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

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
Cecilio

8. Curriculum Leadership Council 2011-2012
CLC December 6, 2011
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
Cecilio

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 Solution Agree Strategy Question Comment
Curriculum Leadership Council
CLC December 6, 2011
Hand Signals
Solution
Strategy
Question
Comment
Agree *

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. WHAT the students are learning
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. How many dots do you see? How did you see them?
Dot Talk
How many dots do you see? How did you see them?
Intent: Participants will experience a Dot Talk.
Talking Points:
Explain to participants that we will now model a dot talk.
Please note that this is an animated slide.

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 x 2

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

26. True/False
Cecilio

27. True/False Number Talk

28. Kirsten says that 10xy-5xy + 4xy equals xy
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.
*Introduce Dilemmas as a type of number talk
*What could come before and after this number talk. Give rationale. 28

29. How many cubes? How do you see them? What is the surface area?
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? In
Out 1 5 3 2 21 13 9
4x+1

32. What’s My Rule?
Input
Output 1 5 3 2 25 9 8
X^2

33. What’s My Rule? X Y 1 5 3 2 26 10
X^2 +1

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

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?
Cecilio
Intent: Participants will review possible questions teachers may ask of their students during a number talk.
Talking Points:
These questions are just a few questions a teacher would ask.
The teacher could also have sentence stems that students use to share out their solutions and strategies. (Especially helpful for EL students.)

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?
Cecilio
Intent: Participants will review possible questions teachers may ask of their students during a number talk.
Talking Points:
These questions are just a few questions a teacher would ask.
The teacher could also have sentence stems that students use to share out their solutions and strategies. (Especially helpful for EL students.)

39. “ 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.”
Why Talk About Math

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