Number Talks Beginning the Conversation

1. Number TalksBeginning the Conversation Office of Early Learning Lynn Baker, NBCT Coordinator, Math Science Partnership lhbaker@access.k12.wv.us

2. Session Goals • Develop a basic understanding of the number talk routine • Connect number talk routine to Next Generation CSOs • Construct number talks for the next 2 weeks of instruction

3. What do you know about number talks?

4. Number Talks • Classroom conversations around purposefully crafted problems. • 5-15 minutes • Focus on strategies • Investigate and apply mathematical relationships • Build a repertoire of efficient strategies

5. 49 x5 =

6. Transition from 21st Century Standards to Next Generation Mathematics Standards • FOCUS • FOCUS • FOCUS • Coherence • Rigor • Conceptual Understanding • Procedural Skill and Fluency. • Application

7. Rigor: Equal intensity in conceptual understanding, procedural skill/fluency, and application

8. Solid Conceptual Understanding • Teach more than “how to get the answer” • Students see math as more than set of mnemonics or discrete procedures • Conceptual understanding supports the other aspects of rigor (fluency and application) Adapted from Achieve

9. Fluency • The standards require speed and accuracy in calculation • Teachers structure class time and/or homework time for students to practice core functions Adapted from Achieve

10. Application • Student use appropriate concepts and procedures for application • Provide opportunities for students to apply math concepts in “real world” situations • Outside of math students are using grade –level-appropriate math to make meaning of and access content Adapted from Achieve

11. Mathematics Fluency: A Balanced Approach From Memory ≠ Memorize

12. Pathway to Fluency

13. Fluency: Simply Fast and Accurate? I Think Not!NCTM President-Linda M. Gojak “Computational fluency refers to fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently. These computational methods that a student uses should be based on mathematical ideas that the student understands well, including the structure of the base-ten number system, properties of multiplication and division and number relationships.” Principles and Standards for School Mathematics

14. Required Fluencies in K-6

15. What does it mean to be fluent in mathematics? • Use understanding of place value and apply properties of operations as strategies to add and subtract; multiply and divide. • Understand subtraction as an unknown-addend problem • Relate counting to addition and subtraction; multiplication to division • Use reasoning strategies: counting on, making ten, creating equivalent but easier or known sums, partial products

16. We Need Students to Compute with: • Accuracy—ability to produce an accurate answer • Efficiency—ability to choose an appropriate expedient strategy for a specific computation problem • Flexibility—ability to use number relationships with ease in computation

17. 13 - 7

18. Number Talks • Number talks are short conversations centered around purposefully crafted computation problems.

19. Number Talks in ACTION

20. Key Components Number Talks • Classroom environment and community • Classroom discussions • The teacher’s role • The role of mental math • Purposeful computation problems

21. Classroom Environment & Community • Safe, risk-free environment • Students participate in discussions, question themselves and peers • Investigate new strategies • Students do not need to sit on the floor • Teachers must also take risks • Teachers & students are learners

22. Your Classroom Environment • What elements do you have in place? • What elements do you need to establish in your classroom? • How will you establish these elements?

23. Classroom Discussions • Quiet time allows all students to think • Students share strategies and justifications with their peers • Consider & test strategies • Investigate mathematical relationships

24. Classroom Discussions • What elements do you have in place? • What elements do you need to establish in your classroom? • How will you establish these elements?

25. The Teacher’s Role • Interrelated roles of facilitator, questioner, listener, and learner • Keep the discussion focused on important mathematics • Begins with the selection of the problem

26. The Teacher’s Role • What elements do you have in place? • What elements do you need to establish in your classroom? • How will you establish these elements?

27. The Role of Mental Math • Encourages students to build on number relationships • Forces students to rely on what they know and understand about numbers • Strengthens students understanding of place value system

28. The Role of Mental Math • What elements do you have in place? • What elements do you need to establish in your classroom? • How will you establish these elements?

29. Purposeful Computation Problems • Encourages students to focus on mathematical relationships • Develop common strategies • Random problems do not develop common strategies

30. Purposeful Computation Problems • What elements do you have in place? • What elements do you need to establish in your classroom? • How will you establish these elements?

31. Let’s Get Started

32. Goals for K-2 • Developing number sense • Developing fluency with small numbers • Subitizing • Making ten

33. K-2 Number Talk Tools • Counting Books • Dot Images • Rekenreks • Five-Frames/Ten Frames • Number Lines • Hundred Charts

34. Five Number Talks Goals for Grades 3-5 • Number Sense • Place Value • Fluency • Properties • Connecting Mathematical Ideas

35. Grades 3-5 Number Talk Tools • Array models • Open number lines

36. Strategies

37. First Steps • Determine starting point • Identify specific strategy • Create problems for number talks for the next two weeks (6 to 10 sets of problems) • Create specific tools

38. Using Questions to Build Fluency Answer Getting vs. Developing Understanding • Do we model questions that students should be asking themselves? • Do our questions move student problem solving forward? • Do questions reveal student thinking?

39. Let’s Practice • Grade level groups 3-5 teachers • Each teacher conducts a simulated number talk

40. Questions

41. Can you make a difference? • 10 min/180 days • 1800 minutes • 30 hours

42. Google Form http://tinyurl.com/NTB2013

43. Thinkfinity

44. Final Quote Often when you think you’re at the end of something, you’re at the beginning of something else. Fred Rogers