Number talks are an effective pedagogical strategy that educators use to engage students in meaningful mathematical discourse and sense-making. Teachers generally use these short talks — often 5 to 15 minutes — regularly at the beginning of lessons. Although number talks, sometimes called minilessons, do not all have the exact same format, they do have some key and common components. One of these key components is the teachers’ role in supporting number talks, which is the focus here. The related videos are clips taken from an online teacher professional development session.

## Why Number Talks

There are numerous benefits to regularly using number talks in classrooms from pre-K to high school, including supporting students’ number and operation sense and building a repertoire of efficient strategies.

In addition, number talks can transform the culture of the classroom to one of inquisitiveness and investigation. Students enjoy discussing their own and others’ strategies in an environment where their thoughts are valued.

Number talks provide an effective way to support students’ mathematical thinking and discourse while allowing teachers the opportunity to model the math with powerful representations (such as ten frames, number lines, and arrays), and teach students how to represent their thinking with more symbolic mathematical representations such as equations.

## Teacher Roles

The teacher has multiple active roles while setting up and faciltating a successful number talk. A fundamental role of teachers during all phases of designing and implementing number talks is cultivator of a safe and nurturing classroom learning community. Number talks both work best in and help build a culture of acceptance, learning, and sense-making. The teacher must carefully craft an environment where all students feel safe to explain their ideas, make mistakes, and thoughtfully critique the ideas of their peers.

Additionally, teachers have other roles when supporting number talks:

- Instructional Designer: carefully select appropriate problem(s) to support a specific strategy or concept
- Presenter: present each problem to the class
- Recorder: record carefully students’ methods and solutions, demonstrating mathematical syntax and use of models
- Discussion Facilitator: facilitate the whole class discussion, encouraging all students to engage with each other’s ideas

## 1. Select Problems

Educators design number talks to support students’ number and/or operation sense. During a number talk the teacher presents a purposeful problem (or problems) to students and gives them sufficient time to solve the problem(s). Number talks are commonly built around a string or set of problems that build in complexity and are designed to support mental math strategies (number and operation sense) — versus teaching children to rely on a memorized algorithm or set procedure.

For example, consider the following string of problems:

10 + 2

9 + 3

19 + 3

19 + 13

This string was designed so the problems increase in difficulty and the last 3 problems include one addend that is 1 away from a landmark or friendly number (here, numbers that are multiples of ten). One strategy that can be used to solve the last 3 problems is decomposing and regrouping so the near-multiple is a multiple of 10: subtract 1 from the second addend (3 or 13), add this 1 to the near-multiple, then calculate the sum using the new addends. With this approach 9 + 3 becomes (9 + 1) + (3 - 1) or 10 + 2, which is the first problem in the string.

## 2. Present Problems

Typically, number talk problems are introduced by the teacher without instruction about how to approach a solution to the problem. Although a teacher may design a number talk around a specific strategy, it doesn’t mean that the students must use that strategy. Number talks give students autonomy over the methods they use to solve the problem(s). Students should be encouraged to choose an efficient and accurate strategy.

Problems can be presented in many ways, incuding as expressions, with manipulatives, and using visual models such as dot cards and number lines.

Strings of problems are presented one at a time, often in order of increasing complexity. Allow sufficient time for students to use mental math to work through each problem before presenting the next problem in a string.

Often students indicate that they are prepared to share their solution and method by quietly placing their thumb against their chests.

## 3. Record Student Thinking

After presenting the problem(s) and students are ready, the teacher carefully records multiple solutions to each problem in a way that allows all students to view and compare all the solutions.

While recording, the teacher demonstrates how to represent students’ thinking with mathematical symbols, expressions, equations, and visual models (such as an open number line or an array). Mathematical representations should both support students and push their mathematical thinking. If appropriate, the teacher may probe the student for more explanation and/or restate student thinking using accurate mathematical words and phrases.

Below are questions a teacher might use when asking students to share their thinking:

- Who would like to share their thinking?
- How do you know that [is accurate]?
- How did you decide to solve the problem that way?
- Where did you get [a number or part of the solution process]?

## 4. Facilitate Student Discussion

The teacher also facilitates the classroom discussion, possibly while students share individual approaches as well as after the example approaches are shared. The discussion should be a group conversation about the strategies and solutions.

Below are questions a teacher might use to facilitate number talk discussions that encourage all students to consider and critique each other’s ideas and strategies:

- Did anyone solve it a different way?
- Did anyone solve it the same way?
- How are [student 1]'s method and [student 2]'s method related?
- Can you explain [student]'s method in your own words?
- Can someone explain how to use [student]'s method for this [other] problem?
- Do you agree with what [student] said? If you don’t, please explain why you don’t agree.

By the end of the discussion, students should agree on accurate solution(s).