Standards for mathematical practice K-2

1. Standards for mathematical practiceK-2 Christina Marinelli RISE Educational Services

2. Mathematical Practices Overview • There are 8 Mathematical Practices that are consistent from kindergarten through 12th grade. • The mathematical practices are presented in the beginning of the standards handbook. They are not explicitly stated within the standards. Teachers will have to decide when and how to teach and practice these skills.

3. When To Teach the Math Practice Standards • “The MP standards must be taught as carefully and practiced as intentionally as the Mathematical Content Standards. Neither should be isolated from the other; effective mathematics instruction occurs when these two halves of the CCSSM come together in a powerful whole.” California’s Common Core Standards for Mathematics http://www.cde.ca.gov/re/cc/

4. Overview Continued • The Standards for Mathematical Practice describe varieties of expertise students should be taught. These practices are based on important “processes and proficiencies” with longstanding importance in mathematics education. The practices were created from two sources: -http://www.corestandards.org/Math/Practice

5. Overview Continued Standards for Mathematical Practice • The second source is the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up • The first source is the National Council of Teachers of Mathematics (NCTM) process standards of problem solving, reasoning and proof, communication, representation, and connections. -http://www.corestandards.org/Math/Practice

6. Standards for Mathematical Practice The Common Core State Standards for Mathematics Kindergarten – Grade 5

7. Math Practices and Standards Connection Standards for Mathematical Content: Skills and understandings students will learn Identified by grade level or course Standards for Mathematical Practice: Processes and proficiencies that students show when engaged in mathematics Identified for students across all grade levels (K–12) Brokers of Expertise State of California Department of Education: CCSS Mathematics: K-12 Standards for Mathematical Practice. http://myboe.org/portal/default/Content/Viewer/Content?action=2&scId=306591&sciId=11787

8. Making Math Practices Practical

9. 1) Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

10. MP 1: Make Sense of Problems and Persevere in Solving Them • Explain the meaning of a problem and look for entry points • Analyze givens, constraints, relationships, and goals • Plan a solution pathway • Monitor and evaluate progress • Check answer using a different method (asking does this make sense) • Understand the approaches of others and identify correspondences between different approaches

12. Learning Objectives Math Practice 1 Repeating Topics • Create a coherent representation of the problem (consider units involved, attend to meanings of quantities, know and use different properties of operations and objects). (MP 2) • Evaluate the reasonableness of intermediate results while solving a problem (MP 8) • Interpret results and decide whether the results make sense, improving the model if necessary. (MP 4) • Listen to or read the arguments of others, decide whether they make sense, and ask questions to clarify or improve the argument (MP 3) • Explain the meaning of a problem and look for entry points • Analyze givens, constraints, relationships, and goals • Plan a solution pathway • Monitor and evaluate progress • Check answer using a different method (asking does this make sense) • Understand the approaches of others and identify correspondences between different approaches

13. Math Practice Learning Objectives 1. Analyze the information in a problem 2. Plan a pathway for solving a problem 3. Represent relationships graphically 4. Analyze relationships mathematically to draw conclusions 5. Identify and explain mathematical patterns 6. Solve problems using skills you know 7. Evaluate the reasonableness of intermediate results 8. Analyze when to use grade level appropriate tools, recognizing insights to be gained and limitations 9. Attend to details while solving a problem 10. Make conjectures about a problem 11. Explain your reasoning 12. Analyze the work/arguments/reasons of others

14. Lessons + Layered Activities • Content Standards • Math Practices • BBDI lessons with content standards from previously taught lessons • Pacing • BBDI lessons with MPs from previously taught lessons

15. How Do I Make This Work in My Class? • “In the higher mathematics courses, the levels of sophistication of each MP standard increases as students integrate grade appropriate mathematical practices with the content standards.” www.cde.ca.gov Mathematics Framework: Overview of the Standards Chapter, Pg 24 Teach and practice the MPs at an appropriate level for your grade/students. The application and expectation may differ from grade to grade, but the students should still be held accountable for practicing the MPs in a way that makes sense for their age group.

16. What does this look like in my classroom?

17. Sample Year at a Glance

18. Sample Year at a Glance Cont.

19. Sample Year at a Glance Cont.

20. Sample First Week of School Using Previous Year’s Content Day 1: Lesson Math Practice Learning Objective # 1 Learning Objective: Analyze the information in a problem Student Practice: Students do not need to solve; just find goals, information, givens, constraints in word problems Teacher needs: 10-14 problems (2 for model, 4 for guided, 6-8 for independent) Teacher tip: Great place to incorporate communication (speaking and listening) Day 2: Lesson Math Practice Learning Objective # 2 Learning Objective: Plan a solution pathway Student Practice: Students do not need to solve; just plan a solution pathway Teacher needs: use same problems as day 1 Teacher tip: Have students use flow map to lay out solution pathway Day 3: Lesson Math Practice Learning Objective # 7 Learning Objective: Evaluate whether intermediate results are reasonable Student Practice: Students solve; have to stop and check for intermediate results Teacher needs: use same problems as day 1 Teacher tip: Day 4: Lesson Math Practice Learning Objective # 11 Learning Objective: Explain reasoning (process) Student Practice: Student use solved problems from previous day to explain process Teacher needs: use same problems as day 1 Teacher tip: You can intro concept of analyze the work of others during guided practice Day 5: Activity (loop) Math Practice Learning Objectives 1,2,7,11 Description: Students are given 4-6 new problems where they apply all previous days content

21. Processing Time Share with a partner what math content you will be teaching in November. Discuss what Math Practice you would want to teach before teaching the content.

22. Use of Sentence Stems and Frames www.cde.ca.gov: Mathematics Framework: Overview of the Standards Chapter, Page 14 of 27

23. What if your teacher couldn’t check your answers before you turned in your math paper? You would probably check it yourself or have a friend check it. Today we are going to look at other students’ work and decide if it is correct or not.

24. Objective at the arguments of others and tell whether they make sense

25. Remember… • Addition: put numbers together 4 + 1 = 5 • Subtraction: take one number away from another 3 – 1 = 2

26. Big Idea Sometimes we need to check our own work or a partner's work to make sure it is correct. Good mathematicians do this to make sure they are completing the problem correctly and their answers make sense.

27. My Turn 9 + 1 8 The answer is incorrect because he subtracted instead of added.

28. Steps • at the problem • at the answer 3. Ask yourself 4. Check the math 5. This answer is correct because _________. This answer is not correct because _______. Did this person add or subtract to get the answer?

29. My Turn 10 - 4 Did this person add or subtract to get the answer? 6 The answer is correct because he subtracted the correct numbers.

30. Your Turn 4 +3 Did this person add or subtract to get the answer? 7 The answer is ________________________________.

31. Your Turn 9 -3 Did this person add or subtract to get the answer? 5 The answer is _________________________________.

32. Your Turn 5 -4 Did this person add or subtract to get the answer? 9 The answer is __________________________________.

33. Your Turn 4 +2 Did this person add or subtract to get the answer? 6 The answer is _____________________________________.

34. A Few Questions 1. What did we learn to do today? 2. Why do we need to check completed work? 3. How do I check completed work?

35. On Your Own 6-8 problems, students analyze completed problems and decide whether they are solved correctly or not and explain why with a sentence frame

36. Which would you teach first?What would the MP look like at your grade level? Kindergarten: OA 2. Solve addition and subtraction word problems, and add and subtract within 10. First Grade: OA 1. Use addition and subtraction within 20 to solve word problems involving addition to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. Second Grade: OA 1. Use addition and subtraction within 100 to solve one and two step word problems involving addition to, taking from, putting together, taking apart and comparing, with unknowns in all positions. • Math Practice: Compare the effectiveness of two plausible arguments and distinguish correct logic from incorrect logic. (MP 3)

37. Math Practice Video