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 episode 36. We are going to be talking all about manipulatives. And things to help make math hands on and visual, thinking back to my first and second year of teaching. Using a lot of these manipulatives was very daunting. Growing up when I was in school, we did not use these kinds of hands on manipulatives that I’m going to be talking about today. And when it was my turn to now teach these and implement them in my classroom, I was at a loss. But over the years, I have gained a lot of confidence through YouTube videos, fellow teachers helping me out and just overall playing with it as I go. I find sometimes that as you learn something and students can see that you are learning as well. You can demonstrate the perseverance and tenacity that a student needs to have when they’re learning something new. So perfection is not needed before you start to use these with your students. 

So up first we have algebra tiles. Now I feel like algebra tiles, at least in the secondary world are a more common manipulative. However, if you have not heard of algebra tiles yet, they are like squares and rectangles, different sizes that represent different variables and terms. So in a basic set, you would have like a unit tile and x tile y tile, maybe an x squared and y squared, and maybe even an X Y tile. One of the reasons I love algebra tiles is because it’s a versatile tool. So it works from maybe sixth grade seventh grade all the way up through Algebra Two in high school. It can be used for combining like terms, distributive property, solving equations, and then in algebra as well it can be used for solving quadratics. If you are interested in learning more about algebra tiles, a creator or teacher I recommend on Instagram is Kristin. Her Instagram handle is Damien’s algebra room. I will link it in the show notes. But she has a whole Instagram highlight dedicated to algebra tiles. And last year at the reignite the math classroom conference 2021. Her entire session was on algebra tiles. So she is a very well qualified person to ask any of your questions when you have questions about algebra tiles. 

Now the second math manipulatives is yellow and red counters. Now these are the foam or plastic little circles that have red on one side and yellow on the other side, I definitely recommend not getting the foam ones, because they are not as durable and long lasting as the plastic ones. Just like with algebra tiles, these are a very versatile manipulative. I know people tend to use red and black chips for showing integers. But I prefer these yellow and red counters. And the reason why I prefer these over the traditional red and black chips is because there’s yellow on one side and red on the other. I can just give an undefined handful to a student or give it to them in a box and not have to worry Are there enough black chips? Are there enough red chips, I just have to make sure there’s enough counters within the box itself. I feel like it saves me a lot of time and energy when I do these instead. And for that same reason. I like to use these as game pieces. So rather than having to find game pieces and have students divide them up into colors, like you would with Kinect for I can just give them the box of manipulatives and have them divided up and each choose a color either yellow or red. This was especially helpful for a game that I found in the filing cabinets from the former teacher of the classroom, it was a coordinate grid, and students were rolling two dice, and it would create a coordinate point. And then they would put their color chip on that coordinate point. And I could just give them a bag of red and yellow counters rather than having to give red and black chips. Unfortunately, I do not remember the name of the game, I will eventually remember it and maybe insert it back into this episode. Or if you hear this, you can always ask me on Instagram. And maybe by the time you asked me, I will have remembered what that game was called. But I’m all for those types of interactive, fun games. 

Moving into manipulative number three is wooden blocks. Now this is something I use more often than I thought I would, especially this year. Now you’ve heard me talk about in previous episodes, this idea of building thinking classrooms and mathematics by Peter Lilienthal. And because of reading this book, I have made sure to have more 3x tasks or more discovery based lessons. And these wooden blocks have been really helpful in implementing that. Now the first concept I use these with was volume, specifically volume of a cube or volume of a prism. And from there, because I didn’t have a better tool, I use these to help students discover the volume of a cylinder. And then from there, a cone and a sphere. I know that probably wasn’t the best tool for the job. But it was what I had at the time. And because of blocks, I had represented one square inch, it helped with the idea of or sorry, one cubic inch, it helped with the idea of volume. With that really fun coordinate plane game that I found in the filing cabinet with the U red and yellow counters, there was another game that utilize the wooden blocks, and it was something about towers. And whenever students would roll the coordinate point, they would place a block there. And their goal was to be the fifth block in that position. And that was how you would win the game. Again, don’t remember the name, but my students had a lot of fun with it. One thing I will say about the wooden blocks is because they are a fun tool, you need to give students time to play around with it and work with them before jumping into a task. This just gives them time to get their building skills out of the way. And so they can focus on the task at hand. 

Now moving into our fourth manipulative is dice. Now I feel like dice are an invaluable tool that you need in your classroom. And the number one way I use these are for my dice boards. To give you a picture of what these dice boards are. It’s a sheet of paper typically in a dry erase sleeve, but you can laminate them as well. And it’s just the bare bone structure of a problem, I’m going to use my linear equation one as an example. So on a piece of paper, I have a graph and a blank linear equation. It says Y equals blank x plus blank, and it has a space under it for them to create a slope and to find the y intercept. And they create these using dice. So they’ll roll the dice and whatever number it is they’ll fill in the blank. So if they rolled a two, two would be their rise than if they rolled a one, one would be the run. And they do that for the y intercept as well. Then using those numbers, they would graph the linear equation. Now one of the things I really enjoy about using dice boards, and using groups of three or just groups in general, is as one student is doing the work, the other two are getting the opportunity to critique and watch someone else do it. I like to say that we all learn from mistakes, but they don’t have to be our own. So if the student who’s doing the work makes the mistake, the team members have the opportunity to work with the student and help them get it correct. And basically dice boards just create an infinite number of problems and possibilities and limit the worksheet making or activity problem making on your end a lot lower and dice boards can be used for about any concept I use it for transformations, linear equations, volume, Pythagorean theorem. If you can name it, you can probably use dice boards that and therefore dice and that is why they are an invaluable tool that you need in your classroom. 

Moving into manipulative number five, this one is more concept specific and that is geometric volume shapes. These are 3d structures that you can typically fill with water or rice To show the volume of a shape. Now what’s really cool is some styles of these geometric volume shapes that you can buy have a removable surface area net inside that you can pull out and students can see the surface area net. So if you teach maybe sixth or seventh grade, maybe you would want to specifically look for those. But if you teach maybe eighth grade, or maybe even ninth grade, you might want to look for the ones that you can fill with water. And the reason why I recommend the ones that fill with water is because it gives students the visual of a cylinder, cone and sphere relationship. You can also find videos of these on YouTube. But I find that if students have the actual ability. Now granted, it takes some classroom management water in the classroom. But if students have the actual ability to practice filling it in a cone fill three cones fill up one cylinder, or two spheres fill up the cylinder, it’s a lot more powerful when they’re doing it themselves than just seeing it now you can get certain packs that’ll have more geometric shapes than just a cylinder, cone and sphere. The one I have also has a pyramid, triangular pyramid, a triangular prism or regular prism. So students can see more relationships between those shapes than just the standard cone sphere and cylinder. 

Now moving into our sixth, manipulative, those are the square tiles. This was another one that I use more than I anticipated. square tiles are very aptly named, they are a square tile that has maybe a little bit of volume to it. And I’ve used the square tiles for the theory and theorem, exponents and linear equation, they all work really well with square tiles. And with the square tiles, the exponents or, more specifically, the square roots was the one I was most surprised with. I was creating a sub plan for estimating square roots. And I came across this video by scaffolded, math and science. And in there she is showing how to estimate square roots using a visual model. And she uses small pieces of paper. But I tried it out for square tiles. So the idea stems from if I have four squared, I’m going to have four into a square. So the stylings of the square is four. And you can use that reverse of if I have 16 squares, the square root of 16 is four, because of the area 16. The side length is four, that kind of idea. So if I have the square root of 19, I can use that to then estimate that it’s bigger than 16 and less than 25. So the square root of 19 is greater than four and less than five. And she still shows a really cool way to then use that an estimate the answer. So I’ll link that below if you want to check that out. And I think that nicely ties in with the Pythagorean Theorem and using square tiles for that. If students have the hypotenuse of 10, they can then find the area of that as 10 squared or 100. And then they can kind of divide those out and see what the length of the two legs could be to then create a high pot noose of 10.

And then moving into our final manipulative. I’m not sure you can necessarily call this manipulative, it’s more like a supply. But I have a very good reason for being on this list. It is an angle ruler. No, these are the magical tool you need. I find a lot of times with protractors they’re not as accurate, but a angle rule We’re gonna give students that precise measurement. And in math, we attend to precision. So the way an angle ruler works is it’s like two rulers attached at the corner. And they can move in and out to create a bigger or smaller angle. And now students will line the center up with the corner of the angle, and just move the top piece to align with the line. And same with the bottom piece, and that will give them what measurement the angle is going to be. These are really helpful for basically anything that has an angle, but I use them specifically for the Pythagorean Theorem. Like I said, I like to do a lot of discovery based things. And one of the discovery based things I did was give students a variety of triangles, have them come up with what kind of angle? Was it acute, obtuse or right angle? And then what are the lengths of the sides? And then from there, how does that relate to maybe the Pythagorean theorem. So using these angle rulers give them a lot more accurate answers, than opposed to a protractor.

And that concludes our seven manipulatives that are going to be helpful for your students. So to summarize, we had algebra tiles, yellow and red counters, wood blocks, dice, geometric volume shapes, square tiles, and angle rulers. If you found this list helpful, I have something even better for you. I have a free guide that is seven math teacher must haves for students success. And these manipulatives are just one of the seven pieces. So if you want to find out what other six things you need to have in your classroom, go ahead and download this guide. The link is in the description or in the show notes on my website. So you can see those six things. Plus one of my favorite pieces that I have within this guide is if you would like to purchase this item, I have a budget version and a splurge version. And you can see the difference between this two. I’ve done my heavy heavy research on Amazon and other websites to figure out what the best one is for the best price. So download that so you can have the seven math teacher must haves for student success. 

And with that, as always, 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.

Transcribed by https://otter.ai