1. Understanding Children’s Thinking Through Number Talks
Sue Dolphin

2. Number Talks are an approach to developing facility with computation that engages children in thinking about numbers and allows them to add, subtract, multiply and divide using the mathematics that is meaningful to them, rather than following procedures that are not.
Kathy Richardson
Fold paper in half. Part 1 – Respond begin day 1. Part 2 – end day 2

3. What is a Number Talk?
a short daily routine (5-15 minutes) where the teacher poses intentionally selected problems for students to solve using the mathematics they know and understand.
ongoing conversations about mathematics that give children the opportunity to develop mathematical competence over time.

7. NUMBER TALK PROCEDURE
The teacher presents the problem and allows the students think time.
The students figure out the answer and use “thumbs-up” signal.
The students share their answers and defend solutions by explaining their thinking.
The class agrees on the answer to the problem.
The steps are repeated for additional problems.

8. The National Council for Teachers of Mathematics states that:
"Computational fluency refers to having efficient and accurate methods for computing.
Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently.”
Principles and Standards for School Mathematics,
NCTM, Reston, VA 2000, p.152

9. Essential Elements of a Number Talk
A safe environment
Problems of various levels of difficulty that can be solved in a variety of ways
Concrete and representational models
Interaction
Self-correction

10. What do you see?
pumpkin
The next 3 slides presents a word, such as pumpkin. Ask the participants what they see when they hear the word pumpkin. Something like this?

11. What do you see?
bear

12. What do you see?
seven
This time “seven” comes up. What do you see? something like this? – “7” We want students to see the quantity. The numeral itself could be anything – it represents a quantity. Just like the letters B E A R have no meaning in of itself – they represent a real object.

13. What Tools/Models Help Students Develop Computational Fluency?

14. Visual flashcards: Dot Cards Toothpick Cards Number Shape Cards
Color Tile Arrangement Cards Pattern Block Arrangement Cards

15. Unifix Cube Towers
Hundred Grids
and beyond

16. Number Composition and Decomposition to 20 Place Value: Tens and Ones
Developing an Understanding of Core Number Concepts through Number Talks
Counting
Number Relationships
Number Composition and Decomposition to 20
Place Value: Tens and Ones
Place Value: Hundreds, Tens and Ones

17. Videos & discussion Here

18. What is the Role of the Teacher?
Provides a safe environment
Selects problems
Provides wait time
Values everyone’s thinking
Records, clarifies, restates
Asks questions

19. The teacher asks questions…
Who would like to share their thinking?
Who did it another way?
Who solved it the same way as Billy?
How did you figure that out?
What is the first thing your eyes saw, or the first thing your brain did?

20. The teacher notices who…
Counts all?
Counts on?
Sees groups?
Composes and decomposes
Uses benchmarks?
Sees relationships?
Uses strategies?
Just knows?

21. Learning How Numbers Work
• Numbers are composed of smaller numbers.
6 = 4 + 2
• What we know about one number can help us figure out
other numbers.
“I know 3 and 3 is 6 so 3 and 4 must be 7.”
• Numbers can be taken apart and combined with other numbers to make new numbers.
“I broke up the 6 into 4 and 2. I put the 2 with the 8 to make a 10
and then I have 4 more which is 14.” .

22. Teaching elementary mathematics does not mean bringing children to the end of arithmetic…Rather, it means providing them with a groundwork on which to build future mathematics.
Liping Ma, Knowing and Teaching Elementary Mathematics, p. 117

23. Remember: Keep it short, 5 to 10 minutes Do number talks daily
Be intentional
Begin instruction where the children begin counting by 1s
If it’s too difficult, make the numbers smaller