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Tuesday, March 17, 2015

Throw Away the Base 10 Blocks

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No, seriously.

Just put them in the trash, already.

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},

"No math tool should ever do the thinking for the kids."

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.


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.

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!

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.

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!

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.

1.  Counting Collections:

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!

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