Early literacy is, without a doubt, my #1 love in teaching. But during my last year as a classroom teacher, teaching math to my 2nd graders was actually my favorite part of our day!
The reason why I loved teaching math so much was because of a daily routine that I implemented at the beginning of each math class. The routine is called a “Number Talk,” and it was extraordinarily helpful in developing my students’ number sense. Starting off each class with a 5-10 minute number talk improved my students’ abilities to communicate about math, use a variety of strategies to solve problems, and think flexibly with numbers. Plus, it was just plain fun.
So how do you implement a Number Talk, you ask? Keep on reading and I’ll walk you through exactly how to do Number Talks in your classroom!
Why implement a Number Talk?
To start with, I think it’s important to understand why I chose to implement this routine. For about a year or so prior to the beginning of that school year, I had been learning a lot about developing number sense in young children. Number sense is the ability to understand numbers and quantities, use numbers flexibly, and perform calculations mentally.
According to research, students in the United States lack number sense. Traditionally, students have relied on rote algorithms to complete math problems, without really understanding what they are doing.
Here’s an example of a problem that many students would use a traditional algorithm to solve:
Let’s say that a second grader was trying to solve this problem. A common error would be for the child to do this:
If a student makes this error, it indicates that she likely does not REALLY understand what multi-digit addition is all about. You and I know that solving this problem requires forming a group of ten out of the ones (6 + 4 = 10), and then adding that group of ten to the others (30 + 10), for a total of 5 groups of ten (50). However, a student who makes the above error is relying upon the algorithm she has learned (and learned incorrectly).
The purpose of developing number sense in students is so that they understand the underlying concepts of the operations they perform (addition, subtraction, multiplication, division). Students who have strong number sense can solve problems in more than one way, and check that their answers make sense.
How do we develop number sense in primary students?
All math lessons and activities can (and should) be used to develop number sense. But it’s also helpful to dedicate a specific portion of your math block to developing number sense.
When I taught Kindergarten, we did a lot of subitizing activities. The purpose of these activities was to teach students to rapidly recognize quantities. I used my interactive white board to quickly “flash” groups of dots to students, and then they would have to tell me how many dots they saw. I also had them explain how they got that answer (i.e. by counting, or seeing a group of 2 and a group of 3, etc.). To read more about subitzing, you can check out this article.
Number sense exercises looked different for my second graders. We used number symbols (0, 1, 2, 3, etc.) instead of quantities of dots. Each day during our Number Talk, students practiced solving different math problems mentally, using a variety of self-selected strategies. They also explained their strategies to each other and to me. These mental math problems increased in difficulty throughout the year.
What materials do you need to implement a Number Talk?
One of the (many) awesome things about Number Talks is that they require VERY little prep and materials! All you need is a chalkboard, dry erase board, or interactive white board and a writing utensil. You’ll also want the board to be right by a place on the carpet where students can sit. Students do not need whiteboards, pencils, or paper. They solve all problems mentally.
To prep for a day’s number talk, come up with 2-4 math problems that you want students to solve mentally. I used Sherry Parrish’s Book Number Talks to choose my math problems, which made planning super easy! At the back of this wonderful book, there are lists of mental math problems for K-5th grade. I chose problems based upon what we were learning in our current math unit, and what strategies I had taught in the past.
How do you implement a Number Talk?
Every day at the beginning of our math block, I gathered students together on the carpet, in front of the white board. Then, I went through the following procedures:
1. I wrote a math problem on the board. I often wrote problems horizontally, rather than vertically, to discourage students from relying upon traditional algorithms. I wrote just one problem at a time.
2. I gave students time to think. Giving your kiddos enough time to solve the problem is essential! I taught my students to give a thumbs-up (low, in front of their bodies), when they had solved the problem. Then, their job was to come up with other, additional ways to solve the problem. For each strategy they came up with, they would hold up another finger. This procedure served several purposes. First, I could see who had solved the problem and who had not. Second, I could gauge when the class was ready to talk about the problem. Third, it kept students thinking at all times, challenging those who solved the problem quickly to come up with additional strategies. Also, when students “show it low” (give the low thumbs-up symbol in front of their bodies), instead of raising their hands high in the air, this is less intimidating for students who require more time to solve the problem.
3. I called on a student to share the answer and a strategy. I would choose one student to share their answer and explain how they had solved the problem. While the child was talking, I was absolutely silent. I wrote on the board exactly what they were telling me, without indicating if the strategy/answer was correct or incorrect. If we were doing a Number Talk with the problem 34+16, here’s what a student might say, and what I might write.
Student: “First, I broke the 34 up into 30 and 4, and the 16 up into 10 and 6. I saw the 4 and the 6. I know that if you add 4 and 6 together, they make a 10. There were already 3 tens from the 34, and one ten from the 16. So I took 3 tens + 1 ten + the ten from the 4+6. That’s 5 tens, which makes 50.
4. I opened things up to the class to determine if the strategy worked or if it didn’t work. Sometimes I asked another child to orally summarize the strategy of the child who had first given the answer. Sometimes I did a “Turn and Talk” and had students summarize the strategy to each other. Then, I asked the class to determine if the strategy worked and if the solution was correct. To prove that a strategy did or did not work, a student had to solve the same problem in a different way. Again, I recorded that strategy on the board, just as I had with the first strategy.
5. Once the kids had come up with one working strategy, I invited students to share additional strategies. Each time a child shared a strategy, I again asked the other students to verify if it worked or not, and to explain why. We had a running anchor chart of different strategies, and if a child came up with a new strategy, we added it to the chart.
Depending upon how long the problems took, we did anywhere from 2 to 4 problems a day. I only put up one problem at a time.
To see this in action, you’ve gotta check out this video. Notice how the teacher really relinquishes control to students. She serves as a recorder of their ideas, not a judge of right/wrong answers!
How do you get students to come up with strategies independently?
When I started our Number Talks at the beginning of the year, students had NO prior experience with this routine. They were not used to solving problems mentally or having to explain their answers. It was definitely a challenge at first, but here are some things that I did to make our Number Talks successful:
- I did some modeling, but only at the very beginning. I provided a lot of support and prompting during the first few weeks of Number Talks. After that, I relied on the kids to model strategies for each other.
- I kept a running anchor chart of strategies handy. On our math bulletin board, I had an anchor chart that we continuously added to. When I taught a strategy during our regular math lesson, I added it to the chart and mentioned how it might be helpful to use during our daily Number Talk.
- I gave them no other option than to come up with strategies and answers on their own. Even if the kids struggled with a problem, I did not intervene. I never provided a correct answer or told a child that their answer was wrong or right. I placed full responsibility on the kids to solve the problems, and they rose up to this challenge. If a problem had given them a lot of trouble, I would have dropped it and returned to it later – but I actually never had to do this!
Go try it!
Without a doubt, our daily Number Talk was my favorite part of our day. I loved giving up control to the students and putting them in charge of their own learning. It was also really neat to hear the different strategies the kids used (and invented!). They often shared ways of thinking about a problem that I had never thought of!
Do you implement Number Talks in your classroom? If not, you have to try them out! I strongly recommend purchasing the Number Talks book. It will give you problems that are ready to go AND it comes with a DVD with Number Talk videos like the one I shared above.
Happy Number Talking!!