Middle School Math Tasks for Critical Thinking

Johanna Kuiper 0:00
I want you to think about this. When the bell goes off to start a class period, how long after that bell rings? Do you start having students think critically about math. In today’s episode, I want to talk to you about how you can get your students thinking as soon as the bell rings to make sure that they are putting their brains in critical thinking mode, to be able to do high cognitive demand problems that will help them deeply understand and learn to love math. And with that, let’s get started.

Johanna Kuiper 0:31
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.

Johanna Kuiper 1:01
Hello, hello, welcome to episode 44. Today, we’re gonna be talking about how to start your math classes to set them up for success. Typically, math teacher start off the day with a warm up. This warm up is usually something from the day before or previous learning to help tie in yesterday into today. Well, that can be really helpful. Sometimes, what I found my first couple years of teaching is it will always take longer than I think it will. Even if I set a timer on the screen, going over it as a class takes too much class time.

Johanna Kuiper 1:37
And that’s why I’ve implemented the idea of new material before old material, meaning I’m not reviewing old material that my students have already learned before teaching them something new. With this, I have rebranded warmups as thinking tasks. And I use this terminology with my students. So today, I’m going to be sharing the thinking tasks that I use on a daily basis with my students.

Johanna Kuiper 2:02
So the first one is which one doesn’t belong, you’ve probably heard of which one doesn’t belong before. But I put the spin on it of which one is unique, something about the which one doesn’t belong, sometimes my students aren’t grasping that idea. So I’ve just rebranded it a little bit to be which one is unique or which one is different. And I like to use this to foreshadow whatever our lesson is going to be about. So when I did transformations, the introduction, I had four different shapes, triangles to be specific, that were moved around inside of a box. And they were asked which one is unique. And they started to practice using terminology like slide turned, flipped, grew shrank, they were using those words that I would later tie into one of the transformations. So it was a great way to start off their thinking towards the goal of that lesson for the day. And with the which one doesn’t belong or which one is unique. I like to give students private thing time to think about it, discuss it with their team, and then I have a sentence frame for them to fill out. And that sentence frame ties into the way I review it. So what I have students do is we always do these on whiteboards, our thinking texts are always on whiteboard, they stand up tuck in their chair, and I play music. When the music is playing, they wander around the room, when the music stops, they pair up with the person closest to them and share their sentence. I like to call this musical partners. And it’s a great way to add in that academic language and those sentence frames to support your students, especially if you have ELLs in the classroom. So I always have the sentence frame on the screen as well as a word bank they could use. And then once they go back to their desks, I have two to three people share what they noticed. And I like to make sure students are sharing maybe one per thing. So if those three students share maybe about option one and two being unique, I might call on people who I either know have the three or four answer or be like, does anyone have a reason why number three or four is different from the rest, just to open up the conversation either for even further. So that is the first type of thinking task I’ll use.

Speaker 1 4:22
The second is crack the code. Now this is something that mathematically enthused Kelly introduced me to a little while ago on her Instagram, and I love them. They’re such a great thinking task for students. So the way it works, it’s a three or four digit number that students are given clues to figure out what it is. I’ll put a picture of it in the show notes on my website, so that way you can visualize what it is. But here is the audio version of it. So they’re given four to five clues with numbers and conditions surrounding them. So for example, the first clue would be 680 to one numbers correct and in the right place. The second one is 614. One number is correct, but in the wrong place. The next one is 206. Two numbers are correct, but in the wrong places. Next one is 738. Nothing in this is correct. And lastly, 781 numbers correct but in the wrong place. Now that students have five clues, they are now tasked with finding the three digit code that will unlock the lock. And it’s really fun to see students work through this. And especially that first time, like, how are they going to approach this problem? And because I’ve done this, maybe five times now, I’ve done four of them with three digit numbers, and then I did a four digit one this past week, they’re using the same strategy every single time to find that answer. And that’s okay. They found a strategy that works. And I think that very first time that I did this problem, we talked about what strategies could we use to solve this, and I got ideas from students to go over it. And then they were able to implement it the next time we did this thinking task. Again, this is a thinking task I do on whiteboards. So students are given three minutes to solve it with their team on their mini whiteboards, I always encourage them to write the numbers down on their whiteboard. And then one of the strategies that students came up with is starting with the clue 738 Nothing is correct. And then at crossing out, or erasing the numbers, 738 and all the other clues, it was really cool that they came up with that. So that is the third type of thinking task that I use in my classroom.

Speaker 1 6:45
The third one that I use is estimation problems, specifically from estimation, one eighty.com. I love these. And part of the reason I love them is because the first couple of estimation 180 Problems day one through I think five are all picturing the same people. And so if I do the day one, which is the height of this man, the second day is the height of the man compared to the woman, and they have to estimate how tall they are. They start being like, huh, then that guy looks familiar. Are you stalking his Instagram page. And it’s just super funny that they’re making the connection, that’s the same person because it is because that’s how they’re supposed to estimate how tall the woman is. Because the day before they learned how tall the man was. And I think the third day is estimating the height of his child. And then it moves on and uses his height to estimate other objects, like one of them is a Ferris wheel. And there are other ones too, like estimating a quarter cup of almonds, how many almonds are in there. And it’s really fun to see students process to see how they’re going to measure or estimate the number or the height of something. So the way I set this up for my students is on their whiteboards. I have them create a T chart with notice and wonder. And I’ll put the picture up. What do you notice? What do you wonder? And I give them two minutes to write two things down for noticing and two things down for Wonder. And then I’m just have them do a quick walk around of their table. What did you notice? What do you wonder. And then I moved them into that estimation piece. Now estimate the height of this or the number of this in the container. And then I have one person from their team go write the number on the whiteboard. And then we talked about what in the picture helps you estimate your number. And then we do a drumroll and I reveal what the answer was. And kids are like, Oh, that was my number. Or ah I was really off. It’s really fun to see students reactions towards whether or not they’re correct or how close they were to getting that answer. So that is the third type of thinking task I will use in my classroom

Johanna Kuiper 9:07
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Speaker 1 9:33
now the fourth type of thinking task I’ll use encompasses a variety of things but it’s all from one website, math mashup. I love these types of problems because you can kind of tailor it to whatever holiday or season you’re in, or just whatever you want it to be. So math mashup takes images and creates math problems with it. So for example, hamburger times hamburger Times hamburger equals taco pizza times pizza times pizzas 27. Pizza times hamburger times pizza is 18. And then taco plus taco plus taco equals what? And students are supposed to come up with what numbers would fit those items to make the math sentence true? And sometimes they’ll give them a stipulation of when you’re done, what if so and so was zero? How would that change the problem, they also have problems that mimic area models. So they’ll have numbers in there, but also some images and students are supposed to come up with the images, or what the missing numbers would be to fit this area model. And they also have some other like math, riddles or challenges as well. But this is a really cool way to get students to do math without them necessarily thinking that they’re doing math, it’s a thinking task to get their brains started and in gear for math class.

Speaker 1 10:56
So those are the four main math thinking tasks that I use to warm my students brains up at the beginning of a class. So which one doesn’t belong slash which one is unique. crack the code math mashup and estimation 180 problems. Some other ones that I won’t go in depth about our number talks, dot talks, math, riddles, word problems, just overall, making students think at a higher level than they might with just regurgitating what they learned the day before. The whole goal with doing these math tasks upfront at the beginning of class, rather than something that they learned the day before, is to get their brain in critical thinking mode, the faster students are in that critical thinking space, the more likely they are going to be able to work through those high cognitive demand problems, that you would do that on grade level or on task with whatever you’re teaching in your classroom. So that is the reason why I like to front load, I think in task at the beginning of class, it doesn’t take more than three to five minutes to do all of this within a class period, which would be your ideal warm up anyway. So if you would like to try out any of these thinking tasks, I will link them down below in the podcast description, as well as the show notes on my website. And with that, oh calculator.

Speaker 1 12:18
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 Miss Kuiper’s classroom.com and click on podcast

Transcribed by https://otter.ai