Base Ten Blocks For Fractions Success

Base ten blocks make fractions much easier to understand. The Fractions page on my website is in serious need of an over haul. Eventually I will get to it. Meantime there Are posts like this.

Here we packed more into the hour (but not too much more from the stand point of CONCEPTS), going over the same concepts using fractions tiles and multi-tens, and drawing them with symbols and practicing problems adding up to less than one. Also did a couple subtraction problems. Then ended with a few that were one and some more...next lesson will contain more symbols less blocks and more on improper fractions. All of this and all we learned was adding and subtracting fractions. Multiplication and division of fractions will come another da, and they are just as easy to present and understand using manipulatives.

Please read this from the POV of how you would present it to your students or kids, and note the common stumbling blocks to be avoided. Base ten blocks and manipulatives allow you to avoid the misconceptions in the first place. Starting with the most common misconception, that some how the rules have changed when we get to fractions. They haven't: we can only combine same kind with addition or subtraction.

I have this one kid I would really like to video tape but I don't want to embarrass him, because he consistently shows a basic lack of understanding of CONCEPTS. This is because he has never been exposed to them.

Asked him to add 1/2 +1/3

His answer 1/5. "Because if the tops are the same you just leave them alone and add the bottoms...or is it the other way around?"

When I showed it was 5/6 using manipulatives there was a lot of "ohh!" and "OK" and "I get it" so we went over the 5 basic concepts focusing on they have to be SAME before we can add them...and because he is still lacking in multiplication skills, I used fractions manipulatives to help him practice multiplication (and addition).  We could skip count this by 3's or by 4's...put the next over lay on and then we will be counting 5's...etc...you don't have to know your multiplication tables in order to do fractions. Use the fractions to help learn multiplication.

I also asked him during the course of adding fractions which was bigger 1/4 or 1/3...of course he said 1/4.

Visually Obvious.

Then before I showed him any of the fractions tiles and asked how many to make a whole one if I have 1/3...he said 3 and how many to make a whole one if I have 4ths?...4 so four is more than three. TRUE. But the more pieces you need the smaller each piece is...puzzled look. But as soon as I get the factions pieces out one look and it's VISUALLY OBVIOUS that 1/4 is the smaller one. "OH!" This child is a teenager.

Not stupid, just never been exposed to math concepts and manipulatives just rules, formula and stuff to memorize long enough to take a test and forget. He is a Classic American Math Student. Had he never met me he could probably have a bright career in climate "science."

We talked about 1/5 and 1/5...how many? 2/5. EASY because they are same. Once we make them the same kind we can add them. x + x is easy because they are same kind...you get 2x. One of something plus another one of the same thing gives you two of something.  Easy.  But if they aren't same kind we better make them same kind so we can add them. Then we talked about the numerator and the denominator. He had forgotten the name of "the bottom one"...de nom, de name, da kind of it...but he did remember the numerator which tells you how numerous the kind is...

"What kind of math is this?"

"Adding and subtracting fractions. About fourth grade level in most public schools..."

"But for your kids it's like first grade."

"Right."

We did several more problems until he got the hang of it using manipulatives...THEN I moved to drawings...and we stopped there. Tonight his sub-conscious gets a chance to put some things together and then we will work on going from blocks to drawings to symbols. Because he is a teenager I can go much more rapidly than if he were 6 or 7.

Then we talked about improper fractions and did about three of those just to give him a taste, ending with...5/6 + 4/9...could you think of a common denominator?

Symbols, Drawings and Blocks

"NO."

So he plays with his sliders on his multi-tens blocks and gets the answer. But still couldn't convert it to 1 and 5/18ths on his own...that's a concept for another day for now one and some more is good enough. Like remembering numbers if you try to remember too many at a time some of them are going to get lost so just a few concepts at a time is best.

Right now the concept of SAME and doing the multiplication is enough. Next I'll add more to that...which will further cement the foundational concepts of making them same before we add them. The rules didn't change we have to understand equivalent fractions and common denominators. With young kids first we play with the tiles then we play with the multi-tens, having multiple lessons in both. With this student he got it all in one lesson because he has more experience and is older and can handle it...if he was 5 we would have done less. Just the one concept of making them same and then practicing adding them using tiles; then maybe some drawing and then some symbols. That might take THREE HOURS. Then on a different day a lesson with multi tens...again another hour or two. Five or six separate classes, spaced out over time. 

Using "sliders" is the fun way to do it. Over all kids like using sliders more. If you don't have multi-tens don't worry you can just use base ten blocks out of your combo kit and get them out a pair at a time,  kids like this too and it's especially good for the hands on experience, it takes longer though which isn't a problem if you are homeschooling. Just for fun I uploaded this to blogger so it's a video you won't find anywhere else.

Can you also see how easy it is to talk about equivalent fractions and learn skip counting while we do?

For those with dyslexic students not that the image is reversed because I used my lap top's camera for all of these pics, but I am able to "flip' the photos but not the video. And it doesn't matter...base ten blocks level the playing field.

Want some Fractions Worksheets made for base ten blocks?

Percentages usually come next after fraction. Showing how to do percentages with base ten blocks is EZ.

BTW if you want to learn how to use the blocks to teach your kids I have SEVEN Hours up so far, but you need a special PT password. Go here for Parent Teacher Training. $15 bucks such a deal....

“A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator, the smaller the fraction.” ~Leo Tolstoy

More Fractions Fun.

You have to do a lot of preparation before you dive in and start adding problems like these.

You need to understand basic concepts like SAME and ONE. But basically all you have to be able to do is count. You don't have to be able to add and multiply although it helps.

Fractions concepts are easy. Any little kid can learn them and understand them, it's that much better if you let them fool around and DISCOVER concepts and how things work for themselves while you give copious amounts of encouragement and direction.

Working with very young students is similar to working with SPED and other "learning disabled" or "special needs" children because often what you have is "developmental retardation" or to be plain many Downs Syndrome and Autistic students who are in their teens are in about the same developmental stage as very young children. Very young children can learn math concepts as proved consistantly on this blog, ergo: SPED kids CAN learn math.

This isn't rocket science. Simple logic.

Here are a five and six year old playing math. Fractions. They have very limited experience with fractions and still can't multiply easily because the don't know their multiplication tables completely yet, but they can learn fractions and begin to understand the concepts. Now if SPED kids and little kids can learn fractions then certainly high school kids and adults can also learn it, even the "problem" children...who aren't particularly disabled or SPED but may be special needs because of circumstances at home, like poverty or parents who use drugs or alcohol etc. Sadly most of you know what I'm talking about because it's more and more common in public schools.

Here they are playing a game where they try to discover the fraction from the disguise it's wearing and they literally get to pull off the disguise once they figure it out.



They do not have enough experience to go about it methodically, but they do have natural thinking skills...and with me as a guide they can be directed to the answers by simple questions. Remember remove the "no" from the lesson. Allow them to explore and discover for themselves. Ask "what if" questions, count, see what they have.

Once we get through some of this we can do some simple addition and see how that works. Also we are headed for story problems and these activities get them ready for that too. There are also everyday math activities that help them make sense of the symbols and numbers when they see them. Also check out this post where they fool around with food and no symbols to help them understand what's going on with fractions.

Also note how the younger boy is very much a participant in this and often gets the answer before his older sibling.



Let them discover and have fun! You will even hear them say "Don't tell us!" The joy of discovery makes learning math (or anything else) FUN.

The whole video in one piece is available on youtube and on my website here. [Link not built yet.]

To get a fractions kit,

check my expanding product exchange:
http://www.crewtonramoneshouseofmath.com/product-exchange.html

Also don't forget these free fractions worksheets.

Fractions Despite SPED

People often ask me if there is a special way to do it for SPED students, the answer is no.

I've had conversations with students that went along these lines. "I know everybody calls you special, but in my class your just like any other kid that's going to learn math. I know you can learn math because you understand English. So quit telling me how special you are and count this."

95% of the time they shock everyone except me...they even shock themselves sometimes. Bear in mind when I met Sarah they weren't even teaching her math because there was "no point to it." they knew she couldn't learn it, and as we say in Hawaii they were wrong but true. She would never have learned math with just paper and pencil and rules and process out of a traditional text book.

(There was a time in my life when I was shocked. After I got over it, I said to myself more people need to see this. And, since no one else has stepped up to the plate it seems to have fallen to me. Hence this blog and my website and the many things that will be made manifest in the next 7 years or so...word is getting out.)

If you try to teach SPED students (or even "regular" students) rules and process the results will be poor. There was a time when I used to have to argue the point but the dismal performance of American math students as reflected by ANY metric saves me the trouble; not to mention that in the 22 years I've been doing this the results have gotten WORSE not better....Fractions and long division still top the list of leaste favorite math subjects pre-algera.

But I digress.

This is an excerpt from an email exchange between myself and a parent of a child with Downs Syndrome.

First off:

Treat them like "normal" kids.

How is her speech, does she speak English well? If she speaks English she can learn math. Period. There are no special needs lessons plans. Do the same lessons you see on the blog and website. You may have to go slower and for shorter periods...but that's it. MAKE SURE SHE gets her hands on the blocks and isn't just watching you play with the blocks. I have had success with downs syndrome, deaf kids, blind kids, autistic kids, kids who climb on rocks...kids is kids no matter what "the experts" tell you. Use all the senses or as many as possible. Play, have fun, learn math. Don't approach it as math time so much as play time. Sing songs. Play games. Watch vids and then DO the stuff in my vids...don't worry about getting it wrong. You can't play wrong.

Sarah is Autistic use your password and check out her page: http://www.crewtonramoneshouseofmath.com/Sample-Lessons-Sarah.html

Here Sarah is doing fractions (again):



After about half an hour she starts "getting it." We have covered fractions before in different ways...we started from scratch, like she had never seen them before and went from there. And this is the result:



As you can see it's becoming easier and easier. You do the same thing with "normal" kids especially younger children. Teachers lament that they have forgotten everything they were taught over long summer breaks. This is normal and natural and often shows mastery has not been attained, although sometimes the are doing as fast as you can write a problem looking very much like mastery has been attained and then a week later they can't remember how to do it. This shows it takes many exposures to put information in long term memory and more than that to make knowledge available for instant recall. Expect this.

She did this one in her head as soon as I wrote it down...however mastery has not been attained, one small change in the process and she gets flustered. As the picture where the problem is scratched out above shows...watch the vid and you'll see what happens when a change is made to the process.

I do the same lessons several times separated by time, they seem new for some, but usually I say the first time it's new, and might seem strange and maybe even a little hard. The next it's I've seen this before, the third time it's I got it already lets do something else. With SPED students it may take an extra time or two beyond that.

If you want to see the whole lesson (you need a password)...just go to Sarah's page. The vid is 24 minutes long. You will see the ups and downs. Here you just see the success. There you will see how we got there...and future vids will make even more sense.

I recommend this for people who don't have SPED students too. The lessons are basically the same...now that she has this lesson mostly mastered and I have watched the lessons, I will emphasize different things, next time we will focus on "filling up the one" and work on improper fractions and then we will be able to do more fractions where we add and then subtract and eventually have to borrow out of that one...we can also go back and forth with reducing fractions and equivalent fractions....then multiplying fractions will be easy and at last division will be covered and you can be assured she will discover WHY we invert and multiply. Again.

If you have teen age students that are doing algebra you might go over fractions again with them because consistantly I see kids in algebra that can't do fractions...or forget how or can sort of do fractions but hate them which is silly when they're so easy.

One last note. Several parents have told me they get lost watching the vids and sometimes don't understand what they are seeing...although it looks fun and easy they don't get it. "Do you have a set of blocks?"

"No."

Therein lies the problem. I can't stress enough that in all the time I've been doing this the ONLY time we lost people is when they didn't have a set of blocks to play with in front of them or wouldn't put their hands on the blocks...the blocks get you through your mental blocks. That's why Jerry used to say "Math is NOT a spectator sport." You have to participate.

If your are an extremely visual learner just watching vids may be enough, but if your are kinesthetic or auditory or a mix where visual is not the primary learning style then hands on is a must. Not saying this to sell you blocks. I'm telling you this because my experience has proven beyond any shadow of a doubt that this is TRUE.

Crewton Ramone's House Of Math

Search this blog for "fractions." (There's like 8 pages of results worth.)

BTW if you want a set of fractions tiles like the ones you see here it's $105.00 shipped to your door and is available on my site at Products and Passwords now. Or order at right. ⇒