Warm Ups: Number Talks and More

In my last blog post, I wrote about creating Doing-Math and Thinking-Math classrooms. One small but important ingredient I’ve found helpful for both is a good warmup activity.

The goal of the warmup activity is to get students thinking and active right away. The barrier to entry should be extremely low, so that everyone can able to participate. It’s a chance for students to limber up their minds and possibly get an early success under their belts.

There are lots of great warmups out there, including games like Don’t Break the Bank and simple arithmetic challenges like Target Number. One teacher we work with has been leading some amazing Broken Calculator challenges as warmups, which has been fantastic to see.

But today, I want to talk about a classic warmup, and one that provides one of the best returns on investment in terms of time and energy required: Number Talks.

Number Talks are one of the best bangs for the buck routines you can incorporate into your math classroom. They’re build number intuition and fluency while giving you insight into how your students think; they support the idea that math makes sense, and you can explain what you see to help it make sense to others.

If you’re not familiar with Number Talks, our how-to guide is here. In a nutshell, the idea is this: pose a simple arithmetic or counting question, along with the prompt to not merely answer the question, but to come up with as many different ways of answering the question as you can. That minor tweak makes the activity more challenging, interesting, and sparks conversations that the students actually get invested in. It takes a few days to help kids learn all the routine, but once they do the benefits are massive.

From teachers who are familiar with Number Talks, the number one request I get is where to find sequences of questions to pose. We’ve written up a bunch of these lately, starting with counting collections of dots, and moving into solving math expressions. If these would be useful for you, please take them for a spin.

There have also been some exciting developments on Number Talk technology recently. My favorites:

• Fraction Talks (for upper elementary, middle school, and high school)
This is a fantastic resource with tons of ideas for extending classic Number Talks into higher grades with fraction-based images.
• Visual Patterns (for upper elementary, middle school, and high school)
These tend to be accessible as warmups only after students have had some practice with how these growth patterns work. For upper middle and high school students, however, these are an effective warm up, and a place you can see the huge payoff in how the numeracy encouraged by doing Number Talks regularly at the lower grades connects to algebraic thinking in upper grades.

• Would You Rather
Leading a Number Talk using a simple comparison question (“Would you rather have 16 dozen dollars or \$150?”) can motivate estimation. Using questions like the ones at the link, where certain aspects may be more poorly defined, can be an interesting way to connect mathematical thinking, common sense, and logical argument.
• Unit Chats
Unit Chats are a new innovation of Christopher Danielson. These are in a nascent stage of development, as you’ll see if you click the link, but I’m very excited about them. The main idea is to show a picture that contains different choices for units (i.e., avocado halves or avocado wholes vs pits?. You’re not just giving an answer + your strategy; you’re giving a unit as well, which has the potential to change the question and the answer.

I recommend finding a warm up that works for you and then making it a habit. Keep it short—5 to 10 minutes is optimal, in my opinion—and make sure it gets students thinking immediately. Try to do it 2-3 times a week at least, or every day if you can. It’s a small adjustment to your teaching routine, and one that can pay off in a big way.

One last thought: most curricula start with an instruction for teachers to “show students” how to do such and such a problem. You can run these teacher demonstrations as Number Talks instead. By giving students a chance to think about the problem first, they’ll be that much more primed to learn when the answer—and the explanation—arrives.