Number Talks
Number talks were developed for classroom teachers to engage students in "mental math" through grappling with interesting mathematics problems. Educators can use number talks regularly as introductions to the day’s mathematical practice, as “warm ups” for other lessons, or as standalone extended engagements with mathematical concepts.
2nd grade: Number of the Day
In this Number Talk, Stephanie Letson engages her 2nd grade students in finding multiple ways to write equations that result in the number 170. She introduces her students with some norms for their learning, such as listening, sharing, writing. She introduces the day’s number by asking them what they notice about the number, and what those noticings (multiple of ten, even number) might mean for their equations. Students work individually, then share in small groups, then share as a whole group. Letson facilitates their discussion and follows student insights when they are offered.

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2nd grade: ¿Cómo se suma?/ How do we add?
In this Number Talk, Katy Arrillaga engages her 2nd grade Spanish bilingual students in a discussion about strategies for mentally solving a problem involving twodigit addition with regrouping. The students share their strategies and evaluate each other’s approaches for solving the problem.

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4th grade: Can This Be True?
In this Number Talk, Elysha Passeggi engages her 4th grade students in a discussion about whether or not the sum of two twodigit numbers can be 238. Students share their responses, defend their thinking, and formulate declarative statements about why the problem is definitively false.

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5th/6th grade: Guess My Rule
In this Number Talk, Fran Dickinson engages his 5th and 6th grade students in divining the function from the input and output numbers. As the learners guess input numbers, the educator generates the output number. After each guess he has one of the learners “graph the point."

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7th grade: What’s the Savings?
In this Number Talk, Debbie Borda and Antoinette Villarin engage their 7th students in mentally calculating the savings received by a student who paid $54 for an item that was discounted 40%. The students in the class first think their way through the problem, then share their strategies with a partner, then share strategies and answers with the class as a whole.

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7th grade: What’s the Savings? 
In this Number Talk, Debbie Borda and Antoinette Villarin engage their 7th grade students in mentally calculating the savings received by a student who paid $54 for an item that was discounted 40%. The students in the class first think their way through the problem, then share their strategies with a partner, then share strategies and answers with the class as a whole.
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Debbie Borda and Antoinette Villarin introduce the day’s number talk. The first step is thinking about “What’s the story? What’s happening in the problem? How is it the same as other problems we’ve been doing? How might it be a little bit different from what we’ve done before?” The problem is “Vinay bought her new iPod for 40% off the original price and paid $54.00. How much money did she save?” The students begin with quiet think time, identifying “how this is the same and how this is different from problems we’ve done before.” In circulating around the pair groups, Borda asks “how is this different from one we did earlier in the week?” Borda transitions the students into solving the problem, first mentally, remembering that when the students have a solution strategy that they are ready to share with a partner, they indicate it to the teachers by showing a “thumbsup.” The students turn and talk to their partner, sharing the solution and the strategy. One student shares that her strategy was to “guess and check” by 5s, starting with 80 and going up. Another shared that he preferred to find percents, saying “Multiplying decimals, I get really confused.” In whole group discussion, students share different ways that they approached the problem.


5th/6th Grade: Guess My Rule 
In this Number Talk, Fran Dickinson engages his 5th and 6th grade students in divining the function from the input and output numbers. As the learners guess input numbers, the educator generates the output number. After each guess he has one of the learners “graph the point."
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Fran Dickinson and his students had done two previous number talks involving “guess my rule?” The difference in this day’s number talk was the graphing of the coordinate values. In his planning, Dickinson and his colleagues decided to set parameters for the learner guesses to keep all of the points in the first quadrant. They had only recently begun investigating coordinate pairs and they thought it would simplify things to have the learners focus. During the number talk, students share different opinions of how to state the rule. Dickinson and his students model “silent signals” for showing agreement and disagreement with one another’s thinking.


4th grade: Can This Be True? 
In this Number Talk, Elysha Passeggi engages her 4th grade students in a discussion about whether or not the sum of two twodigit numbers can be 238. Students share their responses, defend their thinking, and formulate declarative statements about why the problem is definitively false.
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Elysha Passeggi introduces the day’s number talk, reminding the students of a previous number talk in which they were to solve without calculation, instead looking at relationships of the numbers or considering “fact families.” For the first problem of the day, she asks the students to identify “whether the equation is true or false, and how do you know.” Her first problem, 5 + 7 = 12, reaches rapid consensus among the students. The second, 21 + 39 = 50, trips up some students. The students share different approaches to considering the problem. One notes, “You can’t go through it really fast, because then you miss all the calculations.” “Let’s try a challenge problem,” Passeggi says to her students. She gives them a problem where some number is missing; “What number do you need to put in this box to make the number sentence true?” for 8 + 4 = ____ + 5 . The next problem requires the same approach: 12 + 7 = 8 + ___. Passeggi asks “Is anybody noticing anything?” to ask the students to identify the pattern in the two problems. One student shares that “automatically, I know that the one in the box is going to be one less.” She proposes a third problem to “test if that way will work.” After each student shares their way, Passeggi asks the group to raise their hands if they “saw it that way” as well. The students refer to the methods of solving by attaching them to the student’s names, i.e. “I did what Quinn did.”


2nd Grade: ¿Cómo se suma? / How do we add? 
In this Number Talk, Katy Arrillaga engages her 2nd grade Spanish bilingual students in a discussion about strategies for mentally solving a problem involving twodigit addition with regrouping. The students share their strategies and evaluate each other’s approaches for solving the problem.
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Katy Arrillaga and her coach Mia Buljan anticipate the day’s lesson, which is based on the MARS task “Sheep and Ducks.” In their review of the students’ work in a previous task, they discuss how the students showed solid number sense. Arrillaga talks about the routine of number talks, where she strives to build on what they did the day before. Her students have been working on the idea of “friendly 10s,” where the students recognize that a given number is close to a nearby 10. She recognizes that some students like the friendly 10, and some prefer other strategies. She discusses her rationale for selecting certain number pairs so that they will stay close to a friendly 10 that the students are comfortable with; she sets an appropriate level of cognitive demand for the students. In the number talk, Arrillaga engages her students in a discussion of different answers to the addition problem 59 + 37. She gathers different responses from students, which vary but also demonstrate consensus around the correct response. She then asks students to talk about how they solved it, and develops their thinking through discourse, for example by asking, “Where does the 5 and the 3 come from?” One student shares how they “broke” the 7 into 6 and 1, and Arrillaga elaborates, “You broke, you decomposed the number?” Arrillaga attaches each student’s method of solving to their name. Her student Cesar contributes that he wants to use the “Australian Method,” which refers to a previous conversation in which a mathematics coach showed the students how they could use partial sums to solve in addition. The class discusses the “Australian Method” and compares how Noemi’s method differs in its representation of the 16.






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