# Mental Math to Increase Student Computational Fluency and Number Sense

A Number Talk is a brief activity teachers can do with students to help build their computational fluency, number sense and their mathematical reasoning. They don’t need to be longer than 5-15 minutes and they can be done with students at any level.

It’s starts with a problem or a question posed by a teacher.

For example, choose one of the following questions:

• Which is greater, 86×38 or 88×36?
• Are there more inches in a mile or seconds in a day?
• What is 25×29?

But, before you pick up your pencil, try to figure out the answer in your head. It makes it a much more interesting problem.

Number Talks emphasize mental math because the goal is to get students to perform operations with numbers in ways that are meaningful to them, as opposed to just following memorized procedures.

Even the most straight forward looking calculation can have multiple solution methods, especially if you have to calculate it mentally. Here’s what I mean: Before you read any further, take a moment and multiply 18×5 in your head.

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How did you do it?

• Did you do 9×5 + 9×5?
• Did you do 10×9?
• Did you do 5×10 + 5×8?
• Did you do 5×20 – 5×2?
• Did you the standard procedure: 8×5 is 40, write the 0, carry the 4, and then 5×1 is 5 plus the 4 is 9?

If we wrote it out by hand, most of us would be far more likely to use the last method. Having to do it in our head encourages us to use our number sense.

Here’s Jo Boaler talking about how she might create visual representations of several different student methods in solving the problem above:

The goal of number talks is for students to develop computational fluency. In order to do that, they need to understand certain mathematical concepts like the fact that the numbers are composed of smaller numbers and can be taken apart and combined in different ways.

You can do number talks in a variety of ways, but here’s one possible format:

1. Give the students the prompt. Write it on the board, write it on a large piece of newsprint and hang it on the wall, project it.
2. Give students a few minutes to work on the problem in their heads. Tell them beforehand to give a thumbs up when they have an answer. You want to give all students the full amount of time to work on it, without the pressure of competing with quicker students.
3. Ask students to share their answers. Write them up on the board without indicating which (if any) are correct.
4. Ask a few willing students to share their method for mentally calculating their answer. A student does not need to have gotten as far as an answer to share their approach with the group. As students share, teachers writes down what they are saying.

This site, called MathTalks (just another name for Number Talks) was created by a middle school teacher in California named Fawn Nguyen. It came out of her desire to have some record of what the kids were sharing during the number talks (and pattern talks) she was doing in her classroom. She had her students write down the ideas of their classmates, and she did the same, out of respect for student thinking. Afterwards, she couldn’t bring herself to throw out what’s she’d written and so she decided to start a blog for math talks. So you’ll find 28 number talk prompts she used with her students and 3-5 examples of what her students came up with for each one.

She also has a page for Teachers where she explains the way she structures number talks with her students. There are also links to other resources for teachers to learn more about number talks.

If you’d like to see an example of a number talk, check out Cathy Humphreys facilitating one in this video from Stanford Professor Jo Boaler’s online course, How to Learn Math. The actual number talk starts at about 50 seconds in. As you watch, think about how each student takes apart and combines the numbers in different ways.

Adult education students really benefit from doing number talks on a regular basis. Try a number talk with your students, and add a comment below and tell us all how it goes.

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Mark enjoys doing math problems that take weeks, family sing-a-longs and reading late into the night. At 16, he believed the next revolution would be waged through poetry. Now he believes it is adult basic education. But he still likes poetry. Mark has worked in adult literacy and HSE since 2001. He is a founding member of the NYC Community of Adult Math Instructors (CAMI). He was born and raised in Brooklyn where he lives happily ever after with his partner Sarah and their daughter Liv. Follow me on Twitter (@mtrushkowsky)

## 7 thoughts on “Mental Math to Increase Student Computational Fluency and Number Sense”

1. Mark Trushkowsky says:

In 2015, the TASC is introducing one constructed-response question in all of the content areas, including math. These will be questions where students will need to not only give an answer, but to also write some kind of explanation of their process. Number talks are a great way to build student confidence and precision in communicating their mathematical reasoning.

2. I’ve used this as both a class warm-up and a complete lesson. Students really enjoy the challenge of this. And it accommodates all levels by using both low numbers (18×5) and higher numbers. I find, though, that rather than have students call out their answers, it’s more effective if I give everyone a Post-it and have them write the answer down. There’s a danger of mimicry; if a student who hasn’t figured it out hears a consistent number, what’s to say they won’t just repeat what they’ve heard? After collecting the Post-its (making a mental note whenever a student deviates from a majority answer-still, I keep this process anonymous to minimize the public shaming) I write the answers before inviting students up to demonstrate options. Seeing, and devising possibilities–for them, the pleasure is palpable.

3. Kathryn Lent says:

I like this resource and am eager to share with my staff. I agree with you Mark, it seems like it is a great way to build student confidence and precision in communicating their mathematical reasoning. I appreciate your comment Ennis, our students have enough shame around math, I like the steps you have built in to avoid any more.

4. At the 2016 COABE conference, Laura Sherwood (from the Adult Learning Resource Center in Illinois) gave a presentation called, “Integrating Learners’ Diverse Ways of Doing Math into Your Math Instruction” in which she makes a strong case for doing number talks in class, especially with ELL students.