Want to help students to build computational fluency, important reasoning skills, and confidence in mathematics? Number talks are the way to go! Check out the resources below to see how and why.

I love Number Talks. When I start working with schools, Number Talks are what I usually recommend we explore first because they are bite-size and easy to implement, yet they give students so much bang for their mathematical buck. They are a great entry point for teachers to practice facilitating productive mathematical discourse (engaging students in communicating math ideas) and for students to learn the ropes of talking about math. Number Talks are also a key tool in boosting the mathematical mindsets of your students because the framework of a number talk gives students a safe platform to take math risks and feel valued for their ideas. Here are some important things to understand about Number Talks and why you should start implementing them right away.

**What is a number talk?**

A Number Talk is a short **number sense routine** (5 -15 minutes long) through which students practice **mental** computation. During a number talk, teachers present **carefully chosen sequences** of computation expressions or equations and **students communicate** their thinking about the answers through **reasoning** and **justification.**

**What are the goals of a number talk?**

- Building computational fluency (flexibility, accuracy, and efficiency).
- Boosting mathematical mindset and confidence.
- Increasing student abilities to reason and justify.

**What are the protocols that I should implement for an effective number talk?**

- Have students sit in a circle. This sends an important message that all ideas are equally valued and moves emphasis towards the collective conversation and away from a back and forth discussion with the teacher at the center. It’s also a great management tool for inviting participation… students can’t hide behind other students or desks, negative behaviors are less likely because students are physically open to each other, and if negative behaviors do occur, the teacher can get to the student quickly and subtly for redirection (without tripping on anyone else!).
**Use the quiet thumb.**Establishing a signal like a thumb in front of your chest to indicate you are ready with an idea is an important characteristic of a number talk. This private signal helps students to not feel rushed. Sometimes seeing that someone else’s hand is waving in the air is an invitation to stop thinking. “So-and-so has the answer. I don’t need to try anymore.” It also sends a dangerous message that speed is what makes a “good” mathematician, a message we do not want to send! Plus, this is a tool for keeping students engaged who figure out an answer and are waiting for others to have time to think… “Show me two fingers if you’ve figured out another way to solve. Show me three fingers if you can find three ways!”**Use wait time.**Make sure all of your students have ample time to think privately before inviting answers. This will boost participation and help all learners feel they have access to the conversation.**Value mistakes**It’s important that mistakes are accepted and discussed as part of what it means to be a mathematician. Setting up protocols for revising ideas together on a different day, modeling the importance of making mistakes as a learning process, and honoring what IS RIGHT in an idea that is not yet fully formed, are all important in building growth mindsets and ensuring that everyone feels welcome and capable of contribute ideas.**Record student names next to ideas**One key feature of a number talk is that the mathematical ideas are recorded by the teacher as students present them. This helps to make visible that mathematics is about creativity and multiple approaches. When we record the student’s name next to each offered idea, we can further send the message that all ideas are valued and welcomed. (And yes, it’s ok to record an incorrect idea. That leaves record for later revision, emphasizes that ideas can grow and change, and provides formative assessment data for you.)

**How do I choose sequences to present?**

Being intentional about the computation and visual sequences that we present students in a number talk is really important in helping students to make mathematical connections. Lucky for us, a lot of the work in choosing sequences has already been done for us. See the links in my lesson resources for places to start with choosing appropriate sequences.

Jo Boaler, founder of YouCubed.org and mathematical mindset pioneer, offers reasons for why number talks are very important in every math class, across the grades.

Another one from Jo Boaler: This is a classroom demonstration of a dot image number talk with a group of middle school girls. This example shows that dot image number talks can be done appropriately with K-12 students (or even adults!) and shows how visual number talks are a great place to start number talks with any class.

Math coach Kristen Gray has a math routines series on The Teaching Channel with several examples of number talks. Here’s one from a fourth and fifth grade combo classroom considering two-digit by two-digit multiplication. Notice that although many number talks include a series of expressions to consider, this number talk is conducted around one expression only. This allows Kristen to emphasize the value to multiple approaches.

A first grade example from Kristen Gray’s series on The Teaching Channel. During this number talk, Kristen engages students in a number string. She uses questions to make sure that she fully understands what the student is articulating, without making any assumptions about student understanding.

This website gives examples of number strings to use by grade level, accompanied by helpful blog descriptions of classes engaging in the presenting strings. Lots of great resources here.

Nat Banting is a genius and one of my new heroes. He has brilliantly taken the protocols of Number Talks and adapted them to images of fractions that invite students to explore, reason, and engage in dialogue around deep conceptual ideas about fractions. This one is a keeper.

A great place to start with Number Talks is using visual representations... dot cards, ten frames, hundreds and hundredths grids. This site has a lot of these materials organized by grade bands.

This site has K-2 and 3-5 resources taken directly from Sherry Parrish's book that pioneered number talk routines. There are also example number talks with anticipated student strategies under the "free number talks" tab.

Sherry Parrish, who wrote the book that helped start the number talk revolution, wrote this article that outlines five key components of effective number talks: classroom environment and community, classroom discussion, teacher's role, the role of mental math, and purposeful computation problems.

This article walks us through the "nuts and bolts of engaging students in number talks." Though these authors make a specific connection to the power of number talks in high school, this article applies to educators of all ages.

From the first time I read this article, the way I thought about fluency was forever changed. Though Jo Boaler engages us in thinking about brain research around fluency development, she does so in a way that's easy to understand and is accompanied by clear classroom practices to boost fluency. Number talks are her number one suggestion... check this one out.