ACOS 2010 Standards of Mathematical Practice

1. ACOS 2010 Standards of Mathematical Practice

2. Outcomes: • Participants will review the Standards of Mathematical Practice • Participants will analyze K-5 number talks. • Participants will form a global perspective for the school community. • Participants will identify one change they plan to make in their classroom practice related to number talks.

3. Standards for Mathematical Practice • Carry across all grade levels • Describe habits of mind of a mathematically expert student • Make sense of problems and persevere in solving them • Reason abstractly and quantitatively • Construct viable arguments & critique the reasoning of others • Model with mathematics • Use appropriate tools strategically • Attend to precision • Look for and make use of structure • Look for and express regularity in repeated reasoning

4. Make sense of problems and persevere in solving them. #1 When presented with a problem, I can make a plan, carry out my plan, and evaluate its success. • AFTER… • CHECK • Is my answer correct? • How do my representations connect to my algorithms? • EVALUATE • What worked? • What didn’t work? • What other strategies were used? • How was my solution similar to or different from my classmates? • BEFORE… • EXPLAINthe problem to myself. • Have I solved a problem like this before? • ORGANIZEinformation. • What is the question I need • to answer? • What is given? • What is not given? • What tools will I use? • What prior knowledge do I • have to help me? DURING… PERSEVERE MONITORmy work. CHANGEmy plan if it isn’t working out. ASKmyself, “Does this make sense?”

5. Reason abstractly and quantitatively I can use reasoning habits to help me contextualize and decontextualize problems. #2 CONTEXTUALIZE I can take numbers and put them in a real-world context. For example, if given 3 x 2.5 = 7.5, I can create a context: I walked 2.5 miles per day for 3 days. I walked a total of 7.5 miles. DECONTEXTUALIZE I can take numbers out of context and work mathematically with them. For example, if given I walked 2.5 miles per day for 3 days, How far did I walk? I can write and solve 3 x 2.5 = 7.5.

6. Construct viable arguments and critique the reasoning of others #3 I can make conjectures and critique the mathematical thinking of others. • I can critique the reasoning • of others by… • listening. • comparing arguments. • identifying flawed logic. • asking questions to • clarify or improve • arguments. • I can construct, justify, and • communicate arguments by… • considering context. • using examples and non- • examples. • using objects, drawings, • diagrams and actions.

7. Model with mathematics #4 I can recognize math in everyday life and use math I know to solve everyday problems. concrete models • I can… • make assumptions and • estimate to make • complex problems • easier. • identify important • quantities and use tools • to show their relation- • ships. • evaluate my answer and • make changes if needed. pictures symbols Represent Math oral language real-world situations

8. Use appropriate tools strategically #5 I know when to use certain tools to help me explore and deepen my math understanding. I have a math toolbox. I know HOW to use math tools. I know WHEN to use math tools. I can reason: “Did the tool I used give me an answer that makes sense?”

9. #6 Attend to precision I can use precision when solving problems and communicating my ideas. Problem Solving I can calculate accurately. I can calculate efficiently. My answer matches what the problem asked me to do–estimate or find an exactanswer. • Communicating • I can SPEAK, READ, WRITE, and LISTEN mathematically. • I can correctly use… • math symbols • math vocabulary • units of measure

10. Look for and make use of structure I can see and understand how numbers and spaces are organized and put together as parts and wholes. #7 • SHAPES • For example: • Dimension • Location • Attributes • Transformation • NUMBERS • For example: • Base 10 structure • Operations and properties • Terms, coefficients, exponents

11. Look for and express regularity in repeated reasoning I can notice when calculations are repeated. Then, I can find more efficient methods and short cuts. #8 Patterns: 1/9 = 0.1111…. 2/9 = 0.2222… 3/9 = 0.3333… 4/9 = 0.4444…. 5/9 = 0.5555…. I notice the pattern which leads to an efficient shortcut!!!

12. Number TalksHelping Children Build Mental Math and Computation Strategies Grades K-5 By Sherry Parrish

13. Number talks help students develop efficient, flexible, and accurate computational strategies that build upon key foundational ideas of mathematics.

14. Classroom conversations and discussions centered around purposefully crafted computation problems are the at very core of number talks.

15. By sharing and defending their solutions and strategies, students are provided with the opportunity to collectively reason about numbers while building connections to key conceptual ideas in mathematics.

16. Video 3.5 • Third Grade • 7 x 7

17. Key Components of Number Talks Students Teacher Environment

18. Classroom Environment and Community • Safe and risk free • Students are comfortable offering responses for discussion, questioning themselves and others, and investigating new strategies • Culture of acceptance is based on a common quest for learning and understanding

19. Sharing and Discussing Computation Strategies • Clarify their own thinking • Consider and test other strategies • Investigate and apply mathematical relationships • Build a repertoire of efficient strategies • Make decisions about choosing effective strategies

20. Mental computation is a key component of number talks because it encourages students to build on number relationships to solve problems instead of relying on memorized procedures.

21. When students approach problems without paper and pencils, they are encouraged to rely on what they know and understand about the numbers and how they are interrelated. Mental computation causes them to be efficient with the numbers and avoid holding numerous quantities in their heads.

22. Teacher’s Role • Moves into the role of facilitator • Keeps discussion focused on the important mathematics • Helps students learn to structure their comments and wonderings • Guides students to ponder and discuss examples that build upon their purposes

23. Video 5.3 – Fifth Grade • 16 x 35 • Work mentally two ways • Look for Standards for Mathematical Practice

24. Questions to be thinking about: • What are the similarities and differences between the grades? • Classroom community? • Teacher’s role? • Student’s role? • Communication? • How do the content skills build from grade to grade?

25. Standards for Mathematical Practice • Carry across all grade levels • Describe habits of mind of a mathematically expert student • Make sense of problems and persevere in solving them • Reason abstractly and quantitatively • Construct viable arguments & critique the reasoning of others • Model with mathematics • Use appropriate tools strategically • Attend to precision • Look for and make use of structure • Look for and express regularity in repeated reasoning

26. Standards for Mathematical Practice • SMP1: Explain and make conjectures… • SMP2: Make sense of… • SMP3: Understand and use… • SMP4: Apply and interpret… • SMP5: Consider and detect… • SMP6: Communicate precisely to others… • SMP7: Discern and recognize… • SMP8: Note and pay attention to…

27. Purposeful Computation Problems Problems are crafted to guide students to focus on mathematical understanding and knowledge. The goals and purposes for the number talk should determine the numbers and operations chosen.

28. Grade Level Groups-Charts • Write an addition number talk problem. • Solve each problem using at least two strategies students might commonly use.

29. Gallery Walk • How do the strategies build from grade level to grade level? • What math concepts need to be developed at each grade level to allow students to be mathematically powerful? • How does this affect student understanding in future grade levels?

30. Your Practice: A Closer Look • How are the student and teacher roles in your classroom similar to or different from the classroom clips? • Think about a recent math lesson you have taught. What role does a learning community play in your lesson? What opportunities exist for students to learn through inquiry-based tasks? How does your lesson build number sense?

31. What instructional strategies can you incorporate into future math lessons to help support student thinking and mathematical understanding? • Remember to start small in making shifts in your classroom practice related to number talks. What is one change you plan to make?

32. Parrish, S. (2010). Number Talks: Helping Children Build Mental Math and Computation Strategies Grades K-5. Sausalito: Math Solutions.