77. Skip Traditional Math Warmups and Do This Instead

Johanna Kuiper 0:00

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This might be controversial, but I do not do warm ups in my math classroom, at least not in their traditional sense where there is a problem on the screen from yesterday’s lesson or previous content. But I do like the idea of starting off with a bite sized problem that helps put my students minds in math mode. So I’ll be sharing exactly how to do that in today’s episode. Let’s get started. 

Welcome to solving for the undefined podcast. I’m your host, Johanna, founder of Miss Kuiper’s Classroom, the place that equips teachers and creating a healthy math classroom where students can thrive, no matter their academic abilities. But it’s not always about the numbers. And that’s why I’m here, bringing you the formulas to solve your problems, math and otherwise, plus strategies on cultivating that necessary math mindset. And that’s what you can count on. 

Hello, hello, welcome to a brand new episode. Today we are talking about how to do better warm ups for critical thinking in your classroom. And to start us off, I want to share why I don’t do the traditional warm ups in my classroom. So when I think about a warmup, it’s usually content from the day before or previously grade level content, or sometimes spiral review. And the reason I find that challenging is because students either don’t remember how to do it, or they were gone the day before when we learned that concept. Or it’s just not interesting to them, so they’re not gonna do it. And all three of those things become either a classroom management problem for me, or a time of reteaching. And the warm up ends up taking 1015 minutes, when I did not want that I want it to be a five minute quick and done type activity. And it’s turning into a lesson rather than just a warm up to get my students into math mode. And to clarify, I’m not saying doing those problems is wrong. But I think there’s a better time in place for those problems. And it is not at the beginning of our lesson. Instead, I want to give students a problem or a task to do that’s gonna give them a confidence boost that’s low risk, but fun and engaging and still uses math has Critical Thinking collaboration. But overall, the purpose of it is to get that confidence boost at the beginning of class to carry over into the main lesson for the day. 

So jumping in, I have three categories of math adjacent tasks that I like to do with my students. The first being, it’s all about critical thinking. So I’m going to name off some of them, and then I’ll go into more depth on them. So some critical thinking tasks that I do with my students are crack the code, math, mashup problems, number pyramids, magic triangles and magic squares. 

So the first one is actually one of my favorites, and that’s crack the code. And the way these ones work is students are given five different three digit numbers, each with a prompt about what digit is correct or not. For example, the first one might say one number is correct and placed in the right spot. So if it was to six, five, that either means the two is in the right spot, the six is in the right spot, or the five is in the right spot. And their goal is to figure out what is a three digit number to unlock, or to crack the code, then like the second one might say, One number is correct, but wrongfully placed. And so that means if the clue is 234, that means either the two is correct, but in the wrong spot, the three is correct, but in the wrong spot, or the forest correct, and then in the wrong spot. And the next clue might be none of these numbers are part of the code. And so then you can start using some process of elimination to figure out oh, if the one that says nothing is right is 387, then that means the three in the previous clue cannot be the correct number. And then there’s usually one where it’s like two numbers are correct but in the wrong spot. And it just gives more process of elimination for students to figure out what that three digit code is. 

The next one is called math mashup. And this is actually like a branded name like Kleenex versus tissues. Math mashup is like puzzles where it’s three different emojis or three different pictures added together to make a number and there’s like four or five of these and students have to use process of elimination and some number sense to figure out what each of those mean. So like one of the most common ones if I type in math mashup puzzles, is one where it’s like 48 equals gummy bear plus lollipop plus gummy bear and later down the line, it shows that gummy bear equals lollipop. So then I have to think about what three numbers that are the same that add together to create 48. And then once I have that, I can move on to the next clue where it says lime slice plus Ring Pop equals zero. So for me, I know that either Ring Pop, or lime slice has to equal zero because anything times zero is zero. And I kind of go through the process of elimination and figuring it out as I answer or figure out more clues throughout it. And usually the last one in the set is when I add or multiply all of them emojis or pictures together, it equals a question mark. And the goal is to figure out what that question mark stands for. What I really like about these ones is students are doing solving equations type of thinking, without realizing that they’re doing that higher level thinking in math. So if I had just given them 3x equals 48, or something along those lines, they would have been more intimidated by that problem than me giving them 48 equals gummy bear plus lollipop plus gummy bear. So they’re still doing the same style of thinking, but it’s completely different in their brain. 

Next is the number pyramid. And the number pyramid is where you have like three boxes two boxes in one box. And students are typically given like the bottom three, and then they have to add the numbers that are together. To create the next row, add them together to create the final row. And sometimes you’re given just the bottom one, but sometimes you’re given a random spattering all over the pyramid. And so they have to use subtraction as well as addition to figure out the missing numbers. These warmups tend to be a little bit quicker, since it’s just adding and subtracting. But you can do number pyramids with multiplication. But I like the addition and subtraction ones because it also brings some more number sense into it. 

I’m gonna go through the last few the magic triangle and magic square also kind of quickly because I want to get to the other ones. But magic triangle is where the perimeter of the triangle each side has to add up to the same number. So if the goal is adding each side up to 10, how can I use the numbers one through six without repeating to create a triangle that each side equals 10. Magic squares have the same idea but you want each row column and diagonal to add it to the same number. So say the sum is 15. How can I get each row each column and each diagonal to equal 15. without repeating any numbers, I usually start off small by doing a three by three grid. And as students get more comfortable throughout the year, sometimes atheroma four by four, and just see how it goes. I will have links to all of these in the description as well as the show notes. So if what I’m saying doesn’t make sense, or you want to start using these with your students, you have access to them right away. 

Alright, the next category after critical thinking is estimation. Now estimation, I think is a very underrated skill for students to have in the math classroom. But it is huge. So two ones that I like to do our estimation 180 and esti-mysteries. 

So estimation 180 is a website that has 180 days worth of estimation pictures. And the way it works is if you start out with day one, day one is this really tall guy standing in a picture. And the kids goal is to figure out or estimate how tall he is, and use kind of the things in the picture to make an educated guess. And then the next day after students day one have figured out his height. The second day picture is the same man, but this time with his wife and kids are supposed to estimate the height of his wife. And day three adds on to it with their baby. And they have to estimate how tall the baby is. Now not all of them are all 180 of them are sequentially adding more people to the picture and having students estimate the height of the newest addition. But some of them do have pictures that kind of go together. So I think those are great to do like on a Monday, Tuesday, Wednesday, or like three days throughout the week. But there are a lot of like one shot pieces. So whether you want to do it every day of the week, or sporadically integrate estimation 180. There’s lots of fun pictures to choose from. And what’s cool is they’re not all like find the height or figure out how many almonds are in the cup. But there’s lots of different measurements. So maximum aka occupancy of this area, the total weight, the area of this the weight of this. So there’s lots of different measurements that Students can estimate. And that’s what I really, really love about estimation 180. 

Now esti-mysteries are very different than estimation 180. So the way estimate stories work is there is a picture of objects in some sort of container. And then students are given the idea that it’s between one and 100, then they’re given five clues for them to kind of pare down what potential numbers it could be. So if you go to their website, the first one that’s on there is like a glass vase with a bunch of topics in there like this spinning tops. And then the first clue is the answer is greater than 20. The next clue is the answer is less than 41. Clue three is the answer is part of this pattern. 2224 26, meaning that it’s an even number. And then clue four is the answer does not include the digit three. And clue five is the answer is not 2426, or 28. And then students, then after all five clues have to make an estimation. And what’s also great about these is it’s broken down into groups of grade level. So like there’s clues for kindergarten versus clues for first and second grade. And then they have one for grades three through eight. And what’s great about that is the grades through through three through eight is going to have more sophisticated clues. And like number sense ideas, then like the first grade, or the kindergarten one. And to give you a pro tip for doing estimate histories, I give students a 100 chart inside of a dry erase leaves so that their teams can mark off numbers as they go through of like, Oh, if it has to be greater than 20. That means one through 20 is not part of our answer, oh, it has to be an even number. Let’s mark off all the odd numbers. And so it gives them a visual of the process of elimination that they’re going through to make that estimation in the end. So those are the two estimation style warm ups that I do. 

The next one is open warmups. So open, meaning that there is no right or wrong answer or way to think about it. So the first one is which one doesn’t belong or unique or different, however you want to phrase it. And the next one is number talks or dot talks. 

So which one doesn’t belong is typically for pictures or for numbers. And students have to come up with which one of these four doesn’t belong in the group. And what’s really cool about them is, usually there’s an at least one reason for each piece to not be in the group. And that’s what makes it so open. So say it was a picture of 9, 16, 25, and 43. I could say 43 does not belong because it’s not a square number. Or I could say 16 doesn’t belong, because it’s the only even number, or I could say nine doesn’t belong? Because it’s the only single digit number. There’s lots of answers for the styles of problems. 

Then for number talks or dot talks. Yes, there is a specific answer for what the final answer is or how many dots there are. But the point of these ones is not the answer, but how students thought about getting to the answer. 

So dot talks come from Jo Boaler, at least that’s where I learned first about them. And she has a great tutorial video or instruction video on how she uses it with students. But to give you a brief example, sounds like this. She says like, I’m going to show you a doc card. And then I’m going to take it off the screen. And the reason I’m going to do this is because I don’t want you to count the dots, I want you to figure out how many there are without counting. And that’s the important piece right there. Like how many there are without counting, because it’s giving students the opportunity of like, How can I memorize this picture? How can I look at this picture to later know how many dots there were without counting them while the picture was on the screen. And so the example that she uses is, it’s going to be hard to explain. But there are three dots on either side with one.in, the middle and the two outsides are kind of angle so it looks like a greater than and less than sign or a less than a greater than sign with a.in the middle. That’s how I think about it. But that’s the point is you’re having students think about how can they remember this picture after the picture is taken away so that they can remember how many dots there are. And one thing I like to do the first time or two that we do this is tell them the answer afterwards to take out that like anxiety piece of like, Oh, am I correct or not? So I’ll say something like, alright, there were seven dots who would like to tell me how or where they saw those dots? Because again, the point of This activity is not to figure out how many dots there were. But to show students that there is a ton of different ways that they could look at this and still come to the same conclusion that it was seven dots. 

And that’s the same with number talks as well. So a number of talk is given like a small problem like 70 minus 38. And asking students how they would figure that out. And typically you start off with out having them with paper or pencil or whiteboards, and markers. And then later, you will have them write down or record on paper or whiteboard, how they solve the problem. 

And to kind of wrap up why I like open warmups is because it allows any student to engage in the activity, whether or not they are quote unquote, good at math or not. Because there are several ways to think about or complete these problems. So today, we talked about critical thinking tasks, estimation tasks, and open warm up task. So last thing I want to talk about before wrapping up this episode is how to implement this. So first of all, if you already use traditional style warm ups, I would suggest starting with swapping out one day, one of your traditional warm ups for one of these math adjacent warm ups. And then as your students begin to get more comfortable with them start swapping out more days, until you have mostly math adjacent warm ups. Second thing is do not do this as a bell ringer, so it’s not on the screen when students walk in, you want a set time for students to complete this activity. So the way I do it, is after I’ve gone over the agenda for the day, I have students do a supply Roundup, which we’ll talk about in next week’s episode. And then I’ll put a Google slide with the activity on it. And definitely expect anytime that you do a new style of problem for these math adjacent warmups, that it’s going to take longer since it’s new. So for me, the very first time I did a crack the code warm up, it probably took five to six minutes for students to do the problem as well as understand how it worked. But as soon as we got comfortable with crack the code and like the next time we did one, it became a lot quicker because students recognize how they did it last time. So it made it this time easier. But when I first implemented math mash up the first time, it also took a long time. So the next time I did want, it took a little bit less next time it took a little bit less. But what I like to do to kind of keep pace is to use a timer. And I will put that timer on the Google slides so that way all students can see it. And I like to use like funky music kind of timers because it keeps it upbeat. And if there’s music playing students are more likely to talk because they’re not the only person or the only noise happening. So to start off, I would suggest a five minute timer because you can always stop it sooner, or restart halfway through the timer if you need more time. But it just helps keep pace for the activity. 

Last thing I’ll say about implementing these math adjacent warmups is I like to use whiteboards for this. So I have mini whiteboards that I have each group use. And we talked a little bit about this in Episode 75. But having a erasable surfaces increases participation because there’s no permanence of a wrong answer. And I’m using air quotes for wrong answer. So using a erasable surface, whether it’s a dry erase, leave a desk, a whiteboard, that’s going to increase participation, which is going to lead to more students feeling confident because more students did the activity. So that is math adjacent warmups that I use in my classroom to help students critically think collaborate and get that confidence boost at the start of math class.

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And as always, if you have any questions, feel free to reach out to me on Instagram @misskuiper send me a message and I’m happy to answer any and all questions. And with that, I’ll calc-u-later

Thank you so much for tuning into today’s episode. To find all the links and resources to things talked about in this episode, head on over to misskuipersclassroom.com and click on podcast

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