Here you will see students as young as 4 and 5 years old doing algebra and "advanced" math, without ever knowing it's supposed to be hard. You are invited to learn how to use this method...
Here is a good lesson for those with young children. This was a first time student who is being turned off to math at school. We had fun and she wants to come back for more.
What's Under The Cup Quickly Became Her favorite Game
Look for this lesson on the sample lessons page too. You need a password to see the other hours (and hours) of lessons there but here is this one for FREE. Soon Emma will have her own page because she is an excellent case study. She has been labeled ADHD or ADD and is on her way to SPED and I'm sure part of that is due to her not "getting" math and other subjects the way they are teaching it...thus she get bored or frustrated and acts out. This is a 7 year old child. I have seen no indication that she can not learn or stay engaged for 1 hour at a time. But what do I know...?
I am extremely biased against drugs for 7 year olds. I am also dubious when it comes to the ADD and ADHD diagnosis for bright little kids.
Mostly we played games like what's under the cup and making rectangles:
Building Rectangles and Playing Algebra? No problem.
She never figured out that most kids think algebra is harder than subtraction...which she informed me she doesn't like at all because "it's kinda hard and confusing." We will work on addends and clear all this up over the coming weeks. And you can watch the transformation at http://www.crewtonramoneshouseofmath.com/index.html. We didn't do any subtraction at all that she was aware of...but we will soon master that as well as quite a few other math concepts.
BTW password is going to change soon and prices for passwords are going UP this year.
Anyhow, here is a half hour of math...the hour went by in no time at all.
Here is Sarah really getting the hang of adding fractions...now that we have the idea of it, understand the concepts now it's time to move on to something completely different and wholly unrelated, right?
Only if we were in publik skool. NOW it's time to reinforce the concepts and increase the depth of understanding by doing more of the same, only different.
Here we are spending a little time on improper fractions so we know what to do when she "fills up the one." We make a game of it. They are not problems, the attitude is not a chore or drills but see if she can figure it out and how fast. So we do one refresher addition "problem" and then play this game where we rename the pieces and figure how many ones are hiding in there.
This is the beginning of the longer video below so skip this and just watch that one if you aren't pressed for time, or if you just want the idea of it watch this:
In the longer vid we add AND subtract fractions and do some work with improper fractions...she is about a third of the way through fractions...next we multiply which is easy, and then divide...and ten go back and work on more addition and subtraction with bigger number where we need to borrow. For example 3 1/5 - 3/4...
People are now having the opposite problem used to be there isn't anything about Mortensen Math. Now it's there's so much I don't know where to begin or it's overwhelming. GOOD. Now your excuses have to change. Where to start? Where ever you like but get started. Watch a few vids a week, play, practice, repeat.
At that rate it will take you about half a year just to cover the vids that aren't password protected. Go faster if you like slower if you have little kids or SPED kids. Math is a limitless topic. My focus is K thru 12, primary and secondary mathematics depending on where you are from. If you work with Autistic kids or have one, Sarah's page is a good resource although there are huge gaps because we went through a period where I didn't film anything. The longer video here is also there. Soon I will have to break Sarah page up into various topics...
Here she is doing the whole hour lesson condensed into 17 minutes or so. In the beginning you will note that many symbols are missing when we multiply by one but she understands what they mean. The first review of this series Fractions Despite SPED is here.
It doesn't matter what the lesson is with the younger students, it can be aided by practicing addends. Playing with addends makes it all easier. Drilling with addends is not fun but building walls and filling trays and racing to fill trays with addends IS fun. Right now she is getting the hang of it but soon she will race me and may even beat me like Sarah does. Kids naturally like competition.
We did a lot of things in our hour one of them was finding out what pie means...
c/d = ∏ and yes ∏ = 3.14 but now we see what it means...
We played with fractions:
And at last we built some addends. No magic to it. Just solid conceptual understanding of the basics.
She is 10 so the emphasis will be using fractions to learn addition and multiplication...same with the algebra when we do algebra the emphasis is not so much on algebra as it is on multiplication, the algebra is just along for the ride as it were. If this sounds odd to you spend a little time digging around this blog and over at the house of math.
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.]
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.
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.
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. ⇒
This is a simple introduction to fractions tiles. Fractions concepts are great for teaching counting and multiplication to young students.
Most students hate fractions because after four years of learning math one way suddenly the rules change. You can't add
1/2 + 1/3 and get 2/5...some kids will put 1/5
showing an utter lack of understanding and confusion about the rules. But the rules haven't changed. They just didn't understand them in the first place or more likely were never even taught the rules properly to begin with.
If you go back to the 5 basic concepts, you will find under concept 2, we only count things that are the SAME. Also it's key to understand that numbers have two parts the what kind part and the how many part. Fractions are cool because they tell you the how many and what kind all in one place, whereas with whole numbers you need to understand place value.
Note how in this introduction we don't cram in adding fractions in the first lessons all we do is play with simple concepts. We see how many make up a one, and we count and we learn their names. Later we will learn about numerator and denominator and build on the concepts of "same" or equivalent fractions. Also we will use other base ten blocks to represent fractions and fractions concepts. One crucial concept is the idea that x/x = 1. Right now they are seeing 2/2 = 1 and 3/3 = 1 and so fourth on up to 9/9...let them discover that anything over itself is 1...except for our hero. Plus they will discover this concept from multiple angles. Right now it's counting (three of three is one), but later it will also be division, (three is contained in three one time).
But for now we just play a little and tell stories about fractions wearing disguises.
In this fractions intro I cover the same info but without video. Be sure to get the free fractions worksheet. It's free. Note with me "free" doesn't mean "give me your email address." It means free. If you want more, get a password if not I don't want to waste time with you and an email list.
It should be quite obvious you can use fractions to teach counting and addition and multiplication. These students are advanced so the lessons are easy and fast but if you had a student that hadn't even mastered counting to nine these same fractions tiles would help them learn that. Compare and contrast with the thinking that says they have to have mastered multiplication before they learn fractions which is still ridiculously prevalent in math instruction in the USA and elsewhere.
The fractions page at the house of math has been in disrepair for about a year now...but that is getting fixed. It is very near the top of the to do list now. Look for more updates and improvements to that page over the next 30 days as I cut videos and add lessons and hopefully some more pdf's. Right now there are some videos there and a list of terms but it will become much more cohesive shortly.
Next there will be a video where we add simple fractions and find out what 1/2 plus 1/3 is and more importantly WHY, and we won't just learn some silly rule about multiply this, this and this...and then add this and this...but keep this the same...stay tuned.
BTW if you want a set of fractions tiles like the ones you see here it's $105.00 shipped to your door and will be available on my site at Products and Passwords shortly.
There are plenty of games you can play that teach math. At Crewton Ramone's House of Math there are pages of them. The page called "how to teach addition" has a bunch of games for addition but there are games for multiplication and algebra and more on my site and here on this blog. I put fun first grade math activity in the title but it could just as easily be a fun preschool math activity or a fun kindergarten math activity.
This is a story Jerry Mortensen came up with for teaching addends below ten...the numbers are having a party. Addends* are quite important and help students with many other aspects of mathematics (like subtraction). They are a basic building block that so many systems skip completely.
With little kids you want to play math...not drill math, and you need to play it enough so that they attain mastery and have instant recall. 2 + 2 = 4 is instant for most kids but 4 + 3 can take a a little longer and then 7 + 5 takes longer than that and they may resort to fingers. Get them off their fingers...but you start on their fingers.
There are only 45 addends in all. They should be mastered but don't spend all your time just doing addends, play other math games, do multiplication, sing songs, do algebra, fractions, problem solving etc. WHILE you are mastering addends...and all of these topics can be used TO master addends...and multiplication. Math is a language: it all goes together.
This idea of segmenting it down into individual parts that never become a cohesive whole ISN'T working.
*Addends: two numbers added together that make up another number. 7 + 3 are addends of 10 for example.
You can end up doing square roots, or distance formula or Pythagorean Theorem...or in this case we ended playing with radicals. You could also start playing with completing the square or finding the difference of two squares...all of these concepts are centered around squares, although some math text books and therefore some math teachers seem to have forgotten this. Really it's about squares.
We have built square numbers before, but this time we ended up expressing numbers in terms of radicals.
We talked a little about why we call them radicals, used our imaginations to make a two into a square and played around with the ideas. I was under the mistaken impression that we had done this before but actually this was his first introduction to them, had I know that we might have used some clay to really conceptualize the fact that we were turning these numbers into squares. I have quite a bit of video and pages and posts devoted to this topic. This should be a clue as to its import.
The sad thing is that it is SO EASY and yet so many kids come to me frustrated and unable to do what their classes require...because they are confused with rules and process. Like factoring polynomials once they see how easy expressing numbers as a radical is they actually get mad. All we are doing is playing around with squares. After a few lessons like this when they see the way it is presented in school and it makes sense...the symbols and lessons are just short hand as it were, for making squares and applying them to mathematics.
The nice thing with this student is he will never know it's supposed to be hard...in fact a lot of times he makes it harder than it is because ever since he got bumped up to Honors Math he tends to over think things...and do whatever it is the hardest way possible.
The second part of this video takes it up a notch replete with some Jazz and blender sounds in the back ground. Eventually this will be on a password protected page...and I really should make a PDF or two...
This positive factoring of polynomials is easy and fun for all ages. At the house of math we also do negatives, higher powers and more. If you would like to see problems like this factored then you need a password and there is an abundance of material on the advanced algebra page.
We did problems like to to help work on integers, this nine year ld has little problem with basic operations, and is having fun with fractions already, we will be covering more on this because right now he understands fractions from the point of view of the rules instead of the concepts. In other words he knows how to invert and multiply but he doesn't know why, he knows how to add fractions but he doesn't understand that he is making them "same" so he can add them...and the concept of multiplying by one is lost. But that's another post, this one is about factoring polynomials and it's many and varied uses for teaching math concepts beyond "just" distributive theory.
With young students you use if for cross teaching addends, addition, and multiplication as well as or in addition to factoring and how the distributive theory works. Once we get into negative factors we can use it to teach integers while we are learning about the distributive theory of multiplication.
This was just the warm up, we got into factoring the problems above and more. You can find them on the advanced algebra page, scroll down near the bottom. You will also find hours of other fun algebra there...but as you will see you need a password.
Here is a little article I'm hoping to get published in a local circular called Mauimama aimed at parents with very young children.
There was a time in the not to distant past when educators and parents thought it better not to confuse young children by teaching them too many languages at once. This was the common wisdom. As it turns out this was completely false. The younger they are, the easier it is for them to learn a new language, pronounce the words correctly and even hear the subtle differences in intonation. In fact, there is a window of opportunity that can be missed if the language is introduced too late.
Math is a language. The longer you wait to introduce math concepts the greater the chances of the child having difficulty with math are. Conversely the earlier you introduce math concepts, the easier math will be as they get older. This may seem obvious to some but the great problem lies in the fact that for the bulk of Americans (including teachers) math was not a positive experience. The thought of inflicting math pain and suffering on their toddler is unbearable. They imagine the poor child suffering through lessons and being exposed to formulas they have to memorize. They want to stave that off as long as possible so that their child can enjoy their early childhood unspoiled by math. Or as with some systems (particularly Asians), the child is taught to write early and then they do endless drills that literally burn mathematical nuero-pathways into their brain that will never be forgotten.
There is a better way. What do children like to do most? PLAY. How about you play math? "Preposterous!" you say. Math is anything but fun. The way you were taught math was probably anything but fun. This is true. There are ways that are quite powerful using manipulatives and blocks that with just a little direction from the parents can instill math concepts in tots without them even knowing they are learning math. They are ways to teach math through play that although the child may know they are doing math it's still fun. Imagine having your kids ask if they can play math. It happens. Try searching Crewton Ramome Math Enrichment.
With little kids up to about seven or eight you can just use your hands and show all the addends for numbers up to 10. Start with one hand, hold up 5 fingers and then grab two. 3 plus what makes 5? 3 + x = 5, 5 + x = 10 etc. How many is in my hand? Same principal but have raisins or something put 4 in one hand 3 in the other close the hand with three and say I have seven how many in this hand?...if they get it right they get to eat the three raisins, and you can say 7 minus 3 is 4. If you have big wooden blocks there should be a block that is equal to two smaller blocks and maybe even 4 smaller blocks, Have them show you "half." Then "a quarter" or one fourth show them two fourths is the same as a half. Keep it simple and fun. Don't make it a lesson, make it a game, or just point things out while playing with blocks.
There are now many pages and hours of FREE videos that show direct proof that math can be fun. Little kids actually like algebra, it's fun! They don't need to write symbols to learn math concepts. For little girls an early positive math experience is especially crucial. What does it do for a child's self esteem to be considered smart at math? Have fun. Play math. Learn how.
