Crewton Ramone In The Classroom.

Here are a few vids I've made while playing around at Haiku School with 1st and 2nd graders using base ten blocks.

We do math that is supposedly advanced for their age. Most of the time the kids don't seem to notice. We fool around with problem solving and algebra, Pythagorean Theorem and addition, multiplication and division. All it is is counting. No concept is beyond the child if presented at the child's level.

Teachers and teachers aides are always amazed at what I take for granted. Several teachers aides commented that they were doing the same thing at the local community college while they attempted to get their teaching degrees. Many of them are being held up because of the math. "Why don't they teach it this way?" is a common question.

I'll get into that some other time. I am building a six hour Audio Course that will cover that (briefly) and a whole lot more. Should be done this summer. To start off here is a rant. Fed up with teachers who tell me kids can't do simple algebra. Teachers can't do simple algebra, not the kids.



Then here is a CLASSIC lesson with first graders. We learn addends for 10 and nine and the nines multiplication table to boot.



Here is another lesson with is a lesson with 1st graders factoring polynomials but what we are really doing is learning addends and multiplication:



As one teacher put it when they get back to the stuff they are doing for "grade level" they ace it. Also In the 1st grade class I go to for an hour a week they blew away their piers on the standardized tests. Especially in "algebraic thinking" but also in general computation. These scores are confidential or I'd share them. Here is more:



I've been fooling with this for 23 years now. I have heard every excuse in the book from teachers as to why they can't do this their classrooms. This post is about removing excuses. ANYBODY can do this. I can train you. You can train yourself. I am working on courses that you can buy for a few bucks to help you implement this in classrooms or in your home or homeschool.

Meantime get a password for 24 bucks and start watching some vids and reading pages that interest you in your spare time. (That's a bit of a joke, my mom was a classroom teacher I know you don't have a lot of spare time.) Once you figure out how AWESOME this is you'll find the time.

Here are second graders doing slightly more advanced play. They are making square polynomials and you can hear the excitement in the room. It's fun. They know they are doing stuff that's supposed to be "hard." In kid culture algebra is hard, but they often ask for it by name.



Here is a lesson on square numbers:



We are getting ready for Pythagoras. Before you dive into more complex concepts it's good to get them used to the elements they will be faced with before hand...like squares and square root. Very important to know what the symbols mean.

And just for fun I took a trip down the radical path. Why. Because you can.



The we played with Pythagoras. The thing to remember is all we are doing is using our counting skills.



The classes with the first graders are about an hour long and 90 minutes with the second graders. I don't expect you to watch all these vids in one sitting but here they all are in one place. You can share them with teachers you know and they can get to them as time permits. Any young ambitions teacher that would like to turn these into lesson plans are welcome to do it...

It is hard to film and teach all at the same time, plus I am hampered by rules about filming children and etc. So I don't make many vids. Hopefully there will e another post like this before summer with a bunch more fun vids for you to watch.

95% of the time we have a great time. Once in a great while things can get rough. I had a Monday morning class with a substitute teacher where the second graders were having a hard time due to lack of sleep

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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."

Spring Sale

SPRING SALE IS OFFICIALLY OVER.

Here are the sale prices. This a real sale but there is one small catch: no cash refunds so make sure you know what you are ordering. The process is simple: look over this price list and pick what you want. Email me. I will send you a paypal invoice that you can pay with any credit card. If you use paypal there are other options too. Shipping is free to the USA only. And it has gone up to International Destinations. But with the sale it's almost like getting free shipping. Almost. Australia is ridiculously pricey.

If you do the math you will find that the Deluxe Curriculum Starter Kit comes to 500.00 at the sale prices. Told you it was a good deal.

Anyhow here is contact info:

http://www.crewtonramoneshouseofmath.com/contact.html


I get plenty of spam already even with these precautions. The idea with the 300 books is perhaps you get together with some people and order as a group and get even better prices...that way a set of Smiley face books is only 50 bucks, or a set of level 1 is only 50 bucks...but you need to order 6 sets (300 books) so for example one person could order smiley face and level 1 that 100 books another person level 1 and 2 that's another 100 books, and another person could order level 2 and 3 for a total of 300 books and you get the discount...get it? Maybe 6 people order one set of books each. Or two people get 150 books each...or whatever.

Here are my ordering pages with vids on kits and books:

Kits:
http://www.crewtonramoneshouseofmath.com/product-exchange.html


BOOKS:
http://www.crewtonramoneshouseofmath.com/Mortensen-Math-Books.html

This is a great deal:

Combo Kit Reg $91.00 SALE: $65.00

Multiple Tens Kit Reg $42.00 SALE: $30.00

So now you can get both for 95 bucks!!! And it INCLUDES shipping to the USA.

And when you order thru me you get an annual password on orders over 50 bucks...if you guys go in on a case everybody gets a password. If you order something small I still give you a password just not an annual password.

You may note not everything is on sale but pert near. Good time to get the last of the VHS tapes, you can turn them into DVD's for personal use yourself....just don't try and sell them.




MORTENSEN MATH

SPRING SALE 2013

MAR 30 - JUN 29, 2013

SPRING SALE IS OFFICIALLY OVER.

SPRING SALE 2013 MAR 30 - JUN 29 PRICE LIST:







SHIPPING IS FREE TO CONTINENTAL USA destinations.





SPRING SALE 2013 MAR 30 - JUN29



Dear Friend of Mortensen Math, Thank you for contacting us today!

Let me know what you want to order for sure and instruct me to send you an email invoice.

Follow the LINK in the eInvoice to pay through PayPal. You don't have to be a member to pay with a card online there.

Our Sale Prices may not be "up" on our Website yet but will be soon.



When you decide what you want to order send us an email with details and then watch for an "email eINVOICE" from us through PayPal. Use the LINK in the email to go to PP and pay. You don't have to be a member of PayPal. Can still pay with a card online.



For help deciding what you might need for your particular student(s) feel free to email or call with further questions. EMAIL IS GREAT because we can thoughtfully respond in better detail!



WE WILL BE OFFERING LIVE CHAT SOON!




NOTE: If you order a case (300 bks - mixture ok) of Bks - receive QVP (Quantity Volume Pricing)

Reg QVP case price for Bks = $1.75 per bk @ $525 per case. SALE: $1.00 per bk; $300 per case (300 bks)

No additional special Discounts apply.

This is a very good deal.



PRINTED PUBLICATIONS SALE - BOOKS & MANUALS



A "STRAND" of books is a particular area of "math discipline" or "isolation of difficulty" (Montessori term) or a particular group of "math concepts" such as:



Smiley Face Bks (50 bks) with the following "strands": Reg $157.50 SALE: $75.00

Smiley Face Counting

Smiley Face Addition

Smiley Face Subtraction

Smiley Face Multiplication

Smiley Face Division



"Facts Mastery" Bks:

Addition Facts Mastery (time tests, rote practice of facts) (10 bks) Reg $31.50 SALE: $15.00

Multiplication Facts Mastery (same) (10 bks) Reg $31.50 SALE: $15.00



"Level" Books with 5 "strands" per (most) Levels

The "strands" are: (10 bks in each "strand")

Algebra, Arithmetic, Measurement, Problem Solving & Calculus

The "Levels" are 50 bks per (most) Levels:

L1 Bks (50 Bks) Reg $157.50 SALE: $ 75.00

L2 Bks (50 Bks) Reg $157.50 SALE: $ 75.00

L3 Bks (50 Bks) Reg $157.50 SALE: $ 75.00

L4 Bks (30 Bks): Algebra, Problem Solving, Calculus (also Measurement Level 4 will be available soon):

Reg $94.50 SALE: $ 45.00

L5 Bks (10 Bks): Calculus: Reg $31.50 SALE: $ 15.00





Chemistry Level 1 Bks Reg $31.50 SALE: $15.00



There are 4+ Manuals available currently, and more to be available this year:

Manual Level 1 Reg $16.10 - NOT AVAILABLE FOR A FEW WKS - CURRENTLY ON BACKORDER. SALE: $10.00

Algebra Level 1 Guidebook REG $32.20 SALE: $16.00

Manual Level 2 REG $32.20 SALE: $16.00

Manual Level 3 REG $48.30 SALE: $24.00

Getting Started Manual REG $13.80 SALE: $5.00

Games & Activities Manual REG $13.80 SALE: $8.00



ANSWER KEYS ARE AVAILABLE BUT NOT ON SALE



KITS ON SALE



Combo Kit Reg $91.00 SALE: $65.00

Curriculum Starter Kit Reg $350.00 SALE: $300.00

Fractions Kit Reg $105.00 SALE: $75.00

Triangle Tray Kit Reg $9.80 SALE: $5.00

Numeral Identification Kit Reg $28.80 SALE: $20.00

Number Picture Fun Kit Reg $56.00 SALE: $45.00

Addition Subtraction Kit Reg $28.00 SALE: $20.00

Having A Party Kit Reg $91.00 SALE: $40.00 (includes a VHS tape and we will also Backorder a DVD for you to be sent separately as soon as available before FALL)

Want To Be A Ten Kit Reg $91.00 SALE: $40.00 (includes a VHS tape and we will also Backorder a DVD for you to be sent separately as soon as available before FALL)

Newton Deluxe Kit Reg $151.20 SALE: $99.00 (includes a VHS tape and we will also backorder a DVD for you to be sent separately as soon as available before FALL)

Algebra Kit Reg $150.00 SALE: $99.00 (includes a DVD)

Multiple Tens Kit Reg $42.00 SALE: $30.00



SKIP COUNT KIT - COLORING BKS # 2-9 + SKIP COUNT AUDIO TAPE (CASSETTE TAPE) + A SKIP COUNT AUDIO CD

REG $48.00 SALE: $30.00



SKIP COUNT AUDIO CD ONLY REG: $18.00 SALE: $10.00



ALL VHS TAPES ORDERED STANDALONE: $4.50 (NO ALGEBRA VHS AVAIL)

TITLES:

EXPLORE AND DISCOVER

PRE-SCHOOL

HAVING A PARTY

WANT TO BE A TEN

NEWTON



ALGEBRA DVD STAND ALONE REG $30.00 SALE: $20.00


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No cash refunds. Credit exchange only with RMA#.

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Again this is a real, actual sale not a make pretend sale. Take advantage of it.

SPRING SALE IS OFFICIALLY OVER.

Base Ten Blocks Teach Addends And Multiplication Of Nines.

Here is a classic lesson using base ten blocks. You could easily do this for 1st graders on up through highschool. The older kids tend to go ohh and ahh more...this class was especially unimpressed because they'd seen it once before. These are first graders and this is the nines times table. Obviously something is different here because many older students struggle with nines.

This is a short compound lesson, they can see addends for nines and tens, they can see all the combinations and why it works out that way and they can make sense of it for themselves.

We then went on to build pyramids like you see in this post and we only did nines and tens, this reinforces the lessons on making change and the algorithms surrounding "numbers are made up of other numbers" and "want to be a ten" plus gives them the first 10 multiplication facts for nines all in one short lesson.

Any teach can add this to their "canned lessons" and get good results. Here is the video:



By the time they see it the third time this will be super easy...imagine what they could know by 2nd grade if they had math like this an hour a day instead of an hour a week.

Of course at the end I pointed out a bit about square numbers with 81 and 9 because this was a lesson on nines. We talked about what the symbol means, that squares have sides that are the same, and that you can shape numbers into squares and that it's easy to count one side.

Share this information with parents and teachers you know.   More at:



Crewton Ramone's House Of Math.

Addition & Multiplication With Base Ten Blocks (Using Algebra)

Here is another video showing how you use base ten blocks to bring home the basic concepts of addition and multiplication. A very simple concept for very young students to grasp is numbers are made out of other numbers. You need to talk about addends...they get it when you tell them you can make a 5 out of a 3 and a 2. There are 45 addends but rather than doing the same thing over and over again for a whole year, addition in first grade for example, using worksheets and flashcards and drills...why not play and have fun and do many different activities that teach the same thing. Building towers, pyramids, walls and math towns are all activities that teach addends. (Search crewton ramone pyramids or crewton ramone addition) Variety is the spice of life.

 You teach addends, multiplication and the algebra is just along for the ride.

Here is another slightly more advanced way to teach three things at once using base ten blocks. You teach addends, multiplication and "the algebra is just along for the ride." Before you do this you get very comfortable with ONE x² before you add two or three. And you might check out this page that shows you how to present the basic concepts of addition and subtraction using manipulatives too. While you are using two of them you can really bring home the addends if you have a set of multiple tens. If you only have single blue (or whatever color you have) bars, not so much; BUT you can still get addends done if all you have is single bars just name the groups of x and add those.

As an added bonus you are factoring polynomials. I have discovered that a lot of older students have trouble with algebra because they haven't ever mastered their addends and they don't have their multiplication tables mastered either...yet they passed math several years in a row and find themselves in high school.

I left a few things out of the graphic because it was getting too busy. You should also see 9 + 9 and of course 1 + 1 (the x-squareds)  But when counting it up they may do 9 + 1 and 8 + 5 to get 23...at any rate LOTS of math goes on with each problem and the subconscious doesn't miss any of it...

Older students can take the time to draw the problems and write down the symbols. Younger students need speed and repetition so they don't get bored...and taking the time to write it all down slows things down too much...so we just talk about it...this also will come in handy later when you find they can do a lot of math in their heads. No Blocks. No pencil and paper either.




Other comments about this are regarding "mindset". Using algebra to teach basic math works well on all manner of students from various age groups because it changes their minds about math being hard. It's easy and even fun. Once they think it's easy: IT IS. If they think it's hard, math is much more difficult.

The next idea is working with older students who need to master multiplication and all 45 addends using traditional methods can make them feel stupid or inferior because they know they are doing work that is "beneath their level" or that younger kids do...this can be damaging to their self esteem and further turn them off to math. Recently a parent asked me what I thought of the math tutoring a public school had after school..."more math the same way they didn't get the first time. SO lets do it over again and perhaps they will get it this time." Even if they do they will have less than positive associations with math.

If you use algebra and it's fun and easy to start and stays easy, they have fun feel smart because they are doing algebra which they know in kid culture is supposed to be hard AND they get the practice they need to enhance their skill sets in addition and multiplication. Plus playing with base ten blocks is fun--they look like toys. They are toys. Powerful toys that teach math. Toys that make math child's play. In your hands they are powerful tools when used correctly.

They MUST get their hands on the blocks. This way you reach all learning styles and oddly enough several universities have recently made the discovery that the more senses you use the better and easier learning is...and the more learning takes place.

Also note BOTH hands make for a whole brain activity. This is why I have success with so many different students.

 The only way to learn math is to do math, have fun while you're at it.


I found early on as a salesman for this method that sales sky rocketed when we had enough kits for everybody in the room and everybody got their hands on the blocks...they understood it, they saw it made it easy they got a kit. Otherwise it was just more math.

Also athletes and other learners that are more kinesthetic excel using this method, and this is also why we do so well with special need learners.

I have made many posts about using algebra to teach basic operations. See the links below. You can also use fractions to teach addends and multiplication but that's another post and another video.

The previous post Algebra With Base Ten Blocks For Addends And Multiplication this could be considered part 1 and the one you are reading now part 2.

More on using algebra to teach other operations:
Using Algebra To Teach Multiplication.

Algebra its many uses.

Here is an older post, contains no video just words and pictures:

Using Algebra To Teach Basic Operations.

And here is a pile of screencasts on various topics:

Crewton Ramone on Screencast-O-Matic.

Use base ten blocks to explain the distributive property.

Shortly there will be another post with Commander Colby showing how to use algebra for remedial math without damaging the child's self esteem or making them feel stupid or like they are behind.

Algebra With Base Ten Blocks For Addends And Multiplication

Trying to get people to understand that you can use algebra to teach addends and multiplication can be a little frustrating. People (including teachers) are so stuck with the rigid and foolish way we have structured mathematics instruction in the USA that using algebra to teach addition or subtraction or fractions to teach multiplication are practically inconceivable. Compound teaching is; however, a very effective method for teaching math and base ten blocks definitely help.



In the picture above she has to tell me the whole rectangle...x² + 16x + 63...she has to add the x and multiply the 9 and 7...and we do it fast. There are only 45 addends, they need to be mastered. There are only We go through lots of problems quickly as you can see here:



This is video from an actual tutoring session. The little girl has all manner of distractions and yet we cover more math in an hour than she'll get in several days at school. And it's fun. Rather than spending days and days doing the same multiplication problems amd filling out works sheets, why not use base ten blocks and do lots of problems quickly. Remember the brain likes to work quickly. And the more impression it get the more likely the information is to be transferred from short term to mid term memory and finally into long term memory and with more impressions the info is available for instant recall. It is more likely to get there if you are having fun than if you are drilling and it's drudgery. The child is engaged, the brain is engaged learning is taking place.

By the time this video started we'd been playing for a good 10 or 15 minutes. Also it was self directed: she could use any two multi ten blocks she wanted, (these are base ten blocks that make building super fast because we don't have fool with getting out tens or x one at a time).

Also note you still have to work with them to get them to add two numbers instead of counting each block, and the more they do it, the faster they get. Same with the multiplication. All it takes is pratice and it's kind of fun to have the control of making up your own problems. She showed her little brother how easy it was to do algebra..."all you do is count," she says triumphantly.



With drill work and work sheets the brain eventually shuts down and it's boring you may even see them begin to yawn. Be careful with worksheets. Using base ten blocks engages all the senses. It's fun an you get more work done in less time. They learn more, faster.

When you can do your math and you get it, it's fun and it makes you feel good because learning is fun and sets off all manner of endorphins in the brain. Declaring yourself queen of math never hurt anything anyway. I am especially aware of little girls having their self esteem damaged when they fail at math. The psychology of the female is to take it personally, more so than boys as it was explained to me by a person who had a degree in the psychology of mathematics, little girls tend to think something is wrong with them when they don't get it, little boys tend to think there is something wrong with you if they don't get it. This is an over simplification and generalization but it is backed up with direct observation and anecdotal evidence during my travels.

You can play want to be a ten with the multi ten blocks...only it's actually, "want to be a hundred." 3 tens wants 7 tens...etc...7 ten and 6 tens is 13 tens...same blocks we are playing in algebra so 7x plus 6x is 13x...simple.

You will need a password but you can see the same principles at work when we work with negative factors: and we end up practicing adding integers. They learn about hero zero too, and they will often freestyle their way into concepts like the difference of two squares compare them to square algebraic expressions like (x+1)² and SEE what to do. [Soon there will be a link to a page and vid where a ten year old boy does so called, "advanced algebra." Meantime use the links below for more on using algebra to teach basic math.]

Here is another blogpost Algebra For Addends and Multiplication. You can also use algebra to teach remedial math, I have a student who has a hard time with multiplication and subtractions and fractions and...so we do algebra and then evaluate the polynomials for various numbers. This "tricks" him into doing his remedial work while he learns algebra and he doesn't realize we are doing stuff he should have learned already because he likes algebra, it makes him feel smart. Thus preserving his self esteem AND getting the work and practice done that he needs.

And here is a Video just learning about addends and playing and we don't do any algebra. But we could be doing algebra if we wanted and this student liked playing in algebra but in this vid she opted for building a town instead. This vid is about 30 minutes long. We just play blocks. I have been told this is a great video, might be worth your time:



The point is you can use algebra for teaching right along side, concurrently with, so called simple, basic lessons on addition, addends and multiplication.

More on using algebra to teach other operations:
Using Algebra To Teach Multiplication.

Algebra its many uses.

Here is an older post, contains no video just words and pictures:

Using Algebra To Teach Basic Operations.

And here is a pile of screencasts on various topics:

Crewton Ramone on Screencast-O-Matic.

and if you liked this page which is basically Algebra for little kids you should also like Trig For Little Kids too.

Now you can comment here using the blog commenter or with facebook:

3rd Power In His Head

Here is a gem. Don't tell me they have to have base 10 blocks or they will become block dependent using this method. Watch the older boy picture this problem

x³ + 9x² + 23x + 16 =

in his head...counting out the parts as he goes and then give it to me to solve.

This is a lesson on factoring and counting and multiplication...and how to be cool and have fun when you do math. The reason they don't need base 10 blocks is because they have been using base ten blocks...and we are learning by drawing and visualizing. Here is a post on 3rd power algebra where you can get an idea of what it is he is "looking at" in his head. We baby stepped our way here but now you begin to see the POWERFUL results of using this method.




More algebra at CRHOM. If you want to see more "advanced" algebra click on the "advanced algebra" tab.

We watched this together. The youngest boy pointed out that he drew 6x² + 10x + 4 and didn't get very much attention for it. He also told me the factors (you can see the drawing in black in front of him) (3x + 2)(2x + 2). "Come on, that was pretty cool dad." So we are going to make a new vid where he gets as much attention as his brother...

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Simple 3rd Power Algebra With Dboyz

Happy New Year!

Here we play around with algebra concepts. This "simple" problem can be drawn three ways.

x³ + 6x² + 11x + 6 =

(x+1)(x+2)(x+3) =

(x+1)(x+2)*(x+3) =

(x+1)(x+3)*(x+2) =

(x+2)(x+3)*(x+1)

We stay in two dimensions and simply change the sides because in this case the long side can be factored.

In the video we play with it a little and talk about x to the fourth too.

This video had several takes in this take we miss them counting each rectangle carefully before they realize all three have the same amount, they are just shaped differently, that is they have different factors...too bad too because you could really see them using their skills with multiplication and addends. I have written entire articles about the importance of addends and how they need to be mastered. Here they add to their mastery of addends subconsciously.

Keeping it in two dimensions makes the arithmetic easy. You will note I did not write out all the different symbols for all three but we did talk about them and the side that can be factored is drawn again to the right. At this age we are more interested in counting, addition and multiplication and addends than we are in the actual algebra. We make no attempt to set it equal to zero, don't talk about roots, or graphing we are just playing and counting more will be added later after we have done lots of problems with sides that can be factored and ones that can't.

Then when we return to this simple one and when we add new concepts they will be easy, unclouded by concepts that we have already mastered. Math the regular way introduces everything at once and it can be daunting. We use degree of difficulty to baby step our way to the "higher" mathematics. If you have to try and learn all of it at once it can be overwhelming. Better to build a firm foundation. Then when I talk about it having 3 real roots and hero zero that's the only part they have to focus on, the rest is already understood.

Here is an older student working on factoring by grouping. She never got to see these as a kid so it gave her a little trouble at first.

And here we play with a 10, 000 square, just talking about it and understanding the dimensions it represents.

Here we begin to see why Mortensen Math is head and shoulders above other manipulative teaching systems, and how Jerry took the Montessori method and ran with it. These boys are 6 and 7...and as I explain in the video we get to see a synthesis of counting all in one lesson. The algebra is just along for the ride.

More algebra at CRHOM.

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Soh Cah Toa Again.

Here is a fast lesson on the special triangle that is 30, 60, 90 with a hypotenuse of 2. Later, when I talk about the unit circle and dividing all the sides by 2 it will already be somewhat familiar. In the picture above you can see the lesson on Pythagorean Theorem using the blocks to show a 3,4,5 triangle. And bring home the point that we have to take the square root to find the side it's not 25 it's 5 just as it's not 4 on the triangle we are studying it's 2.

During the lesson which I failed to film I used the three period lesson to drive home the names of the sides and we used Pythagoras to help figure out what the hypotenuse HAD to be if the sides were 1 and √3...later I will take an equilateral triangle with sides of 1 cut it in half and talk about the special triangle that is formed. I did this but due to equipment malfunction the little boy accidentally ejected the battery while filming me we lost the lesson. I will record it again another day.



It was good for me as a teacher to spend the time with this student because he asked the exact same questions I get from high school and college students as if he were reading from a script...why does the opposite side change when the hypotenuse stays the same? I usually get them to answer their own questions by asking them questions...

I also think you should approach a lot of this as vocabulary, but not all of it. Many "just memorize it" when in fact you can figure it out if you know the definitions of the words, like hypotenuse: the longest side. We had a discussion about how not all triangles have a hypotenuse, and more.

We already knew x/x = 1 so square root of three over square root of three (√3/√3 =1) being one wasn't a scary concept or hard to understand...he also understand the identity that when you multiply by one you don't really change the thing you multiplied although the symbols may change. Concept based teaching begins to compound.

He also understood that √4 = 2...a common question is where does the 2 come from if the student doesn't fully understand Pythagorean Theorem...I made him do it on the white board (it got erased) at first we had √4 for the hypotenuse but that just a complicated way of saying 2....but the step should not be skipped.

We also applied this same lesson to the 3,4,5 triangle...found Soh Cah Toa for angles and looked at the fractions as RELATIONSHIPS of the sides...for example 3/5 HAD TO BE the Sin 30 on that triangle and he discovered that the opposite side of the small angle was of course shorter than the opposite side of the larger angle (60°) and of course the longest side was opposite the largest angle...the 90. I didn't tell him he figured it out...important concept. You can learn a lot by studying a triangle instead of just memorizing the sides and sin cos or tan for the angles...

Sample Lesson Math Vocab

Here is a sample lesson where we learn a little math vocabulary. It's important to know what the words mean...in the mathematics the words sound funny to little kids because they come to us from the Greeks and from Latin...but the concepts are easily understood.

You should also be able to see how the concepts of area and perimeter NATURALLY lead to practice with addends and multiplication and division. This goes well with basic lessons about addition.



I employ the three period lesson and you will note the repetition and lack of the word "no". If they get point to radius when I ask for diameter I tell them that's the radius show me the diameter...no need for the word NO.

The vid is a little long but it's a useful as a sample lesson and will appear on the Sample Lessons page.

Here is a short vid from a little later in the lesson where we are just playing with blocks and learning and reinforcing addends: