Make Math FUN

I think one of the most common questions I get is how do I make math fun? Well make math play and learning playFUL. Make a game of it. EVERYBODY like games. I have lots of posts about making math fun and interesting.

Here are a few:

Video tutoring making an addends house.
Note there a ton of screencasts for free and there is also a Password Protected Screencast page.

Here is another blog post about making math fun.

And another one where we play with monomials and play find the ones which makes it fun instead of scary. This child happens to be autistic but it doesn't matter and little kids like this game too.

Making a game of it is the beast way to make it fun...followed closely by incorporating it into everyday (math) activities. If you make it into a game all manner of things come into play, the students natural competitiveness will come out and everybody likes to get good at games so they can win at games. If you are smart you will make sure even the losers are winners...

You can teach some math with playing cards but you can also teach math by making up a game from whatever it is you just learned. Making it up together is the best way or having them come up with ideas like this video on polar coordinates where we brainstorm ideas for games (you have to skip to the end).

I once did a training in Utah where the homework over the week end was to come back with at leaste one math game...we had about 50 people in that training and we got well over 50 games and activities from Pre-school to "high school" algebra. If you are new here you might wonder why I have quotations around high school, the rest of you know it's because any little kid can do that algebra and they think it's FUN.

I have students on video begging me for algebra...because the way we do it IS FUN. It's like solving a puzzle. I guy who used to work for AMD figuring out why an AMD processor ran software differently than an Intel processor used those exact words...it's like solving a complex puzzle...and of course the way they solved it was with math. BTW he loved his job and was paid several hundred thousand dollars per year to do it. This is the attitude you have to instil in your students. That math is fun, and beautiful, and joyful...and when they think of math they are crying or conjuring up images of mental torture. I often make popcorn in my classes. The reason for this is manyfold.

First and foremost: I love popcorn. But so do most students and it gives them a positive association with math and me and my tutoring. Especially little kids. The smell of popcorn is associated with fun times...I am not above Pavlovian conditioning.

It doesn't have to be about smells and food although using M&M's or grapes or cookies or whatever snacks you like for addition and subtraction won't hurt anything. But making a game of the math itself is better yet...racing can also make a game of it when you separate kids into teams...I have even used this on video chat where one group is "live" with me and the other group is on the east coast...and they race to factor polynomials...we ended up going and extra half hour. Meantime the kids were literally squealing with excitement. You can create this same atmosphere in your classroom. You probably don't want to do it everyday but maybe once a week on Friday as a reward if they've been good.

Homeschoolers can get together once in a while and have family races where one group of kids gets together with one or more others. Use your imagination. Playing with the blocks makes math fun, but you can make math fun by making a game to ensure they attain mastery of whatever topic it is...often times the game they make will let you know how well they understand the related topic.

Here is a lesson you can use over and over again and make math fun while making the concepts understandable. Too many kids are confused by a whole year of multiplication and then a whole year of division and don't understand that they are indeed inverse functions. How you can separate the two is beyond me...

This is part of a long video (49 minutes it can be found here) and I edited down a little...the idea is you get a real time feel for what happens in a lesson. There's no magic to it you just play math and try and keep it fun. Part of having fun is removing the NO from the lesson. A lot of parents need to work on that...teachers too.




This is a compound lesson where we do multiplication, division, square roots, and word problems as well as area and addends, as well as integers watch as we move fluidly from one topic to the next...these boys are 5 and 7.

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“The only way to learn mathematics is to do mathematics.” ~Paul Halmos

"Almost all creativity involves purposeful play." ~Abraham Maslow American psychologist 1908-1970

"Whoever wants to understand much must play much." ~Gottfried Benn German physician 1886-1956

"Play gives children a chance to practice what they are learning." ~Fred Rogers American television personality 1928-2003

"People tend to forget that play is serious." ~David Hockney Contemporary British painter

"Do not…keep children to their studies by compulsion but by play." ~Plato Greek philosopher 427-347 BCE

"Necessity may be the mother of invention, but play is certainly the father." ~Roger von Oech Contemporary American creativity guru

Quick Lesson Inverse Functions

You need more than one example but this is a quick 3 and a half minute lesson on how to find the inverse of a function.



In this case what is the inverse of

y = -4x² + 2 ?

Due to my math experience I looked at the multiple choice answers and knew which one it had to be...however due to my carelessness when I tried to show him why I got the wrong answer because I left off a negative when I copied down the problem. We did the problem more than once and this vid shows the last time we did it.

Two principals here:

One: NEVER TRUST THE TEACHER.

Two: You aren't wrong you are just getting more information.

Too many parents (and some teachers) are afraid to work with their kids because they might get it wrong and be embarrassed or what have you. Just get to work and see if you can get the answers...sometimes it's good to get the answer first and then look at the problem. I have had more than one student say it's easy when you know the answer. That's true and then with the thought this is easy you can see how to solve the problem and you know where you are going.

Another thing with some multiple choice tests: you can see answers that reflect common mistakes or misunderstandings of concepts that would lead you to pick the wrong answer. Talk about them. Talk about why they would put that answer as a choice on the test. This often helps deepen understanding.

Now in order to learn how to do these it requires more than on 3 and a half minute video. They can get the rule "just switch the variables and solve" but they will forget the rule in just a few weeks...

You need at leaste three examples of which this would be one of the last ones. They should have also spent some time understanding the basic concepts of Hero Zero and No Fun Get Back To One. (HZ & NFGBT1)

Here is the first example I showed this particular student:

y = x² therefore the inverse would be y = ± √x

First we "swap" the variables: x = y² which is the same as y² = x and solve (NFGBT1) by "square rooting" both sides: y = ± √x

Then you just make them slightly more complex: y = x² + 1 etc...

Then you get two thumbs up because they "get it."


"Example isn't another way to teach, it is the only way to teach." ~AE

More at the house of math.

Math Concepts, Conceptualization vrs Memorization

Here is a short vid showing the wee ones doing a little math where you don't have to be there you can set it up walk away and come back and check it...then do more, walk away and check it. Math enrichment for them also means understanding what the powerful machines we have built are doing not just pushing buttons...I would be willing to bet that this six year old understands square root and what it means better than a lot of high school kids and even some college kids...

At this age just using a marker is fun in and of itself...the whole thing was a fun activity...took up about an hour of their day, it could have been shorter or longer depending how much fun they were having and how long their interest was held.

What you see here is a short part of it, but enough to give you the idea. I set up trays of blocks for them to count three different times...some days just one set is enough others times more or less...depending on their mood. Make it fun, not work...stress the concepts not the facts, mathematics is NOT computation. Remove the no from the lesson. If they give an incorrect response make them count again; tell them what they DO have not what they don't have, change the thinking from "wrong" to "acquiring more information."

Remember, it takes 18 exposures to get information back out again. We know that with one exposure the information is indeed stored but retrieval is hard, but after 18 exposures we can get more information from short term to mid term memory, and with more exposures we can move it into the long term memory and with yet more exposures we can make that information available for instant recall. Begin exposing your students to mathematical concepts EARLY. You will need to keep exposing them year after year for them to attain mastery and instant recall of things like addition and subtraction facts, multiplication, division and so fourth, but again you haven't taught them mathematics per se, just facts and computation skills which are how we do mathematics.

"Mathematics is a language plus reasoning." ~Richard Feynman

"Reality is consciousness, consciousness is expressed with language. Mathematics expresses reality numerically." ~me, standing on the shoulders of Terrence McKenna and John Paulos. Nanos gigantium humeris insidentes.

They have played with squares and rectangles before counting and building, here we begin introducing some symbols, later we will introduce more concepts and symbols so that we can write simple sentences like (3)(6)=18, 18÷6=3, 3x=18 and the symbols will make sense.

Same with building addends: 6+4=10, 6+x=10 will be simple and obvious and when explanations involving math terms like "additive inverse" are encountered they will also be understood even though they are cumbersome and oblique to most math students under the age of 12. I remember having 4 boys in 6th grade all bewildered, upset and offended by a set of problems like this:

5 + x = 14........x - 7 = 4

3x=24.............6x=24

3x + 5 = 20.......2x - 8 = 12

3x + 3 = 2x + 7 etc

It took about two sessions to clear all that up and get into negative expressions and I earned a couple hundred bucks in the process. (4 x $25 x 2) and people cannot understand why I find it all so ridiculous now...yet the parents and teachers both failed to explain it in a way they could grasp easily...and in the case of the parents some didn't even try, as soon as they see algebra they throw up their hands and say things like "well, I was never good at math so..." or "I get it but I can't explain it..." or "I don't remember any of that stuff even though I passed calculus with a B"....and are shocked when I tell them I failed calculus. FAILED IT. Not even close. Good thing I did. I can feel their pain and understand why it is they don't get it because I have the benefit of having been taught both ways. One way works and the other...uh, not so much.



These same kids play with 3rd power algebra, fractions, percentages and more. The ability to do all of that consists of countng to 9, being able to tell if something is same or different or not and being able to identify a rectangle.

More sample math lessons, tools and information are available at the house of math.

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