# Throw Away the Base 10 Blocks

Just put them in the trash, already.

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Ok. Let me back up… #longpostalert

More than 20 years ago—TWENTY YEARS—I sat in my 5th grade classroom as someone brought in a *huge* box of orange, wooden base 10 blocks. My 5th grade teacher had won a grant and we got free math tools! So fun and so exciting!

But that was 20 years ago. When manipulatives were just being explored as a way to help kids understand math.

2 years ago I listened to Linda Jaslow, my math instructor for a math leadership class I am taking part in quote Linda Griffith {a well known CGI researcher},

And it changed how I thought about math manipulatives. Specifically, base 10 blocks.

You see, the problem was, my first graders were using the base 10 blocks for anything BUT math. During our math mysteries time, my kids were super pumped to grab those shiny blue base 10 blocks and then used the ten rods to represent the friend that their math mystery was about, or even worse…used a ten rod to represent one of something, a tally mark, the number one…

And, yes, I spent a good 5-10 minutes** every day **working on breaking numbers apart into tens and ones with interactive base 10 blocks during Math Wall. And they totally got how many rods and cubes to use to build 2 digit numbers—even 3 digit numbers.

But, did they really understand our base 10 system?

I don’t think so. Not even close. Because they couldn’t use the base 10 blocks to help them solve math problems *on their own*…well, besides maybe 2 kids out of 25.

We spent most of last year’s math leadership class talking about our base 10 system and how important it is for kids to understand base 10 to be able to add, subtract, multiply and divide successfully and with *understanding.*

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**So, what’s the big deal? Why don’t base 10 blocks work?**

Because they can’t be manipulated and changed. Kids can’t actually build their own group of ten, they just have to know that grabbing 1 ten rod is the same as grabbing 10. And that’s really, *really*, hard to master. As a teacher, I can’t just tell them 1 ten rod is the same as grabbing 10 and expect them to understand. That’s something that takes a lot of experimenting with counting and grouping objects to understand. And if they need to break apart the ten to subtract? Forget about it. You can pretty much count on your typical first grader, taking away the whole ten rod instead of trying to exchange it for ones and only take away part of it.

If you want to be a teacher that just teaches kids the steps and lets them copy you, then fine. It might work. But if you want your first graders to understand and be able to add and subtract 2 and 3-digit numbers *on their own* without your help in remembering a bunch of steps?? Yeah, not gonna happen with base 10 blocks….at least not before they understand the base 10 system.

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**Ok, fine. I’ll trash the base 10 blocks. Now what?**

Last year, I took a suggestion from a Math TOSA in our district and turned my pop cubes into groupable “base 10 blocks.” After taking up the base 10 blocks {and, um, not actually throwing them in the trash…pretty sure I didn’t buy them and that would be a big “no, no.” I just hid them away in storage!}, I passed out our tubs of pop cubes to each group (Find my favorite pop cubes here!). These were actually already on the shelf for kids to use during math mysteries time, but, honestly…they weren’t really using these for tools anyways. Pop cubes are good for one thing and one thing only for 6 year olds: building towers. And guns. Okay, so maybe that’s two things…

Back on track….after passing out the pop cubes, I had the kids build the number 48 in the most efficient way possible. So that whenever I counted their cubes, it would be fast and easy for me to count. I chose 48 because it’s number most of my kids can build at the beginning of the year when we do this, and because it’s high enough that just building a tower of 48 becomes a problem and a few kids will try to break the tower into groups. After giving them a few minutes to build the number, we shared ways we built 48. Lots of my firsties built a big long tower. {{EDIT 9/2015: These are pictures from this same task the next year since I didn’t have pictures at the time of this original post.}}

Some made “creatures…”

And some LITERALLY made the number 48…

But some starting breaking the tower down.

When we did this in early September, I had 2 kids that had made groups of 5’s and no one that made groups of 10’s. {The picture above is the edit from the next year where I did have some group by 10’s}

I had hoped someone would make groups of 10’s, but, hey, sometimes you just gotta go with what you have! And all were predictable and acceptable for my lesson goals: find multiple ways to make the same number and find the most useful way to build a number.

First, we shared one kid’s wacky shaped 48.

I pointed out that he had 4 here, 12 here, etc…and then asked if the shape was made in a useful way for counting? {NO….} I asked, “How could we arrange the 48 cubes so they would be useful for counting?” Some of my firsties responses: “I keep losing track of where we are!” “I can’t see that cube!” Remember, this lesson takes place in September, so the level of understanding isn’t as high as it would be if I did this same lesson now! 🙂

Then, I shared another kid’s tower, and we talked about how long it would take to count to 48 by all counting ALL 48 cubes by ones. I asked, “Is it useful to have to count all 48 cubes by ones? How could we arrange the cubes so they would be useful for counting?” Some firstie responses: “We could count by 2’s! Or 5’s! Or 10’s!”

I shared a girl who had broken hers into groups of 5’s. We counted hers by 5’s and then ones. We all agreed that was faster to count and more useful. Then, I asked, “Is there another way I could count that would be even faster?” My highest math thinker saved the day and said, “TENS!!!!” Thank goodness for those high kids. They help drive our conversation when we are about to make some ground-breaking math discoveries and help make it easier to pull along the others to a deeper understanding.

#thestruggleisreal

I had already planned for no one coming up with the idea to count by 10’s….here was the plan in case that happens to you: “You said we could count by 5’s/2’s. What else do we know how to count by? (10’s) Could we make groups of 10 cubes so we could count by 10’s?”

Once the kids discovered that counting by 10’s would be faster, I had each student build their 48 cubes by making groups of 10s. We did this together and carefully discussed our 8 ones left over and how they do not make a full group of 10. At this point, all of my firsties were on the 10’s bandwagon! So, I had each group make all of the pop cubes from their group’s tub into groups of 10’s and they left the left overs as ones. Then, I told them that we would be keeping our cubes grouped this way all year long. When they clean up after math story problems, they are expected to make sure cubes are in their groups of 10s. We just briefly talked about how much more useful this tool would be when building a big number (“You can build it faster,” “I can just count by 10s now!”…)

And low and behold, the very. next. day. during math story problems, the majority of my kids had those pop cubes out building our 2 digit numbers from our math problem to add!

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**Well, that’s great. But how is that different than my pretty Base 10 Blocks?**

The main reason pop cubes are better is because the kids can build and break the 10s themselves. And because I start the year with having them make them into groups of 10’s, they have a better understanding that their rod of pop cubes isn’t just one. It’s 10. The flexibility to break and build 10 is so SO useful. I have watched on-grade level kids (not just my high kiddos) needing to add 9 more and grabbing a 10 and just taking away one cube instead of counting out 9. That’s a REALLY important idea for kids to be able to decompose off of 10. And that’s something you won’t get with regular ole base 10 blocks.

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**So you, seriously, don’t ever use pretty Base 10 Blocks anymore?**

No, I really don’t. Well, sort of. I still do math wall that has an interactive base 10 blocks slide on it about once a week, but we rarely go over the base 10 blocks slide. And when we do, we just use it for flexibility–How many ways can we build the number 76 with tens and ones. They also practice the base 10 slide during their math wall station during our stations and guided reading group time. But we do not spend significant math instruction time on base 10 blocks. In fact, I would venture to say that my direct base 10 block instruction time has been less than an hour for sure this year…possibly even less than 30 minutes.

Why don’t I use that base 10 blocks math wall slide much? Because my kids don’t need it. Because using pop cubes as a groupable base 10 manipulative has helped solidify their understanding of tens and ones and most of my class just doesn’t need practice with that anymore. This past Valentine’s Day, I copied a place value busy work page I found somewhere on Pinterest (can’t find the original source) for party day. The kids were to count pictures of base 10 blocks and color the number on the hundreds chart to reveal a secret picture–a heart. Not one–not ONE–kid in my class struggled with this. Not. One. Even my lowest kids could count the base 10 blocks and write the number in the blank. Maybe I should’ve been shocked by this considering the lack of instructional time spent with base 10 blocks and the non-existent base 10 blocks in our classroom….but I wasn’t shocked at all. Because when you teach for base 10 understanding instead of teaching for base 10 tools you get more bang for your buck. And your kids can do all of those low level skills that many teachers spend all year working with their kids on. No problem for a kid who has a strong base 10 understanding!

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**Alright I get it. Now, what else besides pop cubes do you use to teach “Place Value”?**

I spend a great deal of instructional time helping my kids develop an understanding of base 10. Besides choosing number sets that help with base 10 during math mysteries and the pop cubes, there are a few other regular activities that really help with base 10.

You can read my detailed blog about Counting Collections procedures and routines HERE. When kids have to count large numbers every single week, they begin to group their collections into groups of 5s or 10s or even 20s to help count more efficiently. Making groups of 10s over and over and over helps solidify the understanding that 10 ones is the same as 1 group of 10. It’s also great for giving kids lots of different visuals (besides a 10s rod) for a group of 10…ten toothpicks, ten pennies, ten in a straight line, ten in a circular group, ten in a stack of buttons…

2. **Math Talks:**

The Number Talks book and my corresponding packet has a whole section on number talks for making tens. Each mini-lesson is set up to get kids to visually see how to make a group of ten to count more efficiently. Each section also has ten frame number talks which I also love for a visual representation of a group of ten. Of all of the number talks, these are the ones I use more than any others.

3. __Math Games:__

These sets of games are specifically designed with base 10 understanding in mind. Of course, many have been around for years and are not my original idea, but I have found that using the handouts that I’ve included for recording really help with base 10 understanding as well as just plain ol’ accountability! *wink*

So, take a deep breath, find all of those tubs of base 10 blocks, and donate them to another teacher whose not brave enough to throw them away. Or put them in your inside recess tubs. Or stick them in your school’s math storage closet. Or, or, or….

Just don’t use them anymore! You can do it! You will be a better teacher for it and your kids will be better math junkies because of it too!

Love this! How do you store these?

In plastic tubs. You can find a pic of how they are store in my round the room section at the top of the blog. Warning: the pic was taken before I got rid of my base 10 blocks, so you will see the tub on the shelf!:)

This is so smart! I also disliked how you can't take apart the tens rods. When teaching 2nd graders addition and subtraction with regrouping, trading back and forth between rods and cubes is another step that they really don't have room for in their working memory. I like to use beans and then ketchup cups for grouping 10. When we get to 3-digit numbers we put 10 small ketchup cups into a bigger cup for 100.

I totally agree with your thinking here! It is so important for kids to build and decompose those tens themselves. I love what you are doing and know your kids will do wonderfully when it’s time for regrouping. I do think the base ten blocks have their place in math instruction though, just not necessarily in 1st grade. Let me explain. Higher place values (hundreds, thousands, ten thousands, etc.) still need to be introduced and practiced using concrete tools. While it is possible to build hundreds and maybe even thousands using pop cubes, the higher you go the less efficient this becomes. Students need an efficient way to model operations in the hundreds and thousands. His is where the base ten blocks are useful. Base ten blocks can even be used to model multi-digit multiplication problems. All of this is much more effective, however, if the students have first been taught to understand ones and tens the way you teach them.

I agree with you – I think Whitney is 100% right that you can't just start off with Base 10 equipment and say "this rod is 10", you have to teach them by making 10s over and over until they 'trust' the equipment mathematically, and this can be done using all sorts of manipulatives to make bars/rods – like the pop cubes she uses here. I might use this method of building numbers before introducing the Base 10 equipment as a 'ready made' version of what the children have been building in previous lessons.

Do you happen to have any research to back this up? I totally agree with this post. I have presented this information before to my learning coach at school and she did not agree with me. I am seeking some kind of research to back this up.

Hi Stacey! While I don't have research (other than experience! 🙂 ) to back up this exact idea that base 10 blocks are less useful than manipulative ten groups, I do have research I base my math instruction off of. It comes from this book, Children's Mathematics (affiliate link): https://amzn.to/2HjJHtT

This book talks about Cognitively Guided Instruction which is just about teaching the way kid's math brains learn. It's discovery heavy instead of giving everything to the kids (which is why I use buildable 10 groups instead of fixed groups like base 10 blocks).

I hope that helps! Feel free to email me if you have any other questions!

Whitney 🙂

thefirstgraderoundup@gmail.com

Hi! i know i'm a kid, but i wanted to share my idea of this post. So i just want to say that i agree with you, but i have some other things to say about this too. First of i would love for the longs, (or ten sticks,) should be able to be taken apart. It would help kids to understand The topic better. However, i don't think that base ten blocks are made for subtracting. If you want to add, then just stack the ones up by the tens, and show how you can add that. Although it would be helpful to have them connect, and come apart, I don't think that you have to trash them. Because they may be good for other things.

I followed your advice and bought a pack of 100 pop cubes. Here’s my experience about six months on:

1. My First Grader couldn’t resist making toy figures and buildings out of them immediately. He treated them like giant Lego pieces! Math wasn’t fun so he ignored that part for days. He quickly lost pieces throughout the house so 1/3rd are now missing.

2. I started showing multiplication by skip counting (lining up a block of 2, then 4, then 6 etc.) He picked up skip counting easily this way. I makes multiplication seem simple as kids can see the patterns and memorise the numbers. When they later start learning multiplication tables, it’s very easy to grasp what it’s about.

3. I tried having him do minus and subtraction using the blocks but it was too slow for him to maintain interest. I then gave up for months, teaching place value instead by sticking graph paper on the wall (literally 1 small square, 10 small squares… to thousands).

4. Then I later discovered they’re really fantastic for geometry! He saw me making a cube out of the blocks and rushed to make his own. So he made a small cube (2x2x2 blocks), then made the next larger cube (3x3x3), and kept going until the blocks were finished. I ask questions along the way (“how many blocks were in this cube? Do you want to know the easy way to find out by just multiplying?”, and so he’s learning how to make and calculate square numbers, square roots and cubing numbers without even thinking this is math. My older child hates math because it never made any sense or had a purpose, but my younger kid loves discovering math as it’s just a way to explain how to play with stuff (like thinking “I wanna know how many blocks I’ve got here so I’ll count them by 2’s as it faster… I wanna make a bigger cube so I wonder how many more blocks am I going to need now?”)

You can make other shapes like a cross, adding extra blocks to make the next bigger cross. There are always patterns occurring, and if a kid’s willing to record their findings on paper they’ll learn even more.

So, geometry is what these blocks have been most useful for in our home. It’s fun, very interactive, and when kids learn the formal rules of math like area, perimeter and exponents it’s going to be very easy to learn and remember because they’re already doing it.

Many thanks for this page! I wanted to share my experience.