1. NUMBER TALKS

2. Hally Third Grade Student Describe Hally’s understandings and misunderstandings. VIDEO

3. Second Grade Student: I couldn’t take seven from three so I borrowed ten. I made the one a zero and the three became a thirteen, and thirteen minus seven is six. That’s just how you do it when the bottom number is bigger than the top. 0 13 13 - 7 6 NEED FOR NUMBER TALKS

4. Traditional View of Mathematics: A discrete set of rules and procedures to be memorized and implemented with speed and accuracy……but without understanding the mathematical logic or numerical relationships that provide the foundation for these rules. VIEW OF MATHEMATICS

5. 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 MATHEMATICALLY PROFICIENT STUDENTS

6.  Our math classrooms must provide opportunities for students:  To grapple with number relationships  Apply numerical relationships to computation strategies  Discuss and analyze their reasoning CREATING MATHEMATICALLY PROFICIENT STUDENTS Number Talks

7. DIRECTIONS 1. When the problem is put up, solve in your head. 2. When you have solved, put your thumb up in front of your chest. 3. Try to solve in a different way. For each different way you solve, put up another finger.

8. HOW MANY OBJECTS DO YOU SEE?

10. 26 + 58 = ?

11.  What is a number talk?  What is the role of the teacher?  What is the role of the students?  Describe the classroom community and environment. VIDEO Third Grade 38 + 37

12. Number Talks Characteristics of Number Talks Classroom Community & Environment Role of the TeacherRole of the Students

13.  Classroom conversations and discussions around a few purposefully crafted computation problems  Short, ongoing daily routine (5 – 15 minutes)  Provides students with meaningful ongoing practice with computation  Intended to help students develop computational fluency  Problems are designed to elicit specific strategies that focus on number relationships NUMBER TALKS

14. Teacher presents problem Students figure it out Students share their answers Students share their thinking Class agrees on the answer FORMAT

15. 1.Classroom environment & community 2.Classroom discussion 3.The role of mental math 4.The teacher’s role 5.Purposeful computation problems KEY COMPONENTS

16. CLASSROOM ENVIRONMENT safe risk-free comfortable accepting respectful clear expectations

17.  Encourages students:  To build on number relationships to solve problems instead of relying on memorized procedures  To develop efficient, flexible strategies with accuracy  To strengthen students’ understanding of place value  Ways to encourage mental math:  Students solve problems without paper and pencil  Write problems in a horizontal format MENTAL MATH

18. 199 + 199 11 199 +199 398

19. TEACHER’S ROLE  Read “What is the Teacher’s Role during Number Talks?”  What should the teacher do during Number Talks?  What should the teacher not do during Number Talks?

20. Teacher Facilitator ListenerQuestionerLearner TEACHER’S ROLE

21.  Select a designated location  Give students time to think by providing appropriate wait time  Encourage student communication and equitable participation  Turn & Talk  Think/Pair/Share  Accept and record all responses without judgment  Ask students to test new strategies  Capture and record strategies so it is accessible to others (notation should be mathematically correct) PROCEDURES

22.  Provide access to tools and manipulatives  Number lines, hundred boards, cubes, counters, ten frames, place value blocks, fraction tiles, etc.  Model how to ask questions & make comments  I agree with _____ because…..  I do not understand ____________. Can you explain this again?  I disagree with ___ because…..  How did you decide to ______? ROLE OF THE TEACHER

23.  Ask students to use finger signals  Number of strategies  Agree/Disagree  Efficient strategy  Keep records of problems posed and the corresponding student strategies  Record student’s name next to the strategy  Document student participation and strategies  Smartboard file  Notebook/Document Camera  Camera  Hold small-group number talks throughout the week  Pull groups based on common needs  Select students who need to be challenged  Work with students who are shy or reluctant to share in the whole group DEVELOPING ACCOUNTABILITY

24.  Require students to solve an exit problem using the discussed strategies  Specific types of problems or strategies  Occasionally give a computation assessment  Consists of a few related problems  Requires students to solve each problem in two ways  Create and post class strategy charts DEVELOPING ACCOUNTABILITY

25.  Start with smaller problems to elicit thinking from multiple perspectives  Offer strategies from a previous student  Put a student’s strategy on the back burner  Limit number talks to 5 - 15 minutes  Be patient with yourself and your students Handout: “Tips for Implementing Number Talks” HELPFUL TIPS & HINTS

26. K-2 NUMBER TALKS

27.  How does the teacher build student fluency with small numbers?  What questions does the teacher pose to build understanding?  What strategies are the students using to build meaning of the numbers?  How does the teacher support student communication during the number talk? VIDEO Kindergarten

28. 1.Developing number sense 2.Developing fluency with small numbers 3.Subitizing 4.Making tens GOALS OF K-2 NUMBER TALKS Describe each goal. What does it mean?

29. “Number sense is an awareness and understanding about what numbers are, their relationships, their magnitude, the relative effect of operating on numbers, including the use of mental mathematics and estimation” ~Fennell & Landis, 1994, p. 187 NUMBER SENSE

30.  Conservation of number  One-to-one correspondence  Compose and decompose numbers  Fact fluency  Subitizing  Making tens  Place Value  Ten ones is one group of 10  How many more to make ten  Compose and decompose 10 GOALS OF K-2 NUMBER TALKS

31.  Dot Images  Five/Ten Frames  Number Lines  Hundred Chart  Story Problems K-2 NUMBER TALK TOOLS

32.  What strategies are the students using to build meaning of the numbers?  How does the teacher build student fluency with small numbers using ten-frames?  What questions does the teacher use to build understanding about decomposing and composing numbers? VIDEO Second Grade 8 + 6

33. 3-5 NUMBER TALKS

34. 1.Number sense 2.Place value 3.Fluency 4.Properties 5.Connecting mathematical ideas GOALS FOR GRADES 3-5

35.  How do the students’ strategies exhibit number sense?  How do the teacher and students connect math ideas throughout the number talk?  How does the progression of problems help students to apply the associative property? VIDEO Fifth Grade 12 x 15

36.  Carefully, purposefully select problems  Based on student needs  Progression of number skills  Anticipate how students will solve the problems  Solve the problem yourself in multiple ways  Use resources to anticipate strategies  Trailblazer’s Teacher’s Guides  Teaching Student-Centered Mathematics PLANNING

37.  Fluency with Dot Images  Fluency using Five- and Ten-Frames  Addition:  Counting All/Counting On with Dot Images  Counting All/Counting On with Double Ten-Frames  Counting All/Counting On with Number Sentences 3 + 9  Doubles/Near-Doubles with Double Ten-Frames  Doubles/Near-Doubles with Number Sentences 7 + 8; 16 + 15  Making Tens with Double Ten-Frames 5 + 6  Making Tens with Number Sentences 6 + 5 + 4  Making Landmark or Friendly Numbers 48 + 13  Breaking Each Number into Its Place Value 16 + 26  Compensation 19 + 26  Adding Up in Chunks 44 + 35 NUMBER & ADDITION

38.  Addition:  Making Tens 2 + 6 + 8 + 3 + 4  Making Landmark or Friendly Numbers 49 + 23  Doubles/Near Doubles 24 + 26  Breaking Each Number into Its Place Value 35 + 26  Adding Up in Chunks 28 + 24  Subtraction:  Adding Up 60 – 49  Removal/Counting Back 50 – 17  Place Value and Negative Numbers 48 – 29  Adjusting One Number to Create an Easier Problem 50 – 24 (49 – 24 = 25; 25 + 1 = 26)  Keeping a Constant Difference 51 – 26 ADDITION & SUBTRACTION

39.  Multiplication:  Repeated Addition or Skip Counting  Making Landmark or Friendly Numbers 25 x 9  Partial Products 8 x 16  Doubling and Halving 15 x 16 (30 x 8)  Breaking Factors into Smaller Factors 4 x 9 (4 x 3 x 3)  Division:  Repeated Subtraction or Sharing/Dealing Out  Partial Quotients  Multiplying Up  Proportional Reasoning MULTIPLICATION & DIVISION

40.  Number Talks: Helping Children Build Mental Math and Computation Strategies  Mental Math  Marcy Cook Resources  Number SENSE Books RESOURCES

41.  Math Perspectives by Kathy Richardson http://www.mathperspectives.com/num_talks.html Video: 4 th grade Area/Perimeter  Inside Mathematics: Number Talks http://www.insidemathematics.org/index.php/classroom-video- visits/number-talks Videos: 2 nd grade, 4 th grade, 5 th grade  get2MATH K-5: Number Talks https://sites.google.com/site/get2mathk5/home/number- talkshttps://sites.google.com/site/get2mathk5/home/number- talks ONLINE RESOURCES

42. Discuss with your grade level:  How can we incorporate Number Talks into our daily instruction?  What practices are we currently doing well and how can we improve?  What types of number talks will we incorporate during the first quarter? REFLECTION

43. Number Talks Characteristics of Number Talks Classroom Community & Environment Role of the Teacher Role of the Students