Base Ten Blocks and Playdoh

Basically what you see here is a math rich environment in action.

Playin is learning. Play with the stuff they like to play with... In this case playdoh and manipulatives, or base 10 bucks.

This screen cast got over 150 hits in a day, I'm pretty sure people were amazed by their ability to multiply more than by the playdoh but you never know with the Internet.

If you like it, share it.

Basically we played and had fun first and learned math concepts second. this play session lasted about two hours you'll the complete lack of symbols interplay we just talked about the concepts, the symbols will come later.

Here you see us playing with addends and subtraction. A lot is going on here... You see Hero Zero wearing his five disguise at the top, first it was a 10 and we made addends for 10 below it and the four-year-old showed me ten take away one in no uncertain terms.

Here we see an addend for seven and a couple cutouts.

Here you can see how the boys lined up and press them in.

And here we are getting ready for addends bigger than 10.

Talk about making impressions, here we see 6+4 really is the same as 7+3, and they're both the same as 10.

So what if they don't line up  perfectly? They still "get it" and that this age the emphasis is on fun not on being didactic with clay. You can't play "wrong."

Cutouts for the one I don't talk about talk much about the video. And you don't see it much here either but we did all kinds of map of the cutouts, mostly adding and subtracting and smooshing together.

Then we started playing with fraction, under my direction... It's play but it's directed play.  "Why don't we..?" "What if we..?" "What would happen if..?""Can you make a square and cut it up?"

Looks like an American cheese single. And right there I got about 100 ideas for lessons with a pack of cheese singles... Eat your math lessons, that will get them subtracting--assuming you like eating processed American mucus forming, chemically enhanced for optimum flavored cheese-like substances. I wonder if I could get Kraft as a sponsor. Anyway I can see lots of lessons that could be done with cheese singles.

Here we talked about one whole, then because it was yellow we cut it into a 4 x 4 square using the four block as a guide. First would cut it in half then we cut each half into it quarters and the make up the other way and we talked about equivalent fractions 1/4 equals 2/8, and they could see it. And then we got those in the house and you get what we see here:

This gives a good chance to practice coming by fours and to see 4/16 is the same as one quarter.  You can also see a relationship of 1 to 3, 1:3, but we did not talk about it at all I mention it here because it's so blatantly obvious we could show it equivalent fractions the other way keep it simple and fun and don't try to stuff too much in there at a time. Older kids and adults might be ready to make the switches between the two but with the toddlers I made sure it was a coherent lesson with no jumps and perception. It's one square with a strip colored in as opposed into rectangles, one over the other to show ratio and equivalent fractions of one third that way. This one square teaches a lot of math to toddlers as it is. his could just as easily been a lesson about right angles and squares and square root.

The older boy wants in on the action since you did such a good job accounting by fours and sixes.

But the younger boy would like to know that he did all the "work."

Bigger is funner. Here we put  together a 6 x 6 square and talked about fractions as we did it can you see that fractions and multiplication go hand-in-hand and that you can't teach one without the other than that you can teach multiplication with fractions.  Why not teach fractions while you teach multiplication or why not teach multiplication with fractions?

Since it was all cut up already or use a six to show one out of six or 1/6 and that was the same as 6/36 or six out of 36. Again they didn't see any symbols and we didn't do any writing during the lesson. But when they do see them, the symbols will make sense.

 Just for fun, here's one of 36. 1/36.

 And since they had some purple Playdoh,  they made six out of 36 themselves. Again I see you ratio listing here 5 to 1 or 1:5, but we didn't do it. You could if your students are a little older. Or as a separate lesson.

 Them we made it smaller and talk about fives and fifths each blue-black is one of five or 1/5th. Of course conking my fives is easy and fun.

 Which is the same as 2/10ths, and here you see them using their imagination to break it into tenths.

 It was fun rolling out the skinny lines and making stuff with them. I missed taking pictures of them playing with the yellow flat and showing other fractions and fraction concepts. But you get the idea.

 And after we played long enough with these concepts we just crunched it all together and started over again.

"What should we do next?" the four-year-old asked.
 "I dunno." I said, "let's just play and see what happens."

Here is a video for the boys help me tell the story. Caution: they may blow your mind with their ability to count.



At the time I made this post using YouTube and Screencast-o-Matic had outages that were commonplace. I put screencasts here for all my teacher friends who have YouTube blocked at skool but then the screencasts stopped working so now I'm going back and finding screen casts that don't work and am replacing them with  YouTube vids or links.

This screen cast is titled "Crewton Ramone play W/Clay Learn Math" on both YouTube and Screencast-o-Matic. People ask me if they can use my material on blogs and web posts, lancer is by all means just a link back to wherever you got it.

Here are couple of old posts where they play and learn math:

More fun math activities.

Math rich environment.

Four-year-old math enrichment.

Find us on Facebook... and at the house of math.

Simple Base Ten Blocks Teach Many Math Concepts.

One of the math moms on facebook posted this pic. 

My response:

Nice, now change the game and make it so he can only use one three...then the other ones have to be a two and a one or three ones, you might mention right now they are all three plus zero and it's more fun to make combinations...same with the four, only use one four and the others have to be addends for four and so on also nothing says you only have to use 4 on the corners, you can use 5 or 6 or 7 or more pillars...then you can play "jenga" an see if you can take pillars out without knocking the whole thing down...then when does fall down just build it again and see who can take the most pillars out before it falls...Also, make a video of it and maybe you could win something.

Many math concepts can be learned with just this one simple exercise. You can slide a 2 into the level that he built with three's and the concept that 2 is "smaller than" three is easily seen...in math we could say less than...and we could show the symbols on a white board if we wanted to but at this age playing blocks and verbal reinforcement is enough. You are creating a math rich environment, where several of the senses are used to learn math and basic math concepts like more and less and addition and of course subtraction.

The mind absorbs all this then later (days, weeks, months or even years) this experience can be drawn upon to make sense of these symbols: 2 < 3...

You could put on the skip count CD or multiplication rock vids on youtube in the background and sing along as you skip count the threes he has used. PLAY, make teaching addition fun; little kids love to sing and they don't much care if you can carry a tune or not as long as you are making a joyful noise.

Anyhow make a vid of your kids playing math and you might win some cool stuff. UPDATE: this part is over but you should still check out primal math for some cool apps...Zombie Fish Bits is fun....

If you'd like a FREE manual on showing how to teach even very young children a super easy way to subtract click this link to my Supremely Simple Subtraction manual. A new Games and Activities Manual is in the works but it will be a while so meantime use the old one. (Takes a while to load so give it a minute...)

Another math mom on facebook posted this pic. 

My response:
Excellent...! Now you can talk to him about the 9 in the corner...you could flip the blocks over and count 1 hundred, 6 tens and 9 units...you could talk about square roots and square numbers playfully with the 9 and the 169...and of course the polynomial...x² + 6x + 9...the square root is one side which is x + 3....and of course (x+3)² = (x+3)(x+3) = x² + 6x + 9 and you talk about economy of symbol...that we don't need to write it twice...you could talk about 13² = (13)(13) = 169...you could have him draw a simple picture of it...and talk about these things while he's making his drawing...note I say could you don't have to...you could write some symbols and show him how those symbols describe his creation the same way words can describe a brown cow...and you do it casually, not drilling him not formal instruction just,  "hey...look at these green ones there--they make a square and we can count the sides or one side...hey look at that! You made all those blocks into a square can you count the sides? What's the blue one called?"

If you are on the base ten side he should say, "10...and three units." Or something like that. And you could say, "what's the name for one ten and 3 units...?"

If they are on the smooth side and you are in base x, the blue one's name is x and three units...

A ton of math concepts can be taught off of this one rectangle...you don't need to cover all of them at once...just a few at a time. Check this post out, it talks about all the things you can use this simple rectangle (square) for, when it comes to teaching math concepts.

Now build one that's 14 or x+4 squared...and then 15...or maybe he wants to make a different shape with his 6x...and make it (x+2)(x+3) or some other combination for 6, 5+1, 4+2, 3+3...still 6x but now a different number fits in the corner...just play math, bigger is funner.

Homeschool Math. Base Ten Block Method Founded In Montessori.

"The teacher must take her materials from the school, and her principles from what she has learnt; and then she must face practically, for herself, the question of this recall. Only her own intelligence can solve the problem, which will be different in every individual case." ~Maria Montessori

I remember Jerry being quite amused that I wanted to be a master trainer yet had no concept or knowledge of Maria's work. I went home to escape winter and I had been reading "The Men of Mathematics" to try and figure out what the hell these guys were thinking, Newton did not develop the calculus to torture high school seniors, and college students. I also read "Innumeracy" by Paulos. He was surprised by this, so he took me down into his basement where he had a library set up and directed me to READ...particularly works by Mario and Maria. It was a large collection of books; I have an affinity for them, so I was quite content to spend hours down there, I found a book on Vedic mathematics, quite a few classics (Socrates, Plato, Aristotle etc) and many more. Jerry was content to have me down there because while I was down there I wasn't bothering him, and occasionally I'd come up with a topic of conversation "worth talking about."

Try to remember my lineage is direct. Me, Jerry. Mario. Maria. I don't recall Jerry (or Maria or Mario) talking about a standard curriculum that was to be applied to every child. Quite the opposite. The teacher was to be trained in such manner that each child's individual interests could be tapped, nurtured and developed. Discovery was directed by the teacher with regard to the child's individual interests.

Therefore lessons were developed for each class and each child in the class on subject matter at hand, in this case math. There was no cookie cutter approach. Even the books he developed were made with the understanding that the student picked where to start and the order. All books were to be completed but how and in what order was up to the individual student. And yes it's a hell of a lot more work, AND the education is far more effective and superior to what currently passes for education in the public school system of the USA. This year's class is not the same as last years class. How is it possible that the lessons would be the same?

"A teacher, by his passive attitude, removes from the children the obstacle that is created by his own activity and authority.". ~Maria Montessori

For example, today we are going to learn trigonometry concepts. The teacher introduces the CONCEPTS then directs the student to discover more and thru socratic method the child discovers axiom and postulate...and the formulas, they aren't hit over the head with them. Once concepts are understood mastery can be attained. Mastery is demonstrated by being able to make up and solve one's own problems. Again: once they understand the concepts all we can do is change the numbers.

"Education is a natural process carried out by the human individual, and is acquired not by listening to words, but by experiences in the environment." ~Maria Montessori

Your job is to create a math rich environment. Place the child in a math rich environment and they will learn math, in their own way and in their own time. This is the education of individuals in groups...how can the lessons be the same, in the same order at the same time. If you were educated in a public school yea verily this is completely foreign to you as everybody pledges allegiance and then opens their text book to page 123, or does the same worksheet in preparation for the standardized test. BTW it has become clear that homeschooled and Montessori students do incredibly well on standardized tests, because again, once the concepts are mastered all the givers of the test can do is change the numbers trying to ascertain if the math is understood or not. This has been circumvented by students and teachers who memorize answers to the test questions, rather than understanding the subject matter well enough to answer any questions. Once they understand addition they can add any two numbers. The principle is the same with regard to "advanced mathematics". The practice is another thing entirely: memorize long enough to take the test.

"Our care of the children should be governed not by the desire to 'make them learn things', but by the endeavor always to keep burning within them the light which is called intelligence." ~Maria Montessori

"The essential thing is to arouse such an interest that it engages the child's whole personality." ~Maria Montessori

Once interest has been pricked discipline and concentration flow as naturally as water downhill, time stands still, and learning takes place.

"The first essential for the child's development is concentration. The child who concentrates is immensely happy." ~Maria Montessori

"Discipline must come through liberty. . . . We do not consider an individual disciplined only when he has been rendered as artificially silent as a mute and as immovable as a paralytic. He is an individual annihilated, not disciplined." ~Maria Montessori

"Teaching is a sacred trust." ~Joyce A. Rogers.

Base Ten Blocks For Fractions Success

Base ten blocks make fractions much easier to understand. The Fractions page on my website is in serious need of an over haul. Eventually I will get to it. Meantime there Are posts like this.

Here we packed more into the hour (but not too much more from the stand point of CONCEPTS), going over the same concepts using fractions tiles and multi-tens, and drawing them with symbols and practicing problems adding up to less than one. Also did a couple subtraction problems. Then ended with a few that were one and some more...next lesson will contain more symbols less blocks and more on improper fractions. All of this and all we learned was adding and subtracting fractions. Multiplication and division of fractions will come another da, and they are just as easy to present and understand using manipulatives.

Please read this from the POV of how you would present it to your students or kids, and note the common stumbling blocks to be avoided. Base ten blocks and manipulatives allow you to avoid the misconceptions in the first place. Starting with the most common misconception, that some how the rules have changed when we get to fractions. They haven't: we can only combine same kind with addition or subtraction.

I have this one kid I would really like to video tape but I don't want to embarrass him, because he consistently shows a basic lack of understanding of CONCEPTS. This is because he has never been exposed to them.

Asked him to add 1/2 +1/3

His answer 1/5. "Because if the tops are the same you just leave them alone and add the bottoms...or is it the other way around?"

When I showed it was 5/6 using manipulatives there was a lot of "ohh!" and "OK" and "I get it" so we went over the 5 basic concepts focusing on they have to be SAME before we can add them...and because he is still lacking in multiplication skills, I used fractions manipulatives to help him practice multiplication (and addition).  We could skip count this by 3's or by 4's...put the next over lay on and then we will be counting 5's...etc...you don't have to know your multiplication tables in order to do fractions. Use the fractions to help learn multiplication.

I also asked him during the course of adding fractions which was bigger 1/4 or 1/3...of course he said 1/4.

Visually Obvious.

Then before I showed him any of the fractions tiles and asked how many to make a whole one if I have 1/3...he said 3 and how many to make a whole one if I have 4ths?...4 so four is more than three. TRUE. But the more pieces you need the smaller each piece is...puzzled look. But as soon as I get the factions pieces out one look and it's VISUALLY OBVIOUS that 1/4 is the smaller one. "OH!" This child is a teenager.

Not stupid, just never been exposed to math concepts and manipulatives just rules, formula and stuff to memorize long enough to take a test and forget. He is a Classic American Math Student. Had he never met me he could probably have a bright career in climate "science."

We talked about 1/5 and 1/5...how many? 2/5. EASY because they are same. Once we make them the same kind we can add them. x + x is easy because they are same kind...you get 2x. One of something plus another one of the same thing gives you two of something.  Easy.  But if they aren't same kind we better make them same kind so we can add them. Then we talked about the numerator and the denominator. He had forgotten the name of "the bottom one"...de nom, de name, da kind of it...but he did remember the numerator which tells you how numerous the kind is...

"What kind of math is this?"

"Adding and subtracting fractions. About fourth grade level in most public schools..."

"But for your kids it's like first grade."

"Right."

We did several more problems until he got the hang of it using manipulatives...THEN I moved to drawings...and we stopped there. Tonight his sub-conscious gets a chance to put some things together and then we will work on going from blocks to drawings to symbols. Because he is a teenager I can go much more rapidly than if he were 6 or 7.

Then we talked about improper fractions and did about three of those just to give him a taste, ending with...5/6 + 4/9...could you think of a common denominator?

Symbols, Drawings and Blocks

"NO."

So he plays with his sliders on his multi-tens blocks and gets the answer. But still couldn't convert it to 1 and 5/18ths on his own...that's a concept for another day for now one and some more is good enough. Like remembering numbers if you try to remember too many at a time some of them are going to get lost so just a few concepts at a time is best.

Right now the concept of SAME and doing the multiplication is enough. Next I'll add more to that...which will further cement the foundational concepts of making them same before we add them. The rules didn't change we have to understand equivalent fractions and common denominators. With young kids first we play with the tiles then we play with the multi-tens, having multiple lessons in both. With this student he got it all in one lesson because he has more experience and is older and can handle it...if he was 5 we would have done less. Just the one concept of making them same and then practicing adding them using tiles; then maybe some drawing and then some symbols. That might take THREE HOURS. Then on a different day a lesson with multi tens...again another hour or two. Five or six separate classes, spaced out over time. 

Using "sliders" is the fun way to do it. Over all kids like using sliders more. If you don't have multi-tens don't worry you can just use base ten blocks out of your combo kit and get them out a pair at a time,  kids like this too and it's especially good for the hands on experience, it takes longer though which isn't a problem if you are homeschooling. Just for fun I uploaded this to blogger so it's a video you won't find anywhere else.

Can you also see how easy it is to talk about equivalent fractions and learn skip counting while we do?

For those with dyslexic students not that the image is reversed because I used my lap top's camera for all of these pics, but I am able to "flip' the photos but not the video. And it doesn't matter...base ten blocks level the playing field.

Want some Fractions Worksheets made for base ten blocks?

Percentages usually come next after fraction. Showing how to do percentages with base ten blocks is EZ.

BTW if you want to learn how to use the blocks to teach your kids I have SEVEN Hours up so far, but you need a special PT password. Go here for Parent Teacher Training. $15 bucks such a deal....

“A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator, the smaller the fraction.” ~Leo Tolstoy

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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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:

Pyramid Playing Produces a Preponderance of Productivity.

Playing with blocks makes math easy and fun for little kids...and given the proper tools and games and activities "just playing" with blocks can teach quite a bit of math. In fact this is how the Mortensen Method was born. One of the plethora of fun games and activities in your arsenal should be building pyramids of blocks. Walls and towers are fun too...entire math towns can be built. These towns can teach addends or multiplication or combinations of these topics and MORE.

Playing and having fun with math is foreign to so many parents they are sure it can't be this easy. Actually it is. You have to direct a lot of the learning but over all you will see a lot of it can be self directed.

Here are a few of vids that focus on just this one activity: building pyramids. Starting with this short one where we made nines:



Here is a slightly longer vid where we made 12's:



And here is a longer sample lesson with a child that has a few cognitive challenges, but you can hear him catching on after a very short time. You won't find this vid because it is UNLISTED. You will also find it on the sample lessons page.

In the past I have said I don't want to hit you over the head with it but due to some comments made by well meaning parents and teachers of late I am going to hit you over the head with it:

"Play is our brain's favorite way of learning."~Diane Ackerman
Contemporary American author

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

This is not a new concept:

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

"Man is most nearly himself when he achieves the seriousness of a child at play." ~Heraclitus, Greek philosopher 535–475 BC

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

"Play is the only way the highest intelligence of humankind can unfold." ~Joseph Chilton Pearce, Contemporary American scholar

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

"Children need the freedom and time to play. Play is not a luxury. Play is a necessity." ~Kay Redfield Jamison, Contemporary American professor of psychiatry

"Deep meaning lies often in childish play." ~Johann Friedrich von Schiller
German poet 1759–1805

"Children learn as they play. Most importantly, in play children learn how to learn."
~O. Fred Donaldson, Contemporary American martial arts master

Now if you so are so foolish as to think that you are wiser and smarter than that partial list of people who understand how important play is, I am sorry for you. Play is not just for recess and math can indeed be taught through play. Further, children who learn this way are not confused when it comes time to take tests, because they actually understand the math the questions on these tests are easy and they usually score not just well but in the top percentile of their peers.

With the manipulatives they can actually SEE what they are doing. It's not like this is another way to do math it is a decoding of the symbols in such fashion that both the conscious and sub-conscious mind can understand and better yet it is presented through play.

If they have Autism EVEN MORE emphasis on FUN is required.

More on the MAKE IT FUN theme. Here are couple of vids where we play math and the math portion is done many times because it's fun to shoot the walls down. They will do it over and over again because knocking down the walls with a Nerf gun is FUN.

These kids are having fun and the little boy you see there is only 5...note that the NO is removed from the lesson and he is encouraged to try and see if the pieces fit to make ten...ask questions: Is that tall enough...is that too short etc...build tens and nines and eights.


Out of an hour this was only a small portion of the math we did...this boy Tamu has Autism and is a little shy, but as you can see he is quite able to join in the fun. The idea is to keep the games quick and not to spend too much time on drill. They will get math facts as a matter of course.

Here what you see is us building a house for a lego craft. I also couldn't bring out the camera much because as soon as I did the dynamic changed, and as I have said before the first obligation is to the parents who are paying me money to teach their child. We also had fun building walls and shooting them but I didn't get these guys on camera.

As it turned out this was just the beginning of a large house...which I also didn't get on camera. Tamu got a lot of math facts presented to him and had fun while it happened. Many more exposures will be required before he "knows them" but this is a good start and the repetition is fun not drudgery.



We also did multiplication as well as addends for other numbers but most importantly we kept it fun and engaging. People always ask me how do you make math fun? Just play math.

Seriously. Get out your blocks and fool around, especially when the children are young. You just play and point out math concepts to them as you go. Simple things like a three and a four is the same as a seven...three 3's is square and the square root is 3...that means count one side...etc. Later when they see symbols the explanations make sense...

For more fun and games check Crewton Ramone's House of Math. This page has become popular: Math with Playing Cards. I keep meaning to add more games because there are a lot more games you can play using playing card this pages only gives you a partial list. Use your imagination and MAKE UP some games of your own.

The blocks are only limited by your imagination. Get creative. Have fun. Play math.

Ratios With Sarah

Ratios are easy. All you do is cross multiply. Why? And what if you for get the rules? Here is a series of videos staring Sarah who is studying for her GED. This series gets cut off before we finish but what is on vid is worth sharing. Remember this kid is autistic...but I don't treat her with kid gloves (anymore), and she is doing quite well with math. Look for other blog posts where she is featured and prepare to be amazed. Also look for a future post where the autistic savant rears it's head...she is beginning to recall math facts and remember seemingly random facts that she has seen before.

{I'll put a link in when I make the post. Note to self.}

In these vid we begin to see what do when presented with ratio problems and rather than give rules on when to multiply or divide we think about the relationships. Once we understand that then we can start making up rules to describe what's happening and what to do to get the answer. Note I give her no rules. Later she tells me the rules...unfortunately I did not get it on video. But by the last video you can see she understands it. Then and only then do we move on.



Note I put the P1 in front to make it easy to search and find the next vid...P1 Crewton Ramone and Sarah Playing Ratios and Relationships.



Note when I say tricky I am using her verbage because there's nothing tricky about these it's just math.



As they understand it they do it easier and faster.



And here is the final one where she shows she understands it.



After these we move on to problems where it's not just whole numbers but fractions but we didn't get any of it on vid...you can see more with Sarah on Sarah's page.

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Using Math Materials To Best Effect

I would Like to introduce you to this woman who has started making vids on Vimeo.

Seriously. Could these kids be any cuter?
And it's even more important to teach girls early because they need every advantage. Our culture puts females at a disadvantage when it comes to math starting very early on.

Here is her channel, Education Unboxed. She has opted to use Cuisenaire Rods, I am hugely biased toward Mortensen Math base 10 Blocks/Manipulatives but she is correct that they are pricey and many parents already have Cuisenaire Rods because they are cheaper. (They are cheaper for a reason IMO.) With just a little work, a few "mods" as geeks and nerds like to say, they can be quite serviceable for teaching math beyond just addition and place value. Her point is to make vids that parents/teacers/homeschoolers can use to put the materials they may already have to better use. I highly recommend her channel and vids and hope she one day makes a blog and website too.

If you can't afford Mortensen math materials, perhaps you can afford a set of the Cuisenaire Rods...and you can get started teaching your kids math and learning math right along side them...with all the FREE suport you get from The House Of Math and this blog and now her vids too you can't afford not to get started and have very few excuses left.



She says she is "just a mom" who wants the best for her kids and wants to help others help their kids too. Even more I want to promote her because so many make excuses that they can't do it because they aren't good at math or don't have a degree or what have you...to which I reply: "just get started." You won't fail and you won't hurt or damage your kids. Errors can be corrected if you make them and can be turned into teachable moments.

My comments and critiques are for her improvement NOT to put her down or denigrate what she is doing. Her point and so is mine that if she (we) can do it SO CAN YOU.

CR:
Another great vid!

OMG: your kids are so cute it brings tears to my eyes.

Fine job removing no from the lesson and telling them what they have. Play a game with yourself how to I remove the negative completely. Instead of it's not 11, show me it's 11 or Hmmm, what's this side called again? (Answer is x, and then plus one.)

Improve your x² by putting a stip of paper over the sides because her observation that it is 10x is correct in this case you can clearly see it. I made a video about this...and it is a common question. Is 10x = x²? And the answer is a little complex involving 10, -10 and multiples of 10; they are after all base 10 blocks. That lesson would be best saved for another day...

Just telling them it's x when they can see it is 10 is usually not sufficient. Solve that problem with a strip of paper. I realize you are improvising with the tools you have and you are doing a FINE JOB.

This; however, is pretty important. Math concepts aren't because mom says so. lol

There is a Montessori concept called "visually obvious." It is visually obvious that that one side is ten...it must be visually obvious that that side and all sides is/are x.

A few side notes. At one point the younger child made and x to the second not an x square, which is good: it was one by nine...you could point that out in a later lesson. x² doesn't always have to be square! Especially if you are doing third power algebra...x³ dosen't have t be a cube either...in fact it will make higher power algebra impossible to present if you try and stay in three dimensions. You may casually mention this if she does it again...that way it's a natural discovery and not a "lesson".

Also they are never wrong. They are just getting more information. (You know this I am just reiterating for those reading.) You are a patent and gentle teacher. You may want to direct them a little more and let them figure out some of their mistakes on their own instead of just showing them so they can have their own ah-ha moment. You accomplish this by asking good questions using control of error and putting them in a situation where they can not fail...each one of those is a full dissertation and they are covered lightly on my concepts page.

Good questions:
Does yours look like mine? How could you make your square look like my square? Show me. How are they same, how are they different, what's the name of this. Etc.

You can also avoid and control error with use of the three period lesson.

Lastly you casually mention they are completing the square when they are in fact completing the square. That is great! You could take a second to ask how they do it...the answer you are looking for is by taking the x and splitting into two parts...this seems small but it's huge. Later when they do the quadratic the (b/2)² will make sense...

I would like your permission to your vids on my website or blog once in a while where they will get more exposure and hopefully encourage others to get started teaching their own kids math. I would also like your permission to put links in these comments because I have covered a lot of this in detail in other places.

Third please contact me via email...info is at my website. Just click the contact tab.
I am a master trainer. I was certified by Jerry to train trainers to train other trainers...not just train teachers to teach kids. The difference is understanding the why of things. You could be a mighty teacher if you wanted to be. You never know where teaching ends...somebody could see your vid and be inspired to do more...a kid could stumble across it and have an epiphany...you're making a positive difference.

One more time: FINE JOB.

Education Unboxed:

Yes, I absolutely do need to cover the sides with paper. I'll be doing that soon!

I THINK I understand what you are saying about "x squared" (not sure how to get the little 2 up there!) not having to be a square. Though I just learned last year that "squared" actually means a square! So, now you're saying that it doesn't HAVE TO BE in a square shape, right? Just that 9 is a square number because it COULD be made into a square? And when it's not in a square shape, then we call it "x to the second?"

Yes, please feel free to post my videos anywhere you'd like. The only reason I made them was to help other people (so they wouldn't have to do the hours and hours of research and reading I've done over the years). And, yes, links in the comments are fine.
I will contact you through your website. Thanks!!!

Then as you can see in this next vid she does...



A couple of notes for ALL teachers including myself: REMOVE THE NO FROM THE LESSON. Migrate to good habits early, but don't worry about doing it wrong if you are wrong just correct the mistake. Some students can be migrated to the correct way just by modeling, they see you doing it correctly so they change to make theirs the same as yours. Occasionally you get the child that wants to be different from you just to be different. These minds are to be encouraged but certain rules are not up for debate, we read left to right for example your blocks should mirror this...here are my comments so far:

Many comments to make. This is great.

Remove the no from the lesson.

Need an equals sign instead of a solidus...

We read left to right...the girls need to be (gently) corrected to put the units in the upper right. It doesn't really matter ( 3 + x )( 4 + x ) = ( x + 3 )( x + 4 ) however ( x + 3 )( x + 4 ) is more correct because we count in descending order. (Count the big ones first.) Also (minor details) move toward putting the parenthesis closer together. Again they aren't wrong they are acquiring more information...and you are simply moving them to more correct notation and mathematical syntax.

Also DRAW pictures. This is the bridge in the mind between the concrete and the abstract. A blend of symbol and blocks is great...
Will add more later.

Keep up the GREAT work.

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Online Math Video Tutoring Is Fun Too

Here are a few Screenshots and vids from some of the Online Math Tutoring I do.

I have found that online math tutoring is fun and the parents have found it is effective. All you need is a set of blocks.

Here is a 12 year old doing some high school math where we are exploring the concept of f(x) and what it means to evaluate algebraic expressions for various values of x. Sound complicated but his 8 year old brother gets it too. We do algebra because it teaches and reinforces basic operations, because of the algebra we have to do addition and subtraction multiplication and division. Their basic skills have improved since I've met them but we rarely drill multiplication facts...

This is one of my favorite students. She is a handful but she she is a free spirit, undisciplined and I dare say a bit naughty at times. But she has a creative mind that needs to be nurtured and rewarded, cultivated not punished for thinking differently and finding the structure of math a little boring. My job is to make computation easy and fun so that later she can "do math" which she will find is far more than computation. Computation is how we do math, but math involves problem solving logic and reasoning.

She is having fun learning addends...I had one parent ask me, "why not just cover the blocks why do you have to put a bag on their head?"
"Because it's more fun."

Building a tower is fun whether you are a boy or a girl. Here we are building the addends for 9 thru 6.  This child is eight. A pox on teachers who think math time can't be play time. She often goes through and tells me all the combinations she has made, although she doesn't have to. Her subconscious also develops a memory for the addends and this makes recall instantaneous.  She doen't have to think or compute...6+3 is the same as 9. We've built it many times. I should have taken pictures of the many times the tower fell over and needed rebuilding...which is also fun. Online Math Video Tutoring is pretty cool. We are as far apart as we can be almost...from Hawaii to the east coast. With the net distance doesn't matter.

After you get them built try playing Jenga with them...take out a block or two without knocking it down. Why? Because it's FUN.

I believe this photo captures a thing called pride. "I did this."  Good for self esteem.  Good for making math fun and giving a positive association with math instead of a negative one.

I find algebra much more useful for teaching math, building towers is fun but so is making these rectangles factoring quadratics not a problem...here she is completing the square and factoring x² + 10x + 25...she gets multiplication, addends, division and algebra all in one lesson. With the towers you get addition and subtraction of addends and fine motor skills but that's about it. Algebra is a much more powerful and effective way to teach more math all at once.



It still amazes me traditional teaching separates the inverse functions of addition and subtraction and multiplication and division. You can see the relationships when you play with the blocks. 6+3 = 3+6 and 9 is made up of a 6 and a 3 in this case so if you make a 9 with a 6 you need three and they see that 9 - 6 is 3 and 9 - 3 is 6...all in one shot where on paper it would take a but to list all those facts. Manipulatives make some operations MUCH faster and easier but eventually you will see paper and pencil really is the much faster way to do math. With Online Math Video Tutoring I can teach anywhere on earth, the concept should still boggle the mind. ANY subject can be taught this way including eye surgery as it turns out but, "dammit Jim I'm a mathematician not a doctor..."



Even when google's vid feed is messed up you can still do a lesson...and algebra is easy even being green. You may also note that I'm pretty generous with what constitutes "one hour" if we are having fun and they don't notice one hour can be 105 minutes...lol...sometimes it's a little less sometimes it more sometimes it really 60 minutes. I stress again with your kids math time shouldn't be rigid but more flexible and the lines between math time and play time should blur and merge.

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Big Blocks Big Fun Big Concepts.

Lately there seems to be a bit of a resurgence in understanding that those big wooden blocks had more purpose than meets the eye.



There are also articles appearing on blogs like this one and others. People seem to be rediscovering a very simple idea. Early is better when it comes to language, and math is a language. Further, the more senses you use the more learning takes place and the easier it is to understand. The brain likes multiple inputs.

Here is a simple wall made with the big blocks, also a lesson on proportion,  wholes, halves and quarters as well as addition and multiplication...just by asking simple questions. What if all the blocks were little ones...well them the bottom blocks would take four...in fact each row would be four...and we can sing a little song about fours as we figure out how many fours it would take if the wall was made of the small blocks, what if we used the halves? Then we'd be counting by twos...  For more advanced students (and teachers) we could do a quick lesson on bases...the most important part is to PLAY.  These kinds of lessons have to be quick and easy and as natural as possible so the kids learn without knowing they are learning...we're just playing using our imagination and asking silly questions as we build stuff.  It's not a formal lesson per se.

Here for sure we are playing. It's a fun preschool math activity AND they learn things that are not so obvious to the casual observer...as Doug Clements explains above.

We talked about the words symmetry, symmetric, symmetrical...

Bust mostly we had fun building a castle.

Then of course there was a little formal math where we practiced all 45 addends...this is a math activity that will be repeated MANY times before the recall is instant and mastery is achieved. Some of the slower teachers will drill these addends over and over again on a daily basis until the students have them down and have acquired a distaste for math in the process. The more enlightened teachers will make this one of a myriad of math activities that keep preschoolers, kindergartners, and first graders engaged for hours over many days and weeks.  Kids never get tired of playing.



Here is another fast easy lesson on finding the area of a rectangle where the students tell you the formula not the other way around. They will forget this in a few weeks, and you can teach it again as a fresh lesson. Seriously. After a a few times they will remember it...internalize it, understand it and not because they looked at these symbols and memorized a formula:

1/2bh = A

The lesson with the blocks above is SO much more powerful than even this lesson:



However, I posted that video several places and the comments about it were how powerful and easy a drawing can be to illustrate the simple concept. I find that presentation creates HUGE "AH-HA" moments in students and teachers alike. Picture worth a thousand words as they say. Kinesthetic experience with blocks worth exponentially more than that...

Learn to use your base ten blocks.

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