

Thursday, December 30, 2010

More Fractions Theory In Practice

Here is a short screencast where I cover some fractions concepts with an Autistic student.

You may want to check out this fractions intro post first if you are unfamiliar with manipulatives or new to this blog.

She was suffering under the influence of TOO MUCH CHOCOLATE so was quite flighty and had a hard time concentrating. It was interesting to watch. But once we got going she settled down and she was fine.

SO we started off playing with the concept of what one is. With my imagination I can name the blocks whatever I if the four block is now a one the unit block is now 1/4.

 Same with the five block, if it's now one then the unit block is 1/5. The fraction's denominator tells us what one is.
 We worked out our way up to this problem where she had to reduce the answer even more. It took some thinking and work on her part. Here the picture is labeled for the people reading this blog, the math terms come with the territory and she will know what they mean because we've used them many times rather than learn a definition or an axiom.
 Then we started doing these kinds of problems. Took about 5 minutes to develop the concept and put the concept into practice...
Anyhow, here is a screencast covering a couple of basic fractions concepts:

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Crewton Ramone is hosting a TEN HOUR LIVE Math seminar on MAUI!


Will try again next month or the month after.

January 21st and 22nd, 2011 Friday 6p-10p & Sat 8a-4p

Maui Beach Hotel. Kahului, Maui.

Cost 100.00 single, 180.00 for couples advance, before Jan 16th,
120.00 single, 200.00 for couples after Jan 16th
Room specials available starting at 99.00 for off island participants...

Works out to around 10 to 12 dollars an hour and you will find it's more than worth it!

Friday will probably wrap up before Ten but depending on the level of enthusiasm and attendance, 4 hours tends to FLY by...

Saturday, we should end well before 4pm but I booked the room late just in case and so that we don't have to rush out.

Take an hour for lunch plus breaks and we will have about 11 hours to get our ten hour training done. Those 10 hours are PACKED believe me. It's faced paced hands on fun.

This will be a standard "10 hour training" where we cover basic operations (addition subtraction, multiplication and division) as applied to whole numbers, integers, fractions, and algebra. In addition there will be a short session on percents and algebraic problem solving. Throw in a few story problems and TEN HOURS whizzes by.

People are always amazed at the time. We used to have a program where we did 10 hours, then 20 hours, then 30 hours, then 40 hours at at the end of each session people were amazed at how fast time seemed to go.

Pre-requisite for the 10 hour training was/is the ability to count to 9, identify shapes particularly squares and rectangles and be able to tell whether objects are same or different. In Utah where the children where especially well behaved we had some very young children come to the of them got on the news there doing 4th power algebra. I was the one who taught his parents to teach him...I wish I had that footage: it's great.

Once you took the ten hour you could go to the 20 hour and so parent commented that even though the trainings got longer and longer it seemed like they got shorter and shorter...because learning is fun and times flies when you are having fun.

Who should come?

If you are a novice, have a set of blocks, never had a set of blocks, are homeschooling, are a teacher and are wondering how to use the manipulatives left on a shelf in your room, have read about using manipulatives and would like to know more, or would just like to become more effective at teaching math in a conceptual way this seminar is for you. In short anybody who teaches math to anybody whether it's parents or if there is a difference between the two. Tutors are especially welcome. So are well behaved children over the age of 11.

The way we teach math putting a grade level on the information is difficult, but this is an introductory course and will cover math through the high school level, although you will quickly see how and why little kids can do algebra, fractions complex story problems and more.

This is a radical departure from the way you (and I initially) were taught math. You will "see and do" not just watch. Math becomes child's play, even "advanced math."

What to bring:
If you have blocks bring them!!! And paper and pencil too!!! You can bring your own lunch and snacks, or go out for lunch or for 4.99 plus tax a box lunch will be provided by the Hotel. Bring healthy snacks. There will be ice water provided.

I need help putting this on and promoting it. I am willing to pay commissions to those who bring paid sign ups in the form of CASH or a reduction in your attendance fee...$20.00 for each paid sign up, $35.00 for each couple.

If you bring four you come for 20.00, bring three couples and you come FREE plus you get lunch. If you can video it you can come FREE. You need your own camera...

I need a videographer to document the whole thing and hopefully I can make a sale-able product out of it.

Those in attendance will get a copy FREE. I also plan on doing a much bigger seminar later in the year which will cost more than 10 times as much but will only be 2.5 times as long which will be marketed world wide via the internet...most will come from the USA, but you never know who will show up to these things. Those who attend this event will be able to come to that event for a substantial discount.

Those attending will also get FREE passwords and other "Bonus" materials as they become available over the coming year.

What will be covered:

Friday evening:

6p Greeting. "Getting to know you." Find out about who is there and who I am. 30 min.

Detailed introduction to the 5 basic concepts, hero zero and NFGBT1 90 min.

Short break

Introduction to base ten manipulatives. Some fast games for getting started and getting to know the pieces. Covers counting and combine-ing (+, -) plus some multiplication and division) 60 min

Introduction to algebra. 60 min


8am Algebra. 60 min

Problem solving algebraic : 60 min


Fractions: about 2 hours

12p-1p LUNCH

Signed numbers. 30 min

Percentages 1 hour.

Playing with basic operations. Addends for making change. Games and activities. 90 min

Q&A / wrap up. Till 4.

Email to reserve your space and get my phone number:

If you would like a quick demo for yourself or your group just email me and we'll arrange it. Also if you would like a seminar like this in your area email me and we can arrange it...

Still working on Webinars and Web conferencing...

4 Year Old Math Enrichment

If I can explain it to a four year old I can explain it to YOU and then you can explain it to your students...

Wednesday, December 29, 2010

Fractions Intro

Fractions are the bane of many a student. In fact some companies spend a lot of money every year training their employees on the topic...rules and process are easily forgotten.

Here is a conceptual introduction on video with very few symbols but with manipulatives and a few pictures...

Start students off with a Three Period Lesson, and then have them show which one is a 1/4 and which is a 1/ many quarters in a half? Let THEM match the symbols to the pieces and let them tell you why the 1/5 goes with the light blue one for example...

As it turns out, fractions are just math and all math is is counting. So let's learn how to count fractions the easy way: when you can see it.

Now that we know the names of the pieces we can start counting them:

We can just count pieces and see what we get. A lesson on Improper Fractions.

We can add them together.

We can make problem solving with fractions simple...and a whole lot more. Go here to see some story problems with a 6th grader and keep in mind I have several students MUCH younger than 12 that can do the kinds of story problems he is doing here.

Find us on FaceBook

Go to the House of Math.

If you have specific questions that go something like this

"How do I show...."

"How do I do this..." Put them in the comments box...

and I will make a video and post eventually...working on a fractions page at the house of math; ran into a couple of snags but it's coming.

Tuesday, December 28, 2010

Improper Fractions

Fractions lessons teach much more than fractions...

This post will have more soon. The screencast is just the fractions portion of the lesson I did on division. All we do is count.

Knowing what one is is VERY important.

We also learn multiplication concepts...but mostly we are just learning how to COUNT.

Find us on FaceBook

Go to the House of Math.

Math Session With 7 And 8 Year Olds

Here is a screencast of a session I did with a couple of students where I finally remembered to bring out my Camera...and snap a few pictures. Even then I should have taken more...We used the same board as we did last week which had what looks like a big scary algebra problem on it...but they know it's easy: all you do is count.

BTW the little girl came to math rather than stay home even though she was sick and throwing up...because it's more fun than staying home and being sick. By the end of class she was feeling much better.

Basically we played with division concepts and notation.

Find us on FaceBook

Go to the House of Math.

Learn more Algebra for a buck.

Monday, December 27, 2010

Economics is Math


People in education are starting to get it. 20 years ago I wanted to make math music videos to teach math...blocks dancing around; math concepts visually obvious and set to day this will happen.

Here at the university level is a video explaining simple economics...which I have argued would be easily understood by a populace with critical thinking skills that had a excellent handle on math. Instead the average American has a difficult time with FRACTIONS...much less ALGEBRA, and even less than that simple economics and money.

"If the people understood the rank injustice of our money and banking system, there would be a revolution before morning." ~Andrew Jackson

Happily for the bankers and politicians the teaching system hasn't even been able to make division concepts clear. The average person can't explain why we invert and multiply if they can even remember to do it when trying a fraction problem involving division.

Just for fun: Three times what is two and five eighths?

3(x)= 2 5/8

Easy or hard? Three times what is two and five eighths?

I rest my case. Soon I'll have a webpage on fractions with video and some blog posts too...and that problem will be duck soup.

Economics is just math and math is just counting...

Apologies for using Youtube, I've been trying to stay away from Youtube because it has been brought to my attention many teachers in Hawaii can't watch Youtube on school connections because it is blocked...this vid is worth your time. I am BTW an Austrian, when it comes to Economics...

Macro concepts like Economics, Climate Science, Physics, Sociology and ANY Philosophy are FAR better understood by people who can do math...

"Woe unto us: we live in a time when neither philosopher, poet, priest or politician can do math." ~Crewton Ramone

If we used music and language that the kids understood, more kids would understand math, not to mention we could make it FUN...I will one day have math music video's. The difference between me and what you see now will be night and day. I once talked to Bill Nye the Science guy and he saw immediately how powerful this could be for math because it's a visual way of presenting math concepts; we can show in a minute what takes 15 minutes to develop with symbols...

The point of this post is we need to move to presenting the mathematics like this, edutainment I believe it's called...I'm getting there.

Find us on FaceBook

Go to the House of Math.

Learn more Algebra for a buck.

Coming SOON: Fractions.

BTW the answer to the question is 21/24...I could see it could you and if you did get it did you remember a rule or a concept like no fun get back to one?

Of course we are easily fooled by men in suits who tell us the answer to debt is more debt and the answer to too much money in the system us more money in the system...the populace can't do MATH.

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Wednesday, December 22, 2010

I was Big In Idaho

Here is a very poor quality screencast containing some vintage footage of a math center I helped open in Idaho along with some commercials for it...I taped it off the TV later I will do a better job and also do some editing as it is dubbed directly from vhs to's 8:33 long.

I put a few minutes of some footage of Jerry Mortensen himself explaining some of the manipulatives he created and I am assured I will be able to sell more manipulatives in the coming year...the multi tens kit, fractions kit and basic operations kit...btw I have two basic operations kits that have the smaller manipulatives thru 1000 or x3 (but no big blue square) if you would like to get one of them let me know just contact me at Gmail.

As I type this I am watching video tape from 1990 when I brought Jerry out to Hawaii to do a seminar, that seminar would change my life. Chalk board... I may put up a few excepts on my website or here on this blog in the coming months as I get the vhs tapes dudbed to DVD...

BTW I spent more time in Utah than Idaho, and helped open centers in SLC, Omaha Nebraska, South Carolina and more. I can't find or don't have video from all those places...this is just some video I happened to find.

Find us on FaceBook

Go to the House of Math.

Directed Discovery With Higher Powers

How would you solve this equation: 4x4 - 2x2 - 4 = 2

I saw this on a math Q and A site.

Hero zero and no fun get back to one.

4x4 - 2x2 - 4 - 2 = 0
4x4 - 2x2 - 6 = 0

You have to know how to factor polynomials.

2(2x4 - x2 - 3) = 0
2(2x2 - 3)(x2 + 1) = 0

or just

(2x4 - x2 - 3) = 0
(2x2 - 3)(x2 + 1) = 0

because hero zero is impervious to division by zero; then just set each factor to zero and solve for x:

2x2 - 3 = 0 and x2 + 1 = 0
2x2 = 3 and x2 = -1

because if one factor is zero the whole thing is zero

x2 = 3/2 and x = ±√-1 [√-1 gives nonreal solution, an imaginary solution, which is ±i ]

x = ±√(3/2)

the real values of x are √(3/2) and -√(3/2)
the imaginary or non real values are +i and -i

I put this here without the blocks or pictures of them because it shows where you can go once you get a feel for the higher powers. Also as a clue or some directed discovery to those who have done some study on this blog and website or have started using base ten blocks but don't have hours and hours of training under their belt yet. Note that

2x4 - x2 - 3

is comprised of a square some rectangles and some smaller squares...and that we could use a big red square the blue x's and the green units to model

2x4 - x2 - 3 instead of basic operations pieces which would be the big blue squares the red strips and the units

really it's the same problem as

2x2 - x - 3 isn't it?
The x's are just raised by a factor of 2...and with our imaginations we can name the pieces anything we want...and you can see if a 12 year old can play with problems like 2x2 - x - 3 and look at them as puzzles not things to be feared and in fact as confidence grows this stuff is fun and challenging...and easily solved given time.

You can see how to do the negatives for a buck on my website. And shortly you will find a video showing this very problem on the advanced algebra page. To get to the advanced algebra page you need a password and currently passwords are a buck. I am told I need to raise the price to 20 bucks because nobody thinks there's any value there for just a dollar. Get it? Any value!!! I assure you there are lots of values there...

BTW this is post 100!!!

250 to go and search engines will start taking this blog seriously...

Monday, December 20, 2010

Algebra For Basic Opps Redux

After a while it gets old, well for the blog and people watching Youtube videos...all we do is form rectangles and count the sides learn about multiplication, addition and division as well as factoring time goes by they get better and better.

Simple drawing powerful math concepts:

Here they are counting up the parts...

Here we see that they had forgotten their addends for 7 and big deal just go back and build a bunch of 7's and 9's and all the other ones they are building 7's and they knocked it over and built it again about five or six times...

The House of Math on FaceBook.

The House of Math

Learn a lot of algebra for a buck.

Playing with X and Y

Factoring expressions like x2 + 3xy + 2y2 is not a problem...

We also did x2 + 5xy + 6y2 as well and off camera we did more problems which were EASY once they understood the concept.

x2 + 7xy + 12y2 etc.

It's EASY to see x2 + 3xy + 2y2 = (x + y)(x + 2y)

x2 + 5xy + 6y2 = (x + 2y)(x + 3y)

x2 + 7xy + 12y2 = (x + 4y)(x + 3y)

Watching me explaining it to little kids should make it easier for you to see how to explain it...

Older kids that have played with these blocks will look at this and go "no big deal" the five year old said we're just giving the units, and x's a new name...the concepts for factoring multiplication and division are the same...

The House of Math on FaceBook.

The House of Math

Learn a lot of algebra for a buck.

Friday, December 17, 2010

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.

Thursday, December 16, 2010

(a+b+c)^2 Bigger is just funner.

Ran across a post from a fellow blogger from India.

Here is a clearer representation of (a+b+c)2

(a + b + c)^2

I just made a quick sketch and did not label it properly but you get the idea quite easily I think. Each side is a+b+c or (a+b+c)2 which if you count up all the parts is

a2 + 2ab + 2ac + b2 + 2cb + c2

Some people would call this advanced algebra but really given time any little kid could count that up...

For the purists out there: as you go from left to right in the drawing it is correct but above the a2 it should be "ab" and "ac", and the other black square should be a "bc" because the pattern is over then up... → ↑ for multiplication.

Just to be sure I gave it to a 12 year old to do and he had no problems with it...just took a while to count and label all the parts.

The House of Math on FaceBook.

The House of Math

Learn a lot of algebra for a buck.

Wednesday, December 15, 2010

New and Improved: Now with more room for your math enjoyment.

Got tired of stuff not fitting and having to make all the videos so small...

Will mess with the colors Purple and yellow oddly enough are not available later...

Meantime enjoy the roomier, mathier new version.

Applying the Quadratic Formula


On youtube:



quadratic formula, completeing the square
Note the standard form should be


quadratic formula, completeing the square
quadratic formula, completeing the square
quadratic formula, completeing the square



Need help with the basics like distributive theory click here.

The House of Math on FaceBook.

The House of Math

Learn a lot of algebra for a buck.

Tuesday, December 14, 2010

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.


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.


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.

Monday, December 13, 2010

More Pythagorean Theorem

Here is a screencast for you adults talking about Pythagorian Theorem in general terms. We haven't really gotten down to the nittey gritty of solving for "C" by square rooting but it becomes visually obvious that if I know two sides of the rectangle I know the third side.

Search Pythagorean Triples and use those to start off don't just pull funky numbers out of your butt. Make sure the student can easily find the square roots without a calculator to start. AFTER they understand the simple concept then you can start showing them that if we know ANY two sides we know the third side; at last we can put in any two numbers and find the third side, BUT START WITH PYTHAGOREAN TRIPLES.

Again the student can see that "C" isn't 25, it's the SQUARE ROOT of 25...they can also SEE that the two little squares have the same area as the big square...

And then we can start figuring out how to find the other side if we know any two sides by using simple subtraction.
If I take out one of the squares what is left is the other square either "a" or "b"...
Once you get 9 + 16 = 25 down and have played with it you can get out another one and in fact this one is a good one to start with when you have younger students...but it might be hard for them to count that high so you could just use the bigger squares for the concept that the two small squares add up to the big one...note you can but 36 in the middle and the eights around the outside just like with 9 and 16...also you might play with concepts around squaring and exponents...try and get them to tell you that although we doubled the side the area is FOUR TIMES as big...

Here is a screen cast talking about the above graphics...

Now go to the pre-calc page at the house of math and watch the screencasts so that we can apply this knowledge to find the distance between two points...and it should be simple to find the sides of triangles too...allow a few seconds for those screncasts to load...the page goes white for a few seconds and it seems like nothing is happening.

The House of Math on FaceBook.

The House of Math

Pythagorean Theorem at the House of Math.

Learn a lot of algebra for a buck.

Sunday, December 12, 2010

Introduction to Pythagorean Theorem

I Introduced a 4 and a 5 year old to Pythagorean Theorem. Really it's that easy.

In the first part of the video you see him factor a problem he's never seen before:

x2 + 8x + 12

The day and week before, he has already done x2 + 8x + 16 a couple of ways once as a problem for completing the square:

x2 + 8x + ?? ?? = What completes the square?

and once as a problem for factoring where he got all the info:

x2 + 8x + 16 and we talked about (x+4)2.

To make it a bit of a challenge I changed it to x2 + 8x + 12. But he's almost at the point where they are all EASY.

Note how his brother builds squares and the quietly arranges them according to size while I am focused on his brother...he received a lot of praise off camera when we reviewed this video together.

Then we played with the concept of squaring the sides of a triangle.

If you build the lesson correctly where your students have to play with the triangles and tell YOU about the relationships (instead of the other way around) you will find 90% of your students will come back with

a2 + b2 = C2!!!

We can also see that later when they see

a2 = c2 - b2 or
b2 = c2 - a2

it will make total sense to them.

This was just the first time they saw this and they will see it many times again before they reach the ripe old age of 7...note how in the video I didn't even write out the equation. We just played with the blocks and got an experience of the concepts. Next time when we do write the symbols that go along with the blocks they will understand what it means instead of just memorizing a formula.

They will also see that a + b > c ALWAYS, although they may make the joke 3 + 4 = 5 they will know it's a joke and that 32 + 42 = 52 is true but 3 + 4 = 5 isn't.

Also note how much faster and easier this lesson is now that they each can skip count by 3's 4's and 5's...and this lesson gave then another chance to practice skip counting.

Stay tuned for an additional video that is a more formal lesson for YOU on Pythagorean Theorem sans little children where we can see how to make "Pythagorean Triples" and understand more about the theorem before we ever have to get out our square rooting skills for numbers that aren't perfect squares.

I talked to a few teachers who never saw a proof of this...they just got the formula and memorized it. I talk to teachers all the time that are amazed by this little demonstration...INCLUDE it in your lessons with little kids.

The House of Math on FaceBook.

The House of Math

Learn algebra for a buck.

Pythagorean Theorem at the House of Math.

“It isn't enough just to learn -- one must learn how to learn, how to learn without classrooms, without teachers, without textbooks. Learn, in short, how to think and analyze and decide and discover and create." -- Michael Bassis

Thursday, December 9, 2010

More 4th Power Algebra

The higher powers of x can indeed be modeled with manipulatives though they seldom are or if they are people use actual cubes and then are unable to go to the 4th these videos we play around with expressions like:

x4 + 7x3 + 18x2 + 20x + 8

x3 + 6x2 + 11x + 6

We take (x + 2) and "cube" it, and a whole lot more. The students you see are 11 and 12...

And pictures like this start to make sense and make "advanced algebra child's play...all we need to do is be able to count...

x^3, 3rd degree algebra,

These should stand alone if you are starting here but it might be good to view and read some other pages first if this is your very first exposure to manipulative based learning for math. See also.

For more on 3rd and 4th power algebra and how to show negative expressions go to my House of Math and click on the "Advanced Algebra" tab. You need a password which you can find by clicking on the Products and Passwords tab...

The House of Math on FaceBook.

The House of Math

Learn algebra for a buck.
In fact you should go there if the above videos didn't make perfect sense to you...lots of free learning and more "advanced" stuff for a buck.

Monday, December 6, 2010

4 Year Old Math Enrichment

A bright 4 year old has a fun time playing math. Before we knew it an hour had gone by. I remembered to take the camera out after about 20 minutes...we had already done some counting, added random numbers together and then started adding pairs, starting easy 1+1 and working our way up to 9+9. All 45 addends will be mastered using base ten blocks. I enlarged the photos in this post a little for those who use Pinterest.

Addends with base ten blocks, addition with base ten blocks
Then we did some multiplication and division.  He likes division because he only has to count one side. We count by eights, then we count the sides, then we count the rectangle and each side. He can see 24 ÷  8 =  3. The three eights are visually obvious too.
Preschool Math Fun, base ten manipulatives, beginer division
Then we have fun counting and building 20 sixes.
Preschool Math Fun, math games with base ten blocks
And even more fun knocking them down.
Preschool Math Fun
A free time wall. He had no rules to follow when he built this wall he just built it. The addends for 10 and some smaller numbers are being learned here people think this is all that base ten blocks are good for, making tens and some place value but you can do so much more.  Again knocking the thing over is the most fun...
addends with base ten blocks, base 10 blocks, manipulatives
On to some algebra puzzles.  I tell him the pieces and he has to turn them into a rectangle. Base ten blocks are great for teaching algebra and addends and a whole lot more.
Factoring Polynomials, Factoring Trinomials usinf base ten blocks
The men help him count the sides.
Algebra, base 10 blocks, Base 10 Manipulatives,
This one problem teaches him about counting, addends, factoring, multiplication and algebra all in one lesson. This took about 15 minutes from start to finish...15 is a lot to handle when you are four.  Note if he had to get out 15 individual units this problem would be nearly impossible and would take a lot longer.
Algebra, base 10 blocks, Base 10 Manipulatives,
He took a while figuring out which blocks to make his 15 with, he has some experience factoring so he knows a 10 and a 5 aren't going to cut it.
Algebra, base 10 blocks, Base 10 Manipulatives,
At last he has decided on 5's.  He uses them to shape the rest of his rectangle. I tell my high school students what this child already knows: the way to factor it lies in the factors of the constant.
Algebra, base ten blocks, Base ten Manipulatives,
Now that he has three fives all he has to do is make those pesky x's form a rectangle.
Algebra, base 10 blocks, Base 10 Manipulatives, factoring
A little more work and he has it.
early algebra
Now his pals can help him  count the sides.
base ten blocks, algebra for toddlers
Just for the fun of it he wrote the factors himself to the best of his ability.
algebra for toddlers
"It almost looks like a 5"
preschool algebra
He was quite proud of his 3. Using base ten blocks to teach concepts and understanding of math is a very powerful thing. Just because they can't write doesn't mean they can't learn math; writing isn't a perquisite for math  anymore than writing is a prerequisite for learning English. You will find that students who learn math this way will be able to do a lot more math in their heads than students taught using the current completely ineffectual way we use now.
x2 + 8x + 15 = (x + 5)(x + 3) is easy and fun to do and completely understood. One means the rectangle the other means the sides. Later we will deepen understanding and add more concepts on top of these basics. Can you see math will always be easy for this child? No fear of new stuff in the future because he has math experience now. Using base ten blocks makes understanding math easy and fun...child's play.

He helps me do the same screen cast:

If you enjoyed this post you will also enjoy this popular post and screencast showing much less structured play with clay for learning math concepts. Math enrichment and a math rich environment go hand in hand.

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Learn more Algebra for a just a few bucks.

Trig for 8 year olds. Just what it says, click the link and find out more.

This post remains popular going on two years later...he was just 4 and 1/4 when we made algebra is no big deal and fractions and multiplication are fun...he is the go to guy in his kindergarten class when kids want to know what to do when they have math.

And now he is the go to guy in 1st grade. Please take a moment and watch the vid on the concepts page under the heading "Early Exposure to Math Concepts Helps Ensure Success." It's only 3 and a half minutes long and should help dispel the myth that you don't want to start math too early. There is no "too early."

Give your young child the advantage in math with my cool counters compendium.

“I care not what subject is taught if only it be taught well.” ~Thomas Henry Huxley

math manipulative book, Base Ten Block Book

Get this book if you have children 7 and under...find out more about it, and a look inside here.  You can get it without a password for just $4.99 People's comments about the base ten block book here.

"Great book for teaching how to use the blocks! Colorful, clear pictures and cute rhymes make the book fun to read and play around with. We printed the book out, and my 5yo loves how many of the block pictures are big enough to put his blocks directly on top of the pictures. The text plays fast and loose with niceties like punctuation, but is engaging when read aloud.

Most of the book focuses on playing with addition facts up to 10, which gives a solid foundation. But it also delves briefly into such topics as square roots, place value, addition of multi-digit numbers, and a glimpse at multiplication. And in true Crewton Ramone fashion, problem solving with 'x' (basic algebra) is sprinkled throughout. A great intro to playing with math." ~CS, GA.