1. Number Talks
TK - 2nd Grades

2. “Teaching math well calls for increasing our understanding of the math we teach, seeking deeper insights into how students learn mathematics, and refining our lessons to best promote students’ learning.”
A Message from Math Solutions
Founded by Marilyn Burns

3. “Teaching math well calls for increasing our understanding of the math we teach, seeking deeper insights into how students learn mathematics, and refining our lessons to best promote students’ learning.”
A Message from Math Solutions
Founded by Marilyn Burns

4. How many do you see?

5. How do you see them?

6. How do you see them?
5 + 3

7. How do you see them?

8. How do you see them?

9. How do you see them?

10. How do you see them?

11. How many do you see?

12. How do you see them?

13. How do you see them?
As 3 groups of 6
= or 6 x 3 = 18

14. 18 As 6 groups of 3 How do you see them?
= or x 6 = 18

15. How do you see them?
As 3 groups of 6
= or 6 x 3 = 18

16. How do you see them?
As 2 groups of 9
9 + 9 = or x 2 = 18

17. How do you see them?

18. A sample of what students would hear during Number Talks
= x 6 = 18
= x 3 = 18
9 + 9 = x 2 = 18
Array Dice Subitizing Repeated Addition Multiplied Sets Groups

19. What is a Number Talks?
A Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing practice with mental computations and the development of conceptual understanding.

20. What is the Goal of a Number Talk?
The primary goal of a Number Talk is computational fluency.
Mental mathematics is a key component of Number Talks because it encourages students to construct numerical relationships and to develop their own strategies instead of relying on solely memorized procedures.

21. In order for children to become conceptually fluent, they need to know particular concepts that go beyond what is required to memorize basic facts and procedures.
Numbers are composed of smaller numbers.
Numbers can be taken apart and combined with other numbers to make new numbers.
What we know about one number can help us figure out other numbers.
What we know about parts of smaller numbers can helps us with parts of larger numbers.
Numbers are organized into groups of tens and ones (and hundreds, tens, and ones, and so forth).
What we know about numbers to 10 helps with numbers to 100 and beyond.

22. What is a Number Talks? Intentional and Planned Math Moments
Short minute sessions
Daily Routines
Practice with Mental Computations
Development of Conceptual Understanding and Fluency

23. Identify the Key Components of Number Talks
Classroom environment and community
Classroom discussions and discourse
The teacher’s role
The role of mental math

24. What is the format for Number Talks?
Basic steps of Number Talks
Teacher present the problem.
Students figure out the answer.
Students share their answer.
Students share their thinking.
The class agrees on the “real” answer for the problem.
The steps are repeated for additional problems.

25. Classroom Discussions
During a Number Talk, the teacher will present the class with a problem. This can be accomplished in a variety of ways:
On the Board
Holding Up an Index Card
Through a Power Point
Using the Document Camera
Teachers provide the students with time to think and formulate solutions mentally.
Using the Number Talk Hand Signals, students indicate when they are have a solution(s).
When most students have indicated they have solutions the teacher will begin the discussion by calling on students.

26. Presenting a Problem

27. Symbols Meanings Thumb Up Thumb Up and Forefinger Out
Place Thumb Up against Chest
This signifies that you are thinking
Thumb Up and Forefinger Out
Hand remains on chest, fingers extended as ideas are thought of
I am willing to share
Thumb and Pinky Finger
Hand Motion
“I agree”
Thinking
Have an Idea
I Agree

28. 163 + 147 How many do you see? I am thinking I am thinking
and I have a solution
I agree with …

29. 163 + 147 How do you see them? I am thinking I am thinking
and I have a solution
I agree with …

30. Class Discussions
Students are now given the opportunity to share their strategies and justifications with their peers.
There are many benefits of sharing and discussing computation strategies:
Clarify their own thinking.
Consider and test other strategies to see if they are mathematically logical.
Investigate and apply mathematical relationships.
Build a repertoire of efficient strategies.
Make decisions about choosing efficient strategies for specific problems.

31. Response Prompts My strategy is ...
My strategy is similar / different because...
I can prove my thinking by...
I would like to revise my thinking...
I heard you say that...
I know my answer is correct because...
I agree / disagree with your answer because...
I would like to add...
Can you explain...
I can connect to this because...

32. Class Discussions
Wrong answers are used as opportunities to unearth misconceptions and for students to investigate their thinking.

33. Teacher’s Role
In the past we as teachers have had the role of “teaching by telling.”
Our role must shift with Number Talks to help students make sense of mathematics by building upon mathematical relationships.
Our role must shift from being the sole authority in imparting information and confirming correct answers to assuming the interrelated roles of facilitator, questioner, listener, and learner.
Our role is to help our students ponder and discuss the problems by posing questions that lead to conversations that build on meaningful mathematics.

34. The Role of Mental Math
Mental computation is a key component of Number Talks because it encourages students to build on number relationships to solve problems instead of rely on memorizing procedures.
One of the focuses of Number talks is for students to focus on number relationships and use these relationships to develop efficient, flexible strategies with accuracy. Mental computations causes them to be efficient with the numbers to avoid holding numerous quantities in their heads.
Mental computations help strengthen students’ understanding of place value.

35. Rationale for Number Talks
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.
Accuracy denotes the ability to produce an accurate answer.
Efficiency refers to the ability to choose the appropriate, expedient strategy for a specific computation problem.
Flexibility means the ability to use number relationships with ease in computation.

36. How to begin... Focus on building number sense
Progress through age related concepts and skills

37. Developing Specific Strategies in a K-2 Classroom
Four Goals for K-2 Number Talks
Developing Number Sense
Developing fluency with small numbers
Subitizing
Making tens
Kindergarten
Fluency Number Talks
1st Grade
Addition Number Talks
2nd Grade
Addition and Subtraction Number Talks

38. Developing Specific Strategies in a K-2 Classroom
Dot Images
Counting On by Ones
Counting On in Chunks
Making Tens
Five Frames / Ten Frames
Doubles / Near-Doubles
Breaking Each Number into Its Place Value and Combining
Adding Up
Counting Back
Removal

39. Number Talk Activity Gather your supplies 10 Index Cards Dots Marker
Using your grade level “String Sheets” create at least two strings you can use with your students on Monday.
Practice your Number Talks with others at your table.

40. Questions to Help Guide Conversations
How many do you see?
Who would like to share their thinking?
How do you see them?
Why did you do that? Tell me more.
Who else started the problem this way?
How did you think about that?
Did anyone else see this in a different way?
What strategies do you see being used?

41. Charting Our Student’s Thinking
As our students communicate their thinking it is important that we chart their thinking.
Just as in the opening example, model what students are communicating.
Asking clarifying questions. Allow the student enough time to answer the question. Be slow to provide them too much assistance.

42. Elementary Number Talks
Resources
Humphreys, C., & Parker, R. E. (2015). Making number talks matter: developing mathematical practices and deepening understanding, grades Portland, ME: Stenhouse .
Parrish, S. (2014). Number talks: helping children build mental math and computation strategies, grades K-5. Sausalito, CA, USA: Math Solutions

43. Thank You for your participation today! Catherine Vittorio
San Bernardino County Superintendent of Schools