Multisensory Math Double-digit Multiplication Using Base 10 Blocks

Using base 10 blocks for a multisensory math experience is crucial to understanding. Using manipulatives to teach multiplication should be both easy and fun for student and teacher. Some children get "a little big for their britches" as my grandmother used to say.  They want to prove that they're a big girl or a big boy by not playing with blocks, because Base 10 Blocks are for little kids...In fact quite a few high school teachers believe the same fallacy.

However, it's finally becoming recognized that adding the tactile and visual components the mathematics makes it much easier to understand. I have PDFs at Crewton Ramone's House Of Math that you can download that say the same, from prestigious schools like Stanford and Cornell.  It's very simple. Maria Montessori figured it out decades ago. Manipulatives make math easier to understand, because it allows for all the senses (Learning Modalities) to get involved.

I have these. I can see now why they are inferior.

Visual auditory and kinesthetic learners polite benefit from using Base 10 Blocks. On this blog and website I show you how to use your base 10 blocks to best effect.  Any-base 10 blocks will work, but some are better than others.  I got this picture and note from a person that just recently purchased a password.

The reason people are so enthusiastic about my website, Is that I don't just give you boring theory, you get actual lessons with actual students, non-rehearsed in real-time.

They still work, it's just that it's going to take a lot longer to build simple problems if all you have is units, rods and flats.

The primary reason these aren't used more or more widely adopted in public schools is it takes too long to build problems...& using base 10 blocks becomes tedious when you have to get units or tens out one by one.

Further, most of them use these only for Addition Subtraction & Place Value & have no idea how to use them to teach algebra, precalculus or calculus Concepts.

All we are doing is counting quickly and accurately, counting quickly without being accurate is no good and counting accurately but taking forever is also no good.  Multiplication is the absolute milestone for counting quickly. At the house of math, We don't just teach the multiplication tables out to 9 x 9,  or even 12 x 12, you want your students to have an easy math life? Help them memorized there multiplication tables out to 20 x 20.

The preferred methodology which is an absolute failure currently in public schools is using worksheets and flashcards ad nauseam. How about we play and have fun instead? Multiplication tables will be memorized easily and quickly By building, playing and singing songs.

All I am showing you are better algorithms. which make Multiplication fast and easy and therefore fun.  Rather than telling you I'm showing you.

Count the big ones first.

The entire video along with "a lot" of other content, is available with a password.  Those that have joined and paid for the superduper supersecret math group already have access on Facebook.  This is not the same as the regular Facebook page.  This lesson will be found on the Sample Lessons Page. & on the password-protected Multiplication Page.  Scroll down, under the green arrow you will see a link that simply says, "more two digit cross multiplication" right above "Playing with Macaroni."

There's a difference between theory and practice. Here is a little bit of theory. on my website you will see theory in practice. The trainings were for August 4 and 11th...If you want to see the long version of the second video Consider a password, or hit my for a buck or two & I'll let you into the Facebook Page.




Information on passwords can be found by clicking here.

On my website, I explain the importance of starting the concrete blocks, moving to pictures, and then finally to symbols.  I also explain that this is the ideal, but practicality may dictate otherwise. You can see that I start in the concrete (Manipulatives) & then have the symbols right alongside the Base 10 Blocks...Soon I am only drawing pictures and she is building them...Above you can see her doing  15×13. This is for her to get the idea or concept of it. You don't want to build every problem. Why would you want to build 59 × 37? Drawing it is fast and easy, and easier than that is just using symbols which is the goal.  If you catch them early enough they'll be able to do it in their heads, which answers the age old question, "What if they don't have the blocks?"

Please take a moment to follow some of the links on this page. Sharing this and liking this post helps out. You might consider donating a dollar a month to https://www.patreon.com/CrewtonRamone

People have been telling me to do this for years now. And I agree patreon makes it much easier to donate your time.  And if you were so inclined please leave a comment below. However, if you want to contact me, use the information on the contact tab, because I might not see your Facebook or other comment for months.

Check out the house of math.

More Compund Lessons With Base Ten Blocks

Part of what makes this method so effective is the idea of compound lessons. Why learn "one thing at a time"? One thing at a time is great when introducing concepts...but once concepts are understood it's more fun to practice more than one thing at a time, which is why I emphasize compound lessons.  And as you can see using base ten blocks to do it makes math fun.

A six year old factors x² + 11x + 30 all by himself and celebrates with his magical math microphone.

People ask me what they should get. Get a combo kit. A set of Multi-Tens and a password or both passwords...and you are good to go. Seriously.  That's it.

In this hour we practiced mostly addition and multiplication but we did activities that were fun to practice them rather than doing worksheets over and over again. Using worksheets to memorize multiplication facts becomes counter productive at some point.

Just building addends over and over again would make math anything but fun. So even with this activity which by itself many kids find fun, we spice it up by racing your brother or mom or who ever happens to be around.  Then we build some pyramids. All kids can benefit from building pyramids, the benefits are manifold. You get fine motor skills, addends which naturally include addition and subtraction skills, and the all important repetition which puts the facts in the memory for instant recall later... 

Here the older boy is feeding his mother and brother combinations for their pyramids. and supervises the construction. They are building 11's, later we could build and find patterns with 11's.

Pretty soon he gets in on the base ten block building action. And his little brother hands over some combinations...sometimes we build all 45 addends at one sitting but today we just did all the ones from 8 to 10 and then 11's and 12's. How many math facts is that?

Children are always quite pleased when they complete one of these...or several of these. Sometimes we build towns or cities or temple complexes or moon bases (or whatever is in their imagination), made entirely out of pyramids built using base ten blocks, but today we played algebra which will give us addends and multiplication too. Started out with problems like x² + 7x +12 and worked our way up. We started there because he already has some experience factoring polynomials and I wanted to start easy...then we went on to x² + 8x + 12, and x² + 8x + 15,  x² + 8x +16...Went thru several with 9x then on to 10x,  those polynomials have lots of combinations.

x² + 9x + 8  you get addends for 9, 1 and 8, and 1 x 8 = 8.
x² + 9x + 14 you get addends for 9, 2 and 7, and 2 x 7 = 14.
x² + 9x + 18 you get addends for 9, 3 and 6, and 3 x 6 = 18.
x² + 9x + 20 you get addends for 9,  4 and 5, and 4 x 5 = 20.   

 

You don't have to do every single one in order...mix it up and have fun.  I did a couple with 10x like x² + 10x + 16 and then x² + 10x + 24...didn't do x² + 10x + 25...which is a good place to start if you want to go down the square numbers and square roots path which are made plain and EASY with base ten blocks.  I had a mom tell me they completed the square with 24 once. I said go back and take a look at that...24 will complete a rectangle but certainly doesn't complete a square. 25 would complete a square...and completing the square is quite a useful skill to have later on when you are graphing polynomials and want to easily convert to vertex form.

Playing with squares and radicals are also fun math activities where you can compound the lessons and learn algebra, addends, multiplication, square roots and more. You decide the emphasis depending on the student. For some older students who are supposedly past addition and multiplication because of their age you can use these techniques for remedial math without them even knowing it.

Instead I gave him x² + 10x + 24 which he got pretty easily but then I gave him x² + 11x + 24, which is a challenge at this age when they are still learning their times tables.  You can see he figured out he needed 8 and 3 to make it work.

Then I gave him a challenge.  x² + 11x + 30...the dilemma after he figured out it was going to be (x+5)(x+6) was finding enough fives or sixes....they were being used in the pyramid...and he found that he could count by 5's but not by sixes as easily...remember this boy is 6 years old, he hasn't mastered his 6 times tables yet but he will....and there won't be tears or frustration. It will be part of fun memories spent playing with his mom instead of being angry at his teacher because of yet another worksheet.

After a little fooling around he decided to make 30 with 6's...which meant he was going to have to bust up his pyramid.

 

Completing the corner was important to him, later you will find students especially older students who know their times tables skip putting the units in because they already know 5x6...and that 5x6 is the same as 6x5...when they are younger this is still a fun discovery.

Challenge completed! It's time for some celebration which is where we came in. Also some high fives with mom never hurt nothin'.

This lesson took place way back in the beginning of October. Just got around to finishing it here.  In this hour we basically practiced math facts in a very disorderly fashion...we didn't just do a bunch of addition or subtraction for an hour. We did both AND we did multiplication and some division AND we factored polynomials but the algebra was just along for the ride...as you can see it wasn't scary or hard and I used it to teach concepts and facts...most teen-agers I know FAIL algebra right at this point because they don't understand the distributive theory and never saw a polynomial until they were 12 or 13 years old...

Positive memories and positive associations with math are so important i don't have words. Wouldn't you rather have your child's or student's early childhood math experience be like this instead of rife with tears and frustration? They won't all be diamonds but more often than not you will find YOU the parent or teacher can make math fun and teach a whole lot of math all at once in compound lessons like this.

Want to get the materials you see in this blog post? GO HERE.

Want a FREE PDF of the polynomials that cover the 45 addends and the multiplication facts that go with them?  Click here: POLYNOMIAL PDF

Dboyz Playing Multiplication Minus Manipulatives.

Here are a couple of vids and links to more on multiplication, and tips on how to make it painless and maybe even fun. Spending a year doing worksheets over and over again is SO LAST CENTURY.



The idea is to mix it up, let fractions teach multiplication, let algebra teach multiplication, as well as story problems...and as in these to vids even when you are doing multiplication keep the drill work to a minimum play with blocks, make squares and rectangles. You can hear them say it's fun when I do the writing because they just have to say the answer. At this age writing is work...too many kids get turned off right here because you make it work. Multiplication makes math easy because it makes counting FAST. So right when they should be getting to the point where the math gets easier and easier because they can count fast, it's turned into work and no fun and boring memorization instead of a gateway to being able to do more complex and bigger problems. Remember math isn't just computation. Computation is how we DO math...but it's not the math.

Base ten blcoks and manipulatives can help make math fun if you use them correctly and you have the right kind of blocks. It's all about SPEED. Counting out lots of cubes or pieces takes too long.

Here we are practicing multi-digit multiplication. Unspoken is a lesson on place value and the names of numbers. Hear the "OH!" from the younger boy?



"They give it to you hard in school."

This way is "Easier than blinking."

The idea is to make it fun and if this is your first time to the blog these two have spent HOURS AND HOURS with blocks before we go here. Here is a page showing them learning some multiplication using base ten blocks.

Notice I do all the writing even though the older boy wants to do some...if we weren't on vid I might have let him do some but it slows things down when I'm trying to make a vid. and youtubers have no attention span. Writing on the whiteboard is fun. Writing in a workbook is not as much fun. You can see I also draw pictures and do a fast lesson on division with it.


When it's bigger it's just more multiplication tables. "Doesn't matter it's easy.

This is a long vid:



YOU write for them and it goes fast and easy. You can have them practice writing but I want them to practice math facts NOT making symbols. Writing slows everything down at this age and makes the books NO fun. Like I have said before be careful with worksheets. They usually take the fun out of math. This is also a great way to spend "quality time" with your kids...

Myth is because they can't write they can't do math...false. That's like saying because they can't write they can't speak English.

When you get right down to it it all we are doing is counting. Adding and multiplication is just counting quickly.

You also see multiplication and division go together...

I also give them exposure to the cubes. They have seen the square numbers before and it's good to now 1728 is a cube and so is 343 and so on...later they will recognize square numbers and cubes when they see them because they have been exposed to them.

I can't stress enough before you do what I'm doing in those vids you play with blocks and draw pictures! These boys have played with blocks for YEARS. Once they do they won't need blocks or symbols either. There are plenty of posts where they do math "in their heads."

Yet More Manipulative Multiplication.

Make learning multiplication fun and easy playing with base ten blocks.

How to get multiplication mastered. You will have practice. There is no way around it. But you can make this practice fun. And you can make it easier by using some basic memory tools. The concept of a peg. And working in a more natural progression that complements the knowledge as it is acquired instead of just a jumble of facts in ordinal order.

Screencast with boys


Starting with Square Numbers and Pairs a lot of the multiplication can be understood. Then it is easy to add another for three's and of course 10's and 5's are easy so then it's easy to add one more or one less. For example fours can be thought of as one less than what ever number you were counting by fives...is of course four so 5 x 6 is thirty and one less six is 30 - 6 = 4 x 6 which is 24. Etc. This needs to be re-cut because the fan messed with the microphone but I STILL haven't had time.

Multiplication


You can use this same thinking with 9's and you can go up AND down with the square numbers...6 x 6 is 36 6 x 5 is 30 one less six and 6 x 7 is 36 + 6 which is 42 and the way you get there easily is with wanna be a ten, six needs 4 to be ten so it takes the 4 out of the six and we get another ten with two left over for 42...4 tens and two. Here is a screencast where I use addends to make multiplication easy for an Autistic student. If it works for her it will probably work for you.  Multiplication by nine is EASY btw. So easy FIRST graders can do it. Click that link and watch the second vid. More explanation:

Using squares as a peg


Multiplication is THE milestone in mathematics and should be taught early and mastered so that all the rest of the math becomes easy...

There are books and worksheets that can help but more than anything you want to PLAY and have fun not beat them to death with math facts that make them hate math and turn them off at an early age. Play with blocks, sing songs do a little each day starting when they are very young and by the time they are 6 or seven most of it will be out of the way. Waiting until 4th grade is INSANITY.

Here is a web page of the books Mortensen uses. The facts mastery books are simply more practice and to be used to reinforce the PLAY you do, which should amount to much more time spent than time you spend on the books.

Also do some web searches for "Crewton Ramone Multiplication"...there are tons of pages and videos on this extremely important concept.  And of course here is the Multiplication page at the House Of Math.

I strongly recommend you follow a lot of the links on this page. I know it's a lot but I can't stress how important multiplication is for making "the rest" of math easy and understandable because it allows you to see patterns and count very quickly. Then search "Crewton Ramone Multiplication" and see the plethora of pages and vids I've made.

Playing With Nines Again

Nines seem to pose a bit of a problem for a lot of students but actually it's one of the easiest times tables because there are so many "tricks" you can use to count and multiply by nines.



Here is another video showing yet another way to do it...there are more ways. Here is counting by nines with younger students.

There is a way to use your fingers too. I have to make a short vid on that one too...meantime here is a short post on a simple way to count rapidly by nines.

11 Year Old Math Enrichment

Here is an 11 year old who is just getting started at the house of math. His primary assignment is to work on multiplication.

While he is doing that, I expose him to various basic math concepts. He has played in algebra and fractions, and he is seeing that multiplication helps because it allows you count quickly. This gives some motivation to work on his multiplication. I specifically tell him (and his parents) not to just drill on multiplication tables but to play games, listen to music, and generally mix it up so it doesn't become tedious and boring.

We also work on addends...addition and multiplication are just ways of counting quickly. We need to be able to count quickly in order to math but math IS NOT computation in and of itself.



In just three lessons he has already come a long way.



The third lesson is a lesson on fractions if you'd like to see it you need a password and you can find it here (currently at the bottom of the page) called Fractions with Koa. My fractions page needs work, but there is a lot of stuff there and I have a few fractions worksheets for beginners up too. You can download the pdfs and see more vids with a password.

Find us on Facebook. And you can find me on twitter too...

Addends, Pythagoras and Math Fun

THIS IS A GREAT LESSON

The 36 minute vid requires a password and for 3 bucks (or 12 bucks for a year pass) it's worth it, if I do say so myself just for this vid alone. I just watched it again. It should really bring home certain points in the method and HOW you use blocks to reinforce the concepts. And that same password gets you onto pages with lots of worksheet PDF's and HOURS AND HOURS more video so you basically have no excuse for NOT using your manipulatives to teach math. All kinds of topics are covered and more all the time...

Here is a short clip from a tutoring session where we took it easy on a Friday afternoon and played...but it was serious play where we learned addends fooled with a triangle, learned lots of math concepts and worked toward mastery...of multiplication and addends using addends to count count by 6's and 7's well past 6x12 and 7x12.. All 45 addends and multiplication tables need to be mastered for instant recall...this will make all the other mathematics easier...and fun. In order to do that you need to make many, many impressions on the mind to build the nuero-pathway to that information. You'll see we go over 7+4 many times in this video...next time he comes back 7+4 be easier to recall and with a few more impressions it will be instant...like 2+2...all 45 need to be mastered.

This is a short segment of a lesson that's 36 minutes long at the house of math! It is a GREAT lesson if I do say so myself...you will enjoy it. Teachers will learn more about the lessons, students will get practice with understanding square root and what it means, we build one triangle, use a protractor, but mostly addends and their many and varied uses for making math EASY.

Check out the sample lessons at the house of math!

OR

You can burn it in there the old fashioned way, the way they do it at some learning centers with math worksheets and timed drills where the facts are repeated over and over again. This is effective BUT you may lose conceptual understanding and it compartmentalizes the information to the point where some students may have a hard time understanding how it all fits together, further you risk burning students out and creating a negative association with math...and just surveying the state of mathematics in this country how's that working out so far?

As you will see at the end of the full length video it's simple to tie it all together...and it's well past time for a different and fun approach.



Here is a little more from the lesson which actually happened before we shot the promo above...



If you want to see the full lesson, (you need a password). One of the things we did was count by 7's, and 6's well past 12 times, and I showed him how we could use addends to do it, we also fooled with a Pythagorean Triple and busted out a protractor to measure some angles...

Here is a two page test he did earlier in the week. Go here for a screencast covering these two pages. The screencast is titled Algebra Test. In the screencast they aren't sideways...

It amuses me no end that teachers and parents cannot understand how playing with blocks can lead to understanding mathematical concepts on such a profound level that 3rd degree polynomials eventually present "no problem." I am doing my best to remove the mystery and lay it as bare as possible...mostly for free. This system works, it's not an experiment it WORKS. It will make crappy math teachers into good math teachers and good math teachers into GREAT math teachers...it allows you to let your students see what the symbols mean. Therefore you can manipulate them...


http://www.crewtonramoneshouseofmath.com/


http://www.facebook.com/Crewton.Ramone

There are now hours of lessons, sample lessons pdfs for down load available with that same password. If you get materials through me you get a year pass to my sites if you already have materials or if you just want to see more, a start is 3 bucks, this gets you 60 days worth of time, for 12 bucks you get a year pass. You may need that much time just to get through the host of information available...and there's more going up every week.



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Multiplication Math Town

Playing and having fun does several things. One of them is giving the child a positive feeling around numbers and math. I have more than a few students who fear math, or hate it. They come to me and have fun and I do my best to break that pattern but then they go back to school and the old pattern runs them over.  Just had a student tell me that she panicked when she took a recent test even though she knew everything on it and had even done some of the problems before...more than once.


"I don't know it was weird, I knew it all and I still froze up and got scared again."  These patterns are powerful and hard to break. Now imagine how much worse it is to NOT know everything and have those feelings...the point is if they feel good about math the learning comes easier. Math should be fun. When it's fun taking a test is just showing off.

Feynman said, "Math is a language plus reasoning." That reasoning leads to critical thinking. 

 So for about half of the lesson we built tens. We did subtraction and then although she always asks for it, we did just about no algebra and she didn't write a single symbol. We worked on counting and then we worked on counting fast which we call multiplication.

 As she built each tower she had to count it. Sometimes she just followed my lead other times she counted on her own...

 The town starts shaping up and she tells stories about each building and what happens there as we go.

 As we play the town gets built and rebuilt and changes...every time we knocked something down on purpose or by accident we counted it all over again...with lots of laughter.

 Just keep playing and adding stuff and pretty soon it starts to look pretty cool.

 Fine motor skills are further refined, counting and playing go together. We are doing multiplication ON a table but we aren't doing multiplication tables.  I was asked about math flash cards or multiplication flash cards and I said, "yes, they are great but not yet!"  When they have their facts close to mastered, they are familiar with for example 2's and 3's, and when you ask them what's 3 x 5 and it's almost on the tip of their tongues THEN flash cards. Using them as a a tool to teach math especially with young ones can lead to some very big misconceptions like the symbols 3 x 3 turn into the symbol 9!! I saw this over and over again during my travels. The kids had no conception that it meant three 3s. Here it's visually obvious as Maria Montessori used to say.

EVERYTHING gets counted, the tens the hundreds, we add, we subtract but mostly we have fun. It's math enrichment, so it should be an enriching experience, not drudgery. Especially when they are little or pre-teen...

Here is a 10  min screencast covering the pics you see above and more:



Find us on Face Book and be sure to go to the house of math for more on other topics.

Playing With Nines

Here is a simple vid where two little boys learn about nines and multiplication using stuff they already know: addends and counting...

The older boy who BTW turns six today said upon review of the video..."I thought they were supposed to be hard."
"Really?"
"Yeah, but that was almost TOO easy."
"Yeah, too easy," chimes in the four year old...

Now it's just practice and more games and more play until the nines are part of their instant recall memory.

I was working with a 14 year old and discovered her multiplication was severely lacking and nines in particular were not there. This same lesson was used to similar effect: she found nines to be easy. I also showed her "one less make a ten."

In other words 3 x 9 is one less than three which is 2 and 3 needs seven to be ten so 27. 6 x 9 is one less than 6 which is 5 and six needs four to be ten so 54. OR you can just take 30 minus 3 or 60 minus 6...unless of course you suck at subtraction because they taught you to count backwards and you're 14 and still 100% dependent on fingers.



That day we also watched Multiplication Rock vids, which upon reflection is where he might have gotten the idea that nines were supposed to be hard...lol...and counted by threes and sixes which they are getting very good at, and talked a little about what numbers they heard that were the same on three (read 3, 6 and 9) multiplication tables.

Those two boys are never going to have the problems with math that I commonly make 40.00 an hour to "fix" with children who are 13 thru 18. Further by the time they are 7 or 8 there will be very little math that high school kids can do that they can't do.

90 Minute Addtion & Multiplication Engagement

Here is a short screencast covering a lesson with two young students of 7 and 8, we managed to spend the whole time just playing addition and multiplication, everything we did was addition and multiplication...even though we did fractions and division...it was still just addition and multiplication.

We practiced concepts we already knew and practiced writing...this is the only way to attain mastery: practice. So this class was pretty easy for them no stretches nothing new really although each time we do multiplication some of the facts SEEM new event though they've seen them before.

Here they have threes on their fingers, and had to work together to show me eight threes...we get practice with threes AND we get practice with addends because they have to decide who will will show what, three and five or four and four or whatever...

Here we took our threes and laid them out and put them in groups of 9,  talked about 3x + 3 and x being 9 in this case, also talked about  9 times 3 plus 3...and of course 10 threes all being 30.

Writing out what they see in symbol form and beginning to get what equivalent fractions mean, we also talk about common multiples.

Here we build rectangles and count the sides, we count them several ways the sides only for example 4x5 and 5x4 and then what if I have a rectangle where one side is 4 and the whole thing is twenty? What's the other side. What if te whole thing is 35 and one side is 7? What's the other side...? Etc...

This sheet shows the fractions and a pause to write out sixes in a matrix where they CLEARLY see the pattern with the symbols...

Once in a great while I give them a worksheet to take home, I am making webpages at Crewton Ramone's House of Math that have free math worksheets, starting with some first grade math worksheets and fraction worksheets...I also have a kindergarten math worksheet for them to practice writing their numbers and learning their addends, of course it can be used with older students too, it takes lots of practice to write neatly. Right now there's only a few worksheets but I remember when I only had a few videos too, last count I was over 70...

One day there will be that many and more printable math worksheets available there. Not all of them are free but you can get a password for a buck and tat lets you get into a page that has all of them PLUS you can get into the advanced algebra page and my password protected screencast channel that shows how to factor negative expressions...a buck goes a long way.  Here is the open channel, I made this as an alternative to my YouTube channel so teachers and students could watch my vids at school.


Anyhow here is the screencast covering the 90 minute session.




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More at CRHOM.com

Equivalent Fractions With The Wee Ones

Equivalent Fractions teaches multiplication. It all goes together so while they learn fractions concepts they learn multiplication or in this case they get to practice it...but when we get to the higher numbers they'll be learning the higher multiplication tables.

It's easy to see that 1/3rd and 6/18ths are the same. They can see it.

People often ask the ridiculous question: "Do they need to have the blocks with them to do math?"

The other night without blocks or even symbols just verbally I asked him what the factors of x² + 3x + 2 where and he looked up for a moment and said X plus one and X plus 2...then before naps today I asked him, "if the sides are x plus 2 and x plus 3 what's the whole thing?"

He thought out loud and said, "one x square, three and two...five x's and four...no I mean six...six would fit in there cuz it's three and two."

No blocks or symbols. It's the same when you teach any language to babies: they hear it FIRST before they ever see an ABC...just because they can't write symbols doesn't mean they can't learn math.

Further the average student can't multiply 15 x 17 in their heads...because they need to have the symbols and a pencil and something to write on. My students can see the answer is 255 or at worst can add 100, 120 and 35...

Here in this video they have seen this a couple of times before without symbols and for the first time they see the symbols for fractions today, and the symbols make sense and are easy to comprehend because they have heard them before.





You can see their progress with multiplication if you have been following this blog...they still can't tell you 4 x 5 off the top of their heads but give them a little time and they can figure it out...and the more we learn fractions the better they'll get.

Find us on FaceBook

Go to the House of Math. (Home Page.)

“Men must be taught as if you taught them not, And things unknown proposed as things forgot.” ~Alexander Pope

Multiplication Tables and More.

Here is a short screen cast covering a tutoring session with an Autistic student.



We did multiplication, subtraction and algebra...and it was all easy and fun.



The House of Math on FaceBook.

The House of Math

Learn a lot of algebra for a buck.

Multiplication Tables

Using Multiplication Tables should be the LAST way you use to teach multiplication. Along with the number line and math flash cards, it is a very effective way to turn kids OFF to math. Still, if used correctly they can all be FUN and teach a lot.

Take a look at the set of multiplication tables below.  Your students can discover a lot from making multiplication families. 3, 6, 9,  are all one family.  2, 4,  8,  are another family...and you can see 6 can be in both families and 7 is out there all by himself...

A student can study these and discover MANY patterns and relationships.

Allow your students to make discoveries about the patterns, and let them tell you what they find.

I cannot stress enough how important it is to start in the concrete with blocks move to drawings and spend time playing BEFORE we start on the multiplication tables. I met many students in may states who thought 3x3 turned into 9 and 3x5 turned into 15 etc. without any understanding whatsoever that 3x3 meant three threes, and 3x5 meant five threes...students who labor under these misconceptions are often taught with tables and flash cards from the get go.

The multiplication table can be used for drills and speed tests but it can also be used to discover patterns. Discovering patterns can be fun even exciting to young students.

Look at the pictures closely, and be sure to watch the screencast. Think about fun ways to present the tables to your students...change your thinking to at first I am going to put them in a position where they can discover patterns not memorize multiplication tables.

Make no mistake knowing the multiplication tables by heart is CRUCIALLY IMPORTANT, however in their zeal to get them to memorize multiplication facts some teachers and parents turn their student off to math FOREVER.

A fun math activity allows them to make their own tables. Make them discover the patterns for themselves. Start with the big red square.

Put a piece of paper on it and make a rubbing...

Very simple and fun activity for students is making their own tables.

Here I made a 10x10 but with a little work you can line up the block and make bigger matrices...

Start simple and then work your way up to more complex tables.

Just for fun I did the square numbers first...

You can also use the square to make smaller tables so you don't need graph paper. Here are the sixes for example...

Make another table and once your students are confident and have had lots of practice over weeks or even months...

You can make a table where the numbers are out of order and they have to know the facts...these are fun to use for racing.

The first column is a warm up then it gets more challenging for younger students...

Here it is filled in. You can also use random matrices like this to make codes by putting the alphabet into the matrix. In this case a=3 b=9 c=21 etc, for more fun you can make codes that include upper and lower case and some punctuation. The matrix below is not big enough for both cases...

You can make any size you want for whatever you want and tailor make you tables to whatever the students needs to work on.

Here is a advanced table for students to work on multiplication past 10, note that the numbers are in order so that patterns can be discovered. This also lowers the degree of difficulty. When they get more advanced you can mix it up like the one above...

Here is a screencast covering the above pictures.


Here is the Multiplication Tables page at the house of math, it contains a link to a page where you can down load and print tables even though it's easy to just make your own or have your students make their own and use it as a fun project.


The House of Math on FaceBook.

Learn to use your Base Ten Blocks at the house of math.