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Jefferson County Schools K-5 Math Back to School Conference

Jefferson County Schools K-5 Math Back to School Conference. Number Talks: Strengthen Students’ Mathematical Reasoning. K-5 Math Survey. Depth of Knowledge. Small Group Instruction. Number Talks. Today’s Purpose.

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Jefferson County Schools K-5 Math Back to School Conference

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  1. Jefferson County SchoolsK-5 Math Back to School Conference Number Talks: Strengthen Students’ Mathematical Reasoning

  2. K-5 Math Survey Depth of Knowledge Small Group Instruction Number Talks

  3. Today’s Purpose To provide teachers with an instructional strategy that is grounded in developing students’ mathematical reasoning and conceptual understandings rather than just teaching rules and procedures without understanding of numerical relationships.

  4. Outcomes • Participants will deepen their understanding of mathematics discourse, including some background and rationale. • Participants will experience Number Talks and consider how they might be used as part of a daily routine.

  5. Focus Questions • How can Number Talks develop students’ mathematical reasoning? • How do Number Talks align to the Common Core Mathematical Practices and Content Standards?

  6. Table Talk • Have you implemented Number Talks as part of your daily routine? What were some of the benefits and challenges? • When in your daily routine could you incorporate the use of Number Talks?

  7. Number Talks • A planned daily routine for whole‐class instruction • Number Sense (efficiency, accuracy & flexibility) • Generalized Arithmetic-conceptual understanding • Reasoning and Problem Solving • Mental Mathematics • Preview-­Review-­Conceptual Understanding

  8. Norms “No one is as smart as all of us are together.” • Respect • Individual think time • Everyone participates • Everyone helps • Leave no one behind • Be positive • Technology courtesy

  9. Four Goals for K-2 Number Talks • Developing Number Sense • Developing fluency with small numbers • Subitizing • Making Fives and Tens • Number Conservation Number Talks -Sherry Parrish

  10. The Teacher’s Role Teacher as facilitator, questioner, listener and learner – NOT teller and explainer. Crafts purposeful problems. Supports discourse to deepen mathematical understanding and knowledge and keeps discussion focused on the important mathematics. Assists students to learn how to structure their comments and wonderings in a meaningful and natural manner. Asks open ended questions – from “What answer did you get” to “How did you get your answer?” and “Why did you choose your strategy?”

  11. Hand Signals • Agree • Solution • Strategy • Question • Comment

  12. Understanding Math Discourse • Talk Moves • Revoicing • So you’re saying the top number in a fraction is called the numerator. • Repeating • Can you repeat what Miguel said in your own words? Classroom Discussions: Using Math Talk to Help Students Learn -S. Chapin, C. O’Connor, N Anderson (2003)

  13. Understanding Math Discourse • Talk Moves (continued) • Reasoning • Do you agree or disagree and why? • Adding On • Please add onto Jimena’s strategy. • Waiting • Please take some quite think time. Classroom Discussions: Using Math Talk to Help Students Learn -S. Chapin, C. O’Connor, N Anderson (2003)

  14. 1st Half Practice Standards: HOW the students are learning 2nd Half Content Standards: WHAT the students are learning

  15. CCRS Mathematical Practices REASONING AND EXPLAINING 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others OVERARCHING HABITS OF MIND 1. Make sense of problems and persevere in solving them 6. Attend to precision MODELING AND USING TOOLS 4. Model with mathematics 5. Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

  16. K-2 Number Talk in Jefferson County Watch the number talk. Refer back to the Key Components. What do you notice? - Classroom environment and community - Classroom discussions - The teacher’s role (facilitating vs. teaching) - The role of mental math - Purposeful computation problems (Think-Pair-Share)

  17. Let’s View a K-2 Number Talk

  18. Let’s View a K-2 Number Talk

  19. Discuss the following… • Classroom environment and community • Classroom discussions • The teacher’s role (facilitating vs. teaching) • The role of mental math • Purposeful computation problems

  20. Various Number Talks

  21. Dot Talk How many dots do you see? How did you see them?

  22. Mental Math After a 20% discount, the price is 80% of the original price. So 80% of the original price is $140. What is the original price?

  23. Mental Math

  24. Number String (Mental Math) 35 x 8 70 x 4 140 x 2

  25. Number String (Mental Math) 3 x 50 3 x 100 3 x 149

  26. True/False

  27. True/False Number Talk

  28. Dilemma Number Talk Kirsten says that 10xy-5xy + 4xy equals xy David says that 10xy-5xy + 4xy equals 9xy Explain the mathematical reasoning that both David & Kirsten used to simplify the expression above.

  29. Spatial Reasoning How many cubes? How do you see them? What is the surface area?

  30. Transformations Rotate the figure 90˚ clockwise. What are the new coordinates of point A?

  31. What’s My Rule?

  32. What’s My Rule?

  33. What’s My Rule?

  34. Number Talk Examples • Dot Patterns • Mental Math • Number Strings • True/False Statements • Dilemmas • Spatial Reasoning • What’s My Rule? • Error Analysis and Coaching

  35. Math Block•Balance procedural understanding and conceptual understanding •Balance whole group and small group •Balance teacher directed and student-focused Debrief Guided Math/ Learning Tasks Number Talks Mini-Lesson

  36. Socio-mathematical Norms • Errors are gifts, they promote discussion. • Share a second sentence to connect your thoughts. • The answer is important, but it is not the math. • Build on the thinking of others. • Ask questions until ideas make sense. • Think with language and use language to think.

  37. Questions Teachers Might Ask • Who would like to share their thinking? • Did someone solve it a different way? • Who else used this strategy to solve the problem? • How did you figure it out?

  38. Questions Teachers Might Ask • What did you do next? • What did you need to know? • Why did you do that? Tell me more. • Which strategies do you see being used?

  39. Why Talk About Math “ Our classrooms are filled with students and adults who think of mathematics as rules and procedures to memorize without understanding the numerical relationships that provide the foundation for these rules.”

  40. 3, 2, 1, Exit Ticket • 3 Things you will do to prepare to implement Number Talks in your classroom • 2 Things you discovered about Number Talks • 1 Question you still have

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