I get asked a lot what math manipulatives I recommend. So today, I’m going to give you my favorite math manipulative resources for elementary students.

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• Making Sense by James Hiebert, et al

Now, most of what I’m going to talk about today is a little insight about using manipulatives in your classroom, and almost all of it comes from one book. The book is called Making Sense and it’s by James Hiebert, et. al. But there’s a chapter in that book about mathematical tools as learning supports. This chapter was a big eye-opener for me. And one of the first things that I wanted to talk about here with you guys, is that tools are a big, broad category.

Manipulatives Are Different Than Tools

If you ask what math tools we should be using in our classroom, that includes things like the language that we speak, how we’re writing things down (our written notation), the resources, and tools like the manipulatives. Oftentimes, we kind of lump together tools and manipulatives as the same thing. But this chapter talks about how they are different. Manipulatives are a small part of the tools that we should be allowing kids to use in the mathematical classroom as they are trying to build their understanding. We see manipulatives as that support tool, but there are so many other things that can support kids beyond manipulatives. So yes, this is about manipulatives, but it is only a small piece of the tools that we should be using in our mathematical classrooms.

Now one of the other big things that I took away from this chapter in the book, was that the mathematical manipulatives don’t inherently have the mathematical understanding that we want to transfer to students.

We see base 10 blocks, for example, and we think, “Oh there’s place value and helping build 10s and ones and 100s.”And for a lot of our kids, that doesn’t transfer. And a lot of times, it is done because we use manipulatives in a prescribed way. We bring the manipulatives out. We teach a lesson on how to use the manipulative. And we tell kids, here is the understanding that you need to have about this manipulative. Instead of letting kids play with the manipulative and build their own understanding about that manipulative and how it connects to the things they already know.

And that leads me to the idea that the tools and manipulatives that we bring into our classroom lead to different understandings. That’s why it’s so important to get great manipulatives and other tools in your classroom and allow kids to use all these different ideas because they build different understandings.

Manipulatives Don’t Provide The Meaning

So let’s take an example of in the early grades when we’re helping kids build an understanding of six. And if the manipulatives that we have are just, like Unifix Cubes, which are great manipulative, but the understanding that kids build from that is often just one to one to one. They’re counting one by one by one to build their understanding of six, versus if we use one of my favorite manipulatives, a rekenrek.

There are lots of different ways that kids might show six on here. And that’s one of the hard parts is that we want to tell kids how to use this thing, we want to say, “Okay, everybody has this. Now, let’s show six by counting out six beads”.

But, it doesn’t matter how they show the six. The only rule on this baby is you have to put white on right. That’s the only rule. And then, we push beads over to the left because that’s the way our eyes read, from left to right. We want to build that understanding for kids, but we can’t tell them. It comes from them experiencing the manipulative and making sense of how they see six.

Some kid might want to count by twos to build their six and their six might have 3 on top and 3 on bottom. And then, some kid is going to count one by one by one, and they might get a six all on the top row. And the cool part about this is that kids can still count one by one by one, but this manipulative starts to build other understandings about six. The kid who does count it one by one by one, once it’s there, they might notice something about six now. They might notice it’s one more than five. They might notice it’s four away from 10.

We can’t directly teach that though. We can bring it out through our questioning. That’s the whole thing with all kinds of manipulatives. We cannot, like, stamp it and say, this base 10 block is worth 10. Learn it, know it, now let’s use it. They need to play and experience it and see it in different ways.

A kid who sees six like this…

What’s the understanding that they are building that’s different than a kid who sees it like this?

And can we build those connections together to build a more cohesive understanding of what six means, and what six looks like? Our manipulatives are there to help build connections, but we cannot directly teach those connections to kids. You need to let kids explore and play with these manipulatives, instead of directly teaching a lesson using the manipulatives.

Manipulatives I Love

Okay, now, on to the manipulatives that I love and I think should be in every classroom. Here’s the deal. This would be a really long video if I went through all of them, so down below are links for you to be able to download my recommendations of top manipulatives.

I may have missed some, but I tried to hit ones that are like, the must-haves. Because budgets are tight, oftentimes, and if you can’t do anything else, these are the things that I would recommend. But don’t buy them just because they’re on the list. Buy them because your students need to develop the understanding that these manipulatives help build. Don’t just blanketly go buy a whole list of manipulatives because we don’t want them just shoved in a storage compartment somewhere because you’re not sure how to use them.

Pick ones that you know your kids need to build that understanding and here’s one of my hints, I guess, with that. Is that oftentimes, we get those manipulatives and then we don’t want to bring them out because we aren’t sure how to do a lesson on them.

We don’t need to teach the kids how to use them. We don’t need to do lessons on certain manipulatives. Bring the manipulatives out and let the kids play and explore.

Let them talk about what they’re noticing and what they’re wondering about with these manipulatives. Let the kids build their own understandings and then you piggyback on that. Don’t have prescribed lessons in mind. Have them there, let the kids explore, and then use that as your jumping off points to decide what’s next.

Alright, I hope that this and the downloads that correspond with it has helped you build your math mind so that you can build the math minds of your students. And just so you know, there is a download for PreK-2nd and one that is for 3rd-5th Grade, because we’re building different understandings, you need different manipulatives. Some manipulatives transfer over into different grade levels, but some don’t. So grab those downloads below.

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