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### Number Talks

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Topics: Mental math, numerical fluency; argument & critique
Materials: White board or projector
Time: 5 – 15 minutes
Common Core: Variable, but especially MP3

This mental math routine creates powerful positive habits for students.

#### Why We Love Number Talks

Number talks don’t replace other instruction, but they are a powerful complement to it. They get all students involved, help them strengthen fluency, intuition, and mental math strategies, improve students’ ability to explain and critique solutions, and allow teachers a valuable window into their students’ thinking. A well-run number talk is an excellent example of Common Core Math Practices 1, 2, 3, 6, 7, and 8.

#### How Number Talks Work

If you implement one type of activity into your class routine, Number Talks might be the most bang for your buck. In many ways, they’re familiar. The teacher writes a simple problem down on the board, and students solve it mentally. The difference is that the students aren’t just looking for the answer: they’re trying to find as many different ways to solve the problem as they can. The key elements to number talks are a de-emphasis on speed and right answers and an added emphasis on process and communication. Here’s how they work:

1. The teacher writes a problem on the board.
It can be as simple (like 9 + 17) or complex (500 ÷ 24) as long as it is appropriate as a mental math problem for the class.
2. Students mentally solve the problem.
They show the teacher whether they have the answer by (quietly) giving a thumbs up at their chest.
This prevents a small batch of quick students from shutting everyone else down.
If students can come up with a second way to solve the problem, they hold up a second finger at their chest.
This means that everyone can keep thinking about the problem even after they have the answer.
After enough time has passed that everyone or nearly everyone has a solution, the teacher asks students what their solution are.
She writes down all solutions; none are given preferential treatment, and she doesn’t say whether they are right or wrong.
4. Students explain their thinking.
Once all solutions are written down, the teacher asks students to explain how they got their solution.
Students explain (from their seat) while the teacher writes the steps they describe on the board.
5. Discussion and consensus.
Ideally, by the end of the discussion, the class should have a list of 3-6 different approaches to the problem, plus a consensus as to what the correct answer is.
6. Followup.
The teacher then has the option to ask a followup questions that builds on the last. (If 9 + 17 was the first question, 9 + 27 or 19 + 17 might be good followups.)

#### Example Number Talk

Teacher: Time for our morning Number Talk.
Everyone consider this question. (She writes 9 + 17 on the board).
(A student starts waving his arm in the air.) When you have the answer, show me with a thumb at your chest. (The student puts his arm down and holds up a thumb.)
If you get more answers, show me by holding up more fingers. (She waits for 30 seconds. Several students are holding up multiple fingers, though many have just a thumb.
The teacher is noting to see if anyone hasn’t solved the problem—this is a great opportunity for formative assessment.
Finally, she begins calling on students for their answers, starting with those who have only one solution.)

Teacher: Lucy?
Lucy: 26. (Teacher writes 26 on the board.)

Teacher: Charles?
Charles: 107 (Teacher writes 107 on the board.)

Teacher: Michelle?
Michelle: 25. (Teacher writes 25 on the board.)

Teacher: Any other answers? (No one has any.)
Who would like to explain how they got their answer? Tyrone?
(The teacher records what the students write as they explain.)

Tyrone: I know that 9 + 7 is 16, and then I added another 10 to get 26.
Sarah: 10 + 17 is 27, and 10 is 1 more than 9, so 9 + 17 must be 26.
Charles: 9 + 1 is 10, and then you put a 7 after, so it’s 107.
Lucy: I counted one by one, but I just realized that I miscounted.
I agree with 26
(Teacher crosses out 25 and replaces it with 26.)
Sam: I respectfully disagree with Charles.
You can’t add the 9 + 1 because the 1 stands for 10.
Charles: But that’s how you add. I did it right.
(Teacher lets conversation continue until class consensus, or near-consensus, is reached.
Meanwhile, she’s noting where students are in their understanding of place value and addition.)

#### Tips for the Classroom

2. Students will be looking to see if you indicate what the right answer is. Don’t favor right answers over wrong ones. Make sure that the explanations are what matters.
3. Taking a few minutes ahead of time to plan out a sequence of questions can be helpful.
(i.e., I’ll start with 9 + 7, since everyone can do that, then we’ll do 9 + 17, then 19 + 17.)
4. Make sure you emphasize the Number Talk protocol—hands at chests rather than waving in the air, for example. This will pay off, and you can use it in other places.
5. Give students constructive language to use in the discussion, like, “I respectfully disagree, because…” and “I agree with _____, because…”
6. Always keep the environment safe and positive.
7. Don’t worry if you don’t reach total consensus on every problem. Sometimes a student will need more time to process. You can move on when it feels like it is time.
8. Number Talks can sprawl if you’re not careful. Doing short (5 minute) Number Talks regularly is more powerful than long ones infrequently.