1. Andrijana Dobra, Tara Seiden, and Nina Singh
Number Talks
K-2
Andrijana Dobra, Tara Seiden, and Nina Singh

2. What is a Number Talk?
A number talk is a short routine that provides students with meaningful ongoing practice with computation. A Number Talk is a powerful tool for helping students develop computational fluency because the expectation is that they will use number relationships and the structures of numbers to add and subtract.

3. Goal of a Number Talk Computational Fluency
Children develop computational fluency while thinking and reasoning like mathematicians. Children are asked to make connections and look for relationships and thus are engaged in "doing mathematics." When they share their strategies with others, they learn to clarify and express their thinking, thereby developing mathematical language.

4. Structure of a Number Talk
1. Teacher presents the first problem in the string: Problems can be presented in different ways depending on the level of the students: on a rekenrek, ten frames, dot cards or a written problem.
2. Students are given time to figure out the answer. To make sure students have the time they need, the teacher asks them to give a “thumbs-up” close to their chest when they have determined their answer. The thumbs up signal is unobtrusive- a message to the teacher, not the other students. When students have the answer, they continue to think of more strategies they could use to solve the problem.
3. Students share their answers. The teacher records all answers on the board before asking for strategies.
4. Students volunteer to share how they got their answers. (At times, students are asked to share with the person(s) sitting next to them.) The teacher records the student's thinking. Several strategies may be presented. Students name their strategy before explaining their thinking.

5. Structure of a Number Talk Continued
5. The class agrees on the correct answer for the problem. The answer a student comes up with initially is considered a conjecture. Models and/or the logic of the explanation may help a student see where their thinking went wrong, may help them identify a step they left out, or clarify a point of confusion. There should be a sense of confirmation or clarity rather than a feeling that each problem is a test to see who is right and who is wrong. A student who is still unconvinced of an answer should be encouraged to keep thinking and trying to understand. For some students, it may take one more experience for them to understand what is happening with the numbers and for others it may be out of reach for some time. The mantra should be, "If you are not sure or it doesn't make sense yet, keep thinking."
6. Steps 1-5 are repeated for the second problem in the string. After students share their solutions and strategies for the second problem, the teacher focuses in on the strategy for the day/week."For the remaining problems in the string I would like you to try the strategy that ______ used. We call this strategy ____________".
7. Students attempt the remaining problems in the string using the focus strategy. Ensure that students leave the Number Talk are able to name the focus strategy. For the final problem in the string you may wish to have students record their thinking on a dry erase board and hold it up as a quick assessment to see who is secure with the strategy. You may also have students use the focus strategy to create and solve their own problem on their whiteboards.

6. Number Talks Hand Signals

7. Kindergarten
We use the rekenrek for number talks to encourage students’ fluency with numbers (specifically 1-20) and increase their ability to explain their mathematical thinking.
Important concepts: there are 5 red + 5 white= 10 beads on top. There are 5 red + 5 white= 10 beads on bottom =20 beads in all. We show our work in “one push” encouraging students to identify groups of numbers, rather than counting one by one. We encourage our students to show/explain their work in multiple ways, understanding that there is not one correct way to find an answer.
Examples: (1) how many are hiding? (2) show me ___. (3) one more/one less (4) doubles (5) 10 and ___ more (teen numbers)
Important questions: (1) How did you get the answer? (2) Are there any other ways to show this?

8. First Grade
Number talks at the first grade level are designed to provide students with opportunities to continue to build fluency with numbers within 100 and develop beginning addition and subtraction strategies. Dot images, rekenreks, and five and ten frames may be used during numbers talks.
Students will focus on these strategies:
Counting all/ counting on
Doubles/near doubles
Making tens

9. Dot Images Rekenreks Double Ten Frame
How many dots do you see? How do you see them?
How many beads do you see? How do you see them?
Numbers 3-9: How many dots do you see? How do you see them?
Focus 10: How many more to make ten?

10. Second Grade
Number Talks in second grade are building on all of the hard work done in Kindergarten and First grades! Students now solve written problems mentally. Occasionally, they will be asked to show their work on whiteboards or on paper. Students will have opportunities to to continue to build fluency with numbers to 20 and develop addition and subtraction strategies within 1000.
Students learn six addition strategies:
Doubles/near doubles
Making tens
Friendly numbers
Place value strategy
Compensation
Adding up in chunks
Students learn two subtraction strategies:
Adding up
Removal

11. How the addition strategies look

12. How the subtraction strategies look

13. Conversation Starters/Questions
Does anyone have a different answer?
Who would like to share their thinking/defend this answer?
Did anyone solve it another way?
How did you figure that out?
Can you explain why you ………?
What was the first thing your eyes saw, or your brain did?
Turn and talk to your partner about which answers are reasonable/unreasonable and why.
Turn and tell your partner how ___ just solved this problem in your own words.
Discuss with your partner which you think is the most efficient strategy and why.
Think of another problem where this strategy would work and be ready to share.
I think the answer is ____.
I think __ is a reasonable/unreasonable answer because ………………
I used the __________ strategy.
First I ……… Then I ………
I agree/disagree with ______ because …………………...
I think the most efficient strategy is ……………. because …………………….
Another problem where this strategy would work is …………