How to Do a "Math Talk" and Why You Should Be Doing Them, Like... Now
Okay, what's a math talk? Sounds boring. It's not! Weirdly enough, students LOVE math talks! So what are they? Allow me to explain...
A math talk is essentially providing your math students with a prompt to spur thought and discussion about something sort of mathy. It could be as simple as counting a collection of objects or as challenging as solving a multi-step equation or word problem. It could involve reasoning, estimating, or explaining new strategies. Whatever the prompt, math talks allow students to think about math in different ways, explore new strategies for problem solving, and explain their thoughts and reasoning with others. So basically a little golden nugget of a math lesson that only takes up about 10 minutes of your class time.
Here's how this goes down. First explain the math talk "rules:"
This is all mental math, you don't need any paper or pencils.
Give everyone a chance to think. NO yelling out answers. When you have your answer in your head, place a thumbs up at your chest (raising hands is distracting and makes others who aren't done thinking feel rushed to come up with an answer).
When I call on a volunteer to answer, you can raise your hand to share and wait to be called on.
All answers, right and wrong, are valuable. Don't be afraid to share a wrong answer. Don't ever make fun of someone for sharing a wrong answer. We accept and learn from every single answer that is shared.
Next, present the math talk prompt. Here are 15 free prompts you can try out (suitable for 3rd - 5th grade) and if you like them, consider investing in all 180 math talk prompts (designed for 4th but would work with most upper elementary students). I like to introduce math talks to my students with something simple, like a dot count:
Ask the question: "How many dots are there?" and allow students to think. They will place a thumb up at their chest when they have an answer. When you see all (or at least most) of the thumbs up, call for volunteers to raise their hand and share.
First, just have them share their answers. Most will likely say "eight." With some harder prompts, you will probably have a variety of answers. Next, call on volunteers to explain how they counted the dots. Like this:
Teacher: "Mandy, how did you know there were 8 dots?"
Mandy: "I saw that there were 3 on top and 3 on the bottom, so that's 6. Then I added 2 more from the sides and that's 8."
Teacher: "Awesome. That's a neat way to look at it. Ben, how did you know there were 8 dots?"
Ben: "I just counted them one by one."
Teacher: "Okay where did you start counting?"
Ben: "The one on the top left"
Teacher: (point to it) "This one? Okay then what?"
Ben: "Then I did the one to the right of it and worked my way all the way around."
Teacher: (model this) "Nice strategy, Ben. Carla, how did you count the dots?"
Carla: "I knew that if there was one more dot in the middle it would be 9. But that dot was missing so there were only 8."
Teacher: "Interesting! How did you know that would be 9?"
Carla: "Because it's like a 3 by 3 array. Three rows of 3 which is 9."
Teacher: "And you knew one less than 9 was 8?"
Teacher: "So cool, I love that strategy."
You can see how something as simple as counting dots becomes a really powerful mental exercise. Students begin to see and think about math from different perspectives and get valuable practice sharing their own thoughts and explaining their reasoning to others. Math talks are a simple way to tap into higher order thinking sills on a daily basis.
Here's another example:
Teacher: "How many cookies could be in this bag? Come up with a good estimate. Thumbs up at your chest when you have your answer. (Waits for all the thumbs). Raise your hand if you want to share your answer."
Students share responses: 10, 20, 9, 12, 8, 15, 25, etc. and the teacher records them on the board.
Teacher: "Who would like to explain their thinking? Louie, how did you come up with your estimate?"
Louie: "Well you can see 3 on the top of the bag. So I pictured groups of 3 cookies going all the way down. It looks like you could fit maybe 5 layers of cookies. So that's 5 groups of 3 which is 15 cookies."
Teacher: "That's a really good strategy for estimating Louie. Who else wants to share? Sam?"
Sam: "I thought there would be more like 20 cookies in the bag."
Teacher: "Why did you think that?"
Sam: "Well because the bottom of the bag is wider than the top. So Louie's strategy works if it was all the same width but it looks like you can fit more cookies at the bottom than at the top..."
The teacher continues calling on students to share their thinking. Then asks the next question.
Teacher: "Now come up with an estimate that is too high. Thumbs up when you have your answer. (Waits for all the thumbs). Raise your hand if you want to share your answer."
Students share their responses and then the teacher calls on volunteers to explain their reasoning.
Jamal: "1,000 would be way too high of an estimate."
Teacher: "How do you know that's too high?"
Jamal: "Because I can see 3 cookies at the top of the bag. Just looking at the size of the bag, I know I could never fit 1,000 cookies in that bag..."
Repeat this with an estimate that is too low.
Tanya: "2 cookies is too low because we can see that there are 3 cookies in the bag. There can't only be 2 cookies if there are already 3 cookies."
Teacher: "That's a great point Tanya. Ben, what is your too low estimate?
Teacher: "How do you know there can't be zero cookies in the bag?"...
Math talks can even incorporate your current topic of study. Take this area and perimeter problem, for example:
The teacher reads the word problem aloud to the class, then asks the question: "Which pen do you think is best for Lena's dog?" When all thumbs are up, she calls on students to share their answers: the 1 by 5 pen, the 3 by 3 pen, etc. She then calls on volunteers to explain their reasoning.
Carla: "The pen that's 3 meters by 3 meters is the best choice because it has the largest area. It has an area of 9 square meters. So that's the most room for the dog to run around."
Louie: "I think the 1 by 5 pen is the best one because it's the longest. So that way the dog can run for a longer distance before he has to turn around."
Tanya: "I picked the 3 by 3 pen like Carla but I didn't think about the area. I just liked that it was shaped like a square and it looked like the dog would have the most room in that pen."
You can see how problems like this provide great practice for considering the reasonableness of answers, especially in real world scenarios. Exercises like this are GREAT for improving problem solving skills and increasing student performance on word problems. After hearing their classmate's thoughts, students may start to second guess their own answers. Louie will probably realize that his 1 by 5 pen, while long, actually doesn't provide much room for the dog at all.
One more example, a bit more advanced:
Mandy: "I got 400. I know that four groups of 25 is 100, like quarters when you're counting money. So, 16 is four groups of 4. So we have 100, four times. That's 400."
Sam: "I got 380. I broke the 25 into 20 and 5. then I did 20 times 16 which is 320 (teacher: how do you know 20 times 16 is 320?) Because 2 times 16 is 32 and then I just put a zero on the end to make it 20 times 16. So then I needed to do 5 times 16 which is 60. Then I added those together. 320 plus 60 is 380. But... I'm just realizing that 5 times 12 is 60 not 5 times 16 so I think my answer is wrong..."
Jamal: "I used the doubling and halving strategy! I just doubled the 25. So 2 times 25 is 50. Then I halved 16. Half of 16 is 8. And then 50 times 8 is 400 because 5 times 8 is 40. So then you just put another zero on the end to get 400."
You can see how math talks can be very simple, like counting 8 dots, or relatively advanced, like solving complex equations in your head. It's best to start simple and work your way towards more difficult problems. This builds students' confidence and gets them used to the format of math talks and how to effectively share their thoughts and explain themselves in ways that make sense. This takes practice but it's so very worth it!
I hope you'll try out math talks in your math classroom. Set aside 10 minutes each class period, or even just a few times a week, throw up a prompt and get sharing! You'll find that your students look forward to math talks each day and you'll be amazed at the improvement in their problem solving abilities! Remember you can try out some free math talk prompts (including the 4 example prompts above) or invest in a year long resource here.