesser priced items to get close to the total? If so, your strategy was to think NUMERICALLY.

25. Did you Combine items in order to get whole numbers? If so, your strategy was to think NUMERICALLY using Base 10.. $3.00

26. Did you Think ALGEBRAICALLY? I have $20.00 to spend and I have to buy 5 different items. Therefore, I should spend about $4.00 on each item. $20.00 5 $4.00

27. If you used any of these strategies, you were thinking like a Mathematician. These strategies INFLUENCED How you approached the problem.

28. If you chose your items based on any of the following: “I picked the items I like.” “I picked items for breakfast. You can’t have breakfast without coffee!” While you might have gotten items for a great breakfast, you did NOT think like a mathematician.

29. Add your strategy to your Frame of Reference I combined items to get to whole dollar amounts. I used my knowledge of base 10 and number sense.

30. Now let’s think about the actual math skills and processes you needed to know in order to solve this problem.

31. Identify the math skills you used to solve this problem and add them to the Frame of Reference. They might be something like… I used adding and multiplying as well as subtracting. I also used “guess and check” as well as estimating.

32. Many students struggle with math vocabulary, so identifying key terms you need to know is another important meta- cognitive skill for problem solving.

33. I used adding and multiplying as well as subtracting. I also used “guess and check” as well as estimating. I need to know what “cost per unit” means.

34. Finally, students should be given time to reflect on how they solved a problem, what they learned in the process and how they might improve their problem solving skills using their understanding.

35. I learned not to get distracted by irrelevant information. I didn’t need to focus on the type of item. I should have just paid attention to the numbers. I need to think about how to solve the problem, before rushing into just trying to solve it. You can solve a problem using a lot of different strategies.

36. I learned not to get distracted by irrelevant information. I didn’t need to focus on the type of item. I should have just paid attention to the numbers. I need to think about how to solve the problem, before rushing into just trying to solve it. You can solve a problem using a lot of different strategies. I used adding and multiplying as well as subtracting. I also used “guess and check” as well as estimating. I need to know what “cost per unit” means. I combined items to get to whole dollar amounts. I used my knowledge of base 10 and number sense.

37. Notice that the information in the Frame of Reference is really the most important part of this problem solving. Students can then use the statements in their Frame of Reference as well as the information they record in the map itself to show their understanding of math concepts and problem solving.

38. I am incorporating the math standards of practice into my daily instruction. Reflection and Closure