Homeschool Math, Games & Activities with Base Ten Blocks for Interger Fun.

Using base ten blocks to teach Homeschool Math is the topic of conversation for a lot of people who have chosen to homeschoool...asking namely, "how am I going to teach these kids math if I failed math...?" And of course your first instinct is to teach math the way you were taught, even though you know from personal experience that it might not be the most effective way to learn math...here is a method that works and has been PROVEN effective--and best of all it's fun...and as an added bonus no number line to start with, just a noisy game kids love.

Here is that simple game for teaching integers.


I was going to make this a much lengthier post, but let's just keep it short and simple. My subtraction manual,  Supremely Simple Subtraction is doing quite well, although I have now had several conversations where the gist of it is there is no way to describe how cool that book is...lol...still getting people who already have it to leave a simple comment is very difficult for a lot of reasons, but as you can see quite a few have done so now. Click that link get a FREE book...well, not entirely free you have to give me your email, but you won't have to worry about getting inundated with emails from me...in fact quite the opposite. There are people who have signed up on various email lists who have to this day not gotten a single email from me since. Even when they WANT an email to inform them of the new password or for notification of one of Mortco's extremely rare sales.

I haven't gotten around to making a list and getting an email program but I have hired an assistant, a Girl Tuesday if you will, and I think she will work wonders in getting things done and freeing up my time...so you may in fact get an email from me in March informing you of a special sale.  And if you miss it you miss it. People have I think at last given up waiting for another sale from Mortco at these prices.  And I warned people that prices were going up, but people are used to gimmicks so they thought prices would go up so we could mark it down and call it a sale...lol...no: prices have actually gone up.  Same with my passwords...there might be two sales this year on them and they are not going to happen again...a Birthday Sale for the elder boy when he turns TEN...he won't turn ten again so don't expect a sale like that again...although the younger says we will also have a sale when he turns ten but that years from now, so I wouldn't wait...


I like this video because you can watch them learn in real time. Play along don't just watch math is not a spectator sport. Also would it be as much fun if it was just me and one student? This is why I like groups. More is learned faster. I have used this game for years and I can tell lots of different stories about kids learning with the number line and getting confused and then this game clearing things up. Also the explanations in Supremely Simple Subtraction work wonders.

I have had cases where the older sibling was taught with a number line and the younger learned with blocks thru me and the younger sibling blew the older sibling out of the water when it came to test time on integers...eventually I will have ten Series C Manuals done, subtraction is book three in the series, book one will be "Groovy Games & Addicting Activities" of which what you see here is just one. Series A Games and Activities is completely free no email or other interaction required there, hard copy costs about $3.20 (plus shipping) from Mortco. Don't say I never gave you nothin'.

You can also use algebra and factoring polynomials to teach integers...but if you want to learn to do so, you'll need a password (then just go to advanced algebra on my website...or be good at digging around on this blog and the internet.  Here is a page regarding the teaching of addition and subtraction and more that you might find useful and may have had a hard time finding on your own.

Note the girls are at no disadvantage whatsoever, and you may note I make an effort to call on the girls more than the boys. The myth that girls can't do math must be busted and laid to rest along side the myth that woman can't learn to read, permanently.  That myth about women and reading was prevalent just a few hundred years ago in western culture.

You can also use cuisenaire rods to play this game, just mark one side with a pen and make that the negative side. No biggie.

A few testimonials:

"By the way, YOU ARE AWESOME! I actually clapped for you when you explained some concept soooo simply and clearly.It is fantastic!" ~K Ontario, Canada.We are excited for math today!!! ~amazed parents from all over the globe.First, I wanted to thank you for being out there and for introducing me to the Mortensen Method. I'm a new homeschooler who's been searching for Math under every nook and cranny of the globe. Worksheets I can make. Flashcards I can draw. Concepts and vision...now THAT'S something to pay for.
EDIT
Also, as a believer in the separation of church and state from an educational standpoint, I felt really at home at your House. Thank you for that, too.
EDITFinally, thank you, thank you, thank you for mentioning somewhere, somehow, in some side comment that I can no longer find in your fantastic maze of a world the work of Liping Ma. I immediately bought her Knowing & Teaching Elementary Mathematics and have been forever changed as a result. It made me rethink the way EVERY subject is taught, learned and subsequently taught again. I never would have even heard of her if it weren't for you. EDITI am extremely eager to start having my "oh, I'm just not good at math, never was" mind blown. ~PF USA

"I've paid a lot more for a lot less." ~amazed parents from all over the globe.

"Ps. Your parents teacher training is great!" ~EM, UK

"The training is crazy. No one is offering anything like it that I know of...and your price is crazy too." ~JC, CA.

"The amount of stuff you get for the money is crazy."~JJ, New Hampshire.

"Just got the Parent/ Teacher Password.CR wasn't lying when he said 1 page was worth the price. Get it for yourself to learn how to think math." ~KY, USA.

" I really like how you do math. My kids do too! We were having problems and you made math good and happier for us. I sincerely say Thank You from the bottom of my heart." ~CS, Ohio.

"So, I am absolutely flabbergasted by the stuff I am learning just hanging out in the House of Math like four to five hours (literally) per day! Before the little one gets up, I'm on. Nap time, I'm on. After bedtime, I'm on with toothpicks bracing my eyelids. Even before purchasing the passwords! It's like a crash course re-education, and I am infinitely grateful..."

Here is a collection of Testimonials.

Just Play Math!

Here is a video of a young student playing math. For us this is a pretty formal lesson. I need to get some video of the boys just playing because as I look over the vids I have, they are not exactly representative of play time. Problem is play is fun and spontaneous and getting the camera out changes that. Observing a thing effects a thing.



 I enjoy this vid because you can see him throwing me some attitude. He wanted to play Legos not make a math a vid. He was also sick... Note the ease with which we breeze through lessons from subtraction to negative numbers.

Listen for the word "no"; it is replaced by me with show me or what do you have etc. We always start in the concrete and we skipped from blocks to symbols without drawing pictures then we went onto multiplication with 7's...

And this inspired a story about the numbers being happy. 7's have to go all the way to 10 before they get happy, 5's get happy after just 2...most get happy after just 5...the "hard" ones don't get happy until 10...3's, 7's, and 9's...

Then when we count all the way to 105 with 7's we get momentarily confused...but we keep counting...the point is we are playing math and we go through the basic operations of subtraction, integers and multiplication in one "lesson."  This is the problem with traditional teaching of the mathematics to young children a lesson on math will be ONE lesson. No flow. Just a compartmentalized lesson on subtraction with borrowing and counting backwards, no movement to integers not shifting gears into multiplication...can you see the "subtraction" that goes on in multiplication when were counting 7's? Seven takes the three out of the next seven and and we get fourteen...etc.

Math. One language.

It has been noted that youtube constantly takes down the vids for multiplication rock. So go to youtube directly and search the vids...or better yet go buy the vids off my page.

Simple Symbols Lesson

The best way to start any lesson on Math Symbols is with a three period lesson. You may need to repeat it once or twice...it's important that they hear you read the symbols and that you add meaning as you go.

Here is a synopsis of about 30 minutes of a lesson on some math symbols. We had also done this several times before. This student is Autistic which doesn't mean can't learn, it means takes more time and impressions to get info into the part of the brain where it can be recalled. This one is often missed by students who have made the rule hard and fast in their heads two negatives equal a positive: -|-3| because they don't understand the concept of absolute value and fail to read the math symbols correctly.



When doing absolute value I often just talk about the block itself doesn't matter what side it's on a four block is "four" long. In her case though this explanation didn't sit as well because she wanted to be sure the block was on the positive side since all absolute values are positive. Other students seem to get the idea of "it's four from here to here" no matter which way you go. This also explains why the difference of two negative numbers is still positive.

Bright young students might inquire why it is that -22 - ^-28 = 6 where all the numbers are negative and we're even subtracting! The answer somehow ends up positive.

The difference can be explained in terms of direction on a number line,  but as far as I have seen number lines and direction help confuse things, not clarify them.  It's not about direction, it's about distance.  The amount of "space" between the numbers, delineated by numbers themselves.  Most kids don't ask. Might be wise not to bring it up especially with students who have poor self confidence in math.  For the inquisitive ones and older students it can quickly devolve into a discussion on philosophy.  How do you know the distance from here to here is four...? Keep it simple instead.

Explain what the math symbols mean and use blocks to bring the points home. Integers are no problem if presented properly.  Look for more lessons on integers here on this blog and at the house of math where Sarah has her own page. The way I see it if you can explain it to Autistic students or little kids in a way they can understand then adults and older students as well as "gifted" students should be duck soup. Most of the time this is true. Often you have to get through math anxiety and other problems first with the older students.

Bottom line keep it simple.

“If you can't explain it simply, you don't understand it well enough”. ~Albert Einstein

I have made 100's of dollars re-explaining integers and reading symbols to all manner of students and have almost universally heard that using blocks makes it easier. Of late I have run into a lot of students who just want something to memorize rather than wanting to understand...understanding concepts is better.

More Autistic Intergers Plus Algebra Too

This is a pretty good lesson for beginners on integers. I believe in introducing integers EARLY. The one thing missing in this lesson is the time consuming task of drawing the problems. This step should not be left out especially for the younger students.

Again you don't want to draw every single problem (or build every single problem with the blocks) but you don't want to skip drawing them either. This vid is a lesson AFTER lessons where we drew quite a few of them. I did not get vid of the preivious sessions where she drew them. On the internet that means it didn't happen...lol..but I assure you it did. DRAWING IS A MUST. It's not optional. Why? Because it works. It bridges the gap between the symbols and the blocks. For some students this gap is wider than others, so more drawing may need to be done.

The drawing and symbols can go together and they can be very simple. In fact the better understood the concepts are, the less complex the drawings need to be, so some kids may start off with complex drawing of whatever it is, in this case integers and you will encourage them to move to simpler drawing and finally symbols only.

Drawings of integers usually involve holes in the ground, not a number line. Or up in Washinton and Idaho and a few other places a log standing on end can be put in holes and then figure out how much is sticking out...make up stories that the kids can relate to in their own situations. In the city that might be telephone poles or whatever. You can also combine drawings and blocks on a white board quite easily...draw a hole 3 deep, and then put a nine block in it. Show the various ways we can write this. -3+9, 9-3, 9+(-3), -3-(-9), etc...



Got to The House Of Math and find Sarah's page, the tab says Sarah SL for the complete vid P1 and P2 and also P3 which is another 6 minutes on algebra with negative factors. These vids might create greater understanding for students and teachers who are NOT autistic or working with SPED students too.

Time To Get Negative.

2x² + 5x + 3, sure, but what about negative coefficients?

I am constantly asked how to show and factor or work with expressions like

x² - 25

or

x² - x - 6

and some people start with a presumption, "That's great but I bet you can't show negatives very well." Well enough to get this autistic kid to get it. Or "...that's great but what about trig?" What you have here is a uniform methodology for the visualization of mathematics...not just the positive part not just the rectangles. Eventually there will be the derivation of πr² up on the sample lessons page, that 1/2 hour alone will be worth the price of admission. There are quite a few vids that I am told are worth the three bcks all by themselves. I am also told by marketers that the "problem" is the price is so low that people think there's no values there. I mean really, what can you get for 3 bucks?

Hours and hours of instruction that's what. Plus PDFs. Did I mention the PDFs?

I raised it from $1, apparently $19.95 is the going rate. MONTHLY. When I start getting some editing and some other paint and polish I will be raising the rates, meantime take advantage of the ridiculously low prices, NOW. It won't be long, this blog is already 3 years old, if you look at the first posts there were barely even pictures...lol...seems like yesterday.

Anyhow, here is Philip getting ready to go negative. Note how he is less than enthusiastic, because he has had bad experiences with integers due to that thing called the number line. I have lots of great stories about children who were taught about integers with this methodology compared to the way they did in school. One where the younger brother started solving problems faster than his older sister who "had learned all about negative numbers in school" but the method she had been taught was confusing and laborious...after seeing what her brother had been taught by me she said what most people say upon learning math this way: "I wish I'd had the blocks when I was learning this..."

For example:

Seems it would make sense to use blocks to teach about squares and the difference of two squares, or square roots or factoring...but they also come in handy for trig, pre-calc, and some basic concepts in calculus which I may never get around to here because there's hardly demand for it...well not nearly as much as algebra. But once you SEE an example of a derivative many light bulbs will start going off. Anyhow, once we are comfortable with factoring positive expressions THEN it's time to get NEGATIVE:



I see so many people who want to do too much too fast. "Okay, since they got that lets do this..." Remember degree of difficulty. Also the other thing to remember is you don't want to use the blocks for every single problem. The point is exactly the opposite...where you don't need the blocks once you understand the symbols anymore than you need pictures in your novels...but they were REQUIRED when you were first learning to read.

When you get to the Sample Lessons Page just look for the tittle "Show me the negatives." There are plenty more example on the password protected screencasts page too...going all the way up to 3rd and 4th power algebra.

BTW: I'd appreciate if a couple of people who do have passwords would comment on their experience with the password protected pages. Is it worth the 3 bucks or 12 bucks or what? If not here than on the facebook page and I'll screenshot it an paste it here.



Via email:

Hi there

Just read your blog where you ask for feedback about the password protected pages.

I visited once or twice with the password below, and the pages are great! The videos/screencasts are especially helpful. My only problem is that here in Africa (Namibia), our bandwidth is not enough to watch the screencasts without constant buffering etc. Far better for me is to be able to download the videos to watch later (and I might add, watch again and again!)

I have downloaded all your You Tube videos which are so helpful. Is there not some way that you can make it possible for us to download those screencasts?

OR, if you had some kind of full blown E-book/video course with an entire curriculum (k-12) in it to download, I’d definitely buy it. (?)

Anyway, thanks again for all the stuff that you’ve posted in various places already. I really is great!

Regards
Carol

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Autistic Integers

Here is the result of several lessons with factoring and integers presented in various manners:

It looks easy, but it took a long way to get here. You can see part of the journey as well as lessons on factoring negative expressions which is part of what I used to teach her to master her integers here at the house of math.

Of course in order to see that page you'll need a password. Passwords are cheap.

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Some Math Lessons for the 5 and Under Crowd

A sample of a lesson with a 4 and 5 year old. You can see their progress with skip counting. Soon you will also be able to see their progress with Algebra...over all their understanding of math concepts increases weekly.

The point is not to just teach little kids little math with little numbers...play and have fun and all kinds of math concepts can be discovered.



Always tell them what they have and make them count it, if they give you a wrong answer. Remove the "no" from the lesson and remember they don't get it wrong they just get more information...

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