DBoyz Playing With 3rd Power Algebra

"You have to make a post, dad. We haven't done anything on Math Genius Making for a long time," says he who be six.

So here is a post but if you are new to base ten blocks and using manipulatives to teach algebra you may be a little lost. A little background can found at The House Of Math that leads to the algebra tab. You might also search Crewton Ramone 3rd Power Algebra...lots of videos that start at the beginning will come back. You can see that I use the algebra to teach other math concepts.

Basically all we are doing is giving a visual representation to the symbols, giving them geometric form makes them much easier to deal with and count. These boys have lots of experience playing with manipulatives so this drawing is just in black and white but you certainly wouldn't want to start here...this is several years of playing around coming to fruition.

But as you can see it's paying off, they can see what they are doing and the symbols have some meaning for them. They understand factoring means form a rectangle and count the sides and it's more akin to a puzzle than a formal math problem. Sometimes they make up their own, sometimes I tell them the symbols and they have to build it and count the sides (factoring), other times I tell them the sides and they have to build it (multiplication), and sometimes if it's a tough one I give them the whole rectangle AND one side they have to count the other side (division), they know division is the easiest because you get the most information. Here is a popular blog post covering division using base ten blocks...there are others too, just search for them. (Crewton Ramone Division.)

Hopefully you can see the benefits to you kids of learning math this way. Just because they can do some of this doesn't mean they have all the multiplication tables mastered and can do large subtraction problems in their heads...it does mean that they understand quite a few math and specifically algebra CONCEPTS that other children their age haven't learned yet and may never learn. We just play around with algebra concepts. This simple problem can be drawn three ways, because it can be factored three ways. It can look daunting to a high school algebra student, but we know it's "easy peezee lemon squeezee."


x³ + 6x² + 11x + 6 = (x² + 3x + 2)(x + 3) = (x+1)(x+2)(x+3)

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

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

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

This video had several takes in this take we miss them counting each rectangle carefully before they realize they all have the same amount, they are just shaped differently, that is they have different factors...

Keeping it in two dimensions makes the arithmetic easy. You will note I did not write out all the different symbols for all three because I wanted to keep it simple but we did talk about them and the side that can be factored is drawn again to the right. These are easy for them to factor and they can see that x² can have two shapes, the one they are used to which is indeed square and the one where it's "hiding."

At this age we are most interested in counting, addition and multiplication and addends than we are in the actual algebra.

I 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 we add new concepts they will be easy and unclouded by concepts that we have already mastered. This is what we mean by degree of difficulty or baby stepping 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 already being understood so it doesn't add to the confusion.

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. Remember, hese boys are 6 and 7...

Supremely Simple Subtraction

Subtraction is easy if you let it. We just fool around and play blocks do some subtraction do some square roots...casual home video style. Here is the subtraction page at CRHOM.

DIY Liposomal Encapsulated Vitamin C or Lypospheric Vitamin C

Here is vid about making Liposomal Encapsulated Vitamin C, note there is already disinfo on the net where they tell you all you need is a blender...that will not make it Liposomal:




We use the blocks to figure out how many minutes in 480 seconds as we make our concoction.

Look over these links:

The link that got me started:

Video: Living Proof: Vitamin C - Miracle Cure?
http://www.3news.co.nz/Living-Proof-Vitamin-C---Miracle-Cure/tabid/371/articleID/171328/Default.aspx

Vitamin C mega-dosing continues to unleash healing miracles around the world
http://www.naturalnews.com/034591_vitamin_C_mega-dose_healing.html

Thomas Levy Talks To Vitamin C Can Cure Coalition Part 1/9
http://www.youtube.com/watch?v=d9Sa02XnteA

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

http://www.crewtonramoneshouseofmath.com/


http://crewtonramoneshouseofmath.blogspot.com/

Counting Fireworks

Little kids like to count. They are curious about "how many?"...use this to your benefit.

Count.



I lit fireworks until my thumb hurt from flicking the lighter because we didn't have a punk. Many more than 216 times lol...no one was hurt (always a consideration when playing with fire and gunpowder) and a very good and exciting time was had by all.

Happy New Year!

Food Fractions Fun.

Bringing home the concepts without using pens or symbols. If you do it enough one day it will click.

People often then lessons at this age are wasted, but actually the mind stores it all and it can come in handy later and they may not even remember how they know or why they know it they just know it.

Also later when we do have a pen out and are making symbols the symbols will make sense and they have experience to draw on...



We were doing lots of math and toward the end of it I remembered to get the camera out. Mostly we were doing simple subtraction and division and then we did some fractions...

This is great everyday math.

It would be indeed be sad.

This vid speaks for itself but the point is simple. You don't need to be able to write to learn math concepts.



The video we are about to do is here and will soon also be on the fractions page at the house of math.

Feed Their Math Brains. Make Milk.

Here are a couple of vids about food...well drink actually. Many people ask me about this so here it is. All you need is a Vitamix or other high powered blender.

Here here is the eggnog vid:



Here is the vid step by step make your own milk out of water, cooked brown rice, oats, cashews, hemp seed, golden flax.

Fun Kindergarten Math Activities

Here is a list of puzzles for my two young problem solvers:

Many older students might find these a little daunting. When presented correctly these problems are easy and fun and teach quite a bit of simple math to the younger students whether they realize they are learning it or not.

They ponder the rectangle.

Algebra is not usually considered one of the most by your average teacher or homeschooler but it is.  See for yourself:



The video above is from a longer (21 minute) video where the 5 and 6 year old ask for more of a challenge because factoring this polynomial posed no problem. They got more of a challenge a little later on.  Algebra is a fun kindergarten math activity if presented correctly. It's just a puzzle. Math requires thinking skills, logic and reasoning. Here the boys develop those skills in stages doing simple mathematics in order to solve the puzzle. They learn to add and multiply while they do algebra,  if we had negative coefficients they would also learn to subtract (you can see that on the password protected pages at the house of math under "Advanced Algebra". As you can see this could even be a a preschool math activity, these boys have been doing math like this since before they were in school. All it is, is counting you could build the rectangles and have them count it. Here they are progressing naturally where they get the symbols and they have to build the rectangles and count the sides. For younger students just counting a complex rectangle can be a lot of FUN. This is math enrichment at it's best. Fun and easy, builds confidence doesn't break it.

Using base ten blocks give them hands on experience. Because they have manipulatives, the playing field is leveled and age doesn't matter: if you watch the whole video you will see there are times when the younger student figures out what to do before his older brother does. The older brother has more experience counting, adding and so forth but they both get to practice their innate problem solving skills.

Keep it fun and your students will want to learn. Algebra is just generic math, and as they play here you will be amazed at the basic concepts they discover for themselves and internalize and are then able to apply to base ten mathematics as well as other problem solving activities in algebra and math in general.

This short vid links to this longer video:



Allow them to work the problems give encouragement but don't do it for them. Very soon you will see they are doing "hard problems" with ease. Math really is child's play.

Erector Set Provides Hours of Fun.

Happened to see one of these sets in Costco, it was at a great price...batteries included...had to get it. I was a bit concerned because the youngest is only 5 and it said ages 7 and up, but my worries were unfounded.

They spent hours and hours building and playing...had to throw a little math in there but over all they spent two days creating their space ships. An hour before Chinese lessons on Saturday, another hour after wards and then first thing this morning until the evening...

Erector Sets; Updated but still hours of enjoyment...they are quite excited to build more, next week this week they built "the good guys".

Teaches cooperation, patience...develops fine motor skills, practical problem solving, the basic mechanics of fasteners, and the list goes on.

Daughters should also be exposed to this...this is part of the reason most men don't have to think about which way to turn a nut or a screw. Both boys had never really put a nut on a screw, nor had they used an allen wrench. So we practiced a little bit first. Once they figured out how to get the nut on they could get the parts out and put them together.

At first it looked a little intimidating but I told them just do one thing at a time and keep going. For the first few hours their spaceships didn't look much like space ships.

Burt as they built the parts and put them together they started getting excited as they could see it coming together. There is an excellent allegory with math here. Imagine if all they ever did was practice putting nuts on bolts. Then endless assembled parts but never got to put the parts together...and had no idea what the parts were for for or how they were going to go together and never got a chance to see the space ship they were building.  That's pretty much the sate of mathematics in the USA. As one person put it all scales no music.

Finding the parts needed out of all those parts was a task in itself...

And once you got the parts then you needed to put them together.

But pretty soon they started looking pretty cool.

The older boys ship took a lot of work and quite a bit of problem solving...he learned very quickly to do things in te right order and follow instructions exactly...he had to take things apart several times and put them back together again..."you weren't wrong you just got more information."

The younger boy's project was easier. 

Putting the stickers on was a lot of fun too. The younger boy especially was excited to put the stickers on...and help his brother choose which ones to put on.

Both of them had moving parts which made them that much more fun.The wings move, there were LEDs for lazers and missiles that shot out.

The younger boy knows his addends for 10 by heart no thinking...now the rest of them have to be mastered. These are the nuts and bolts of math. Making addition and subtraction EASY and allowing him to count effortlessly. This leads to multiplication which allows him to count very, very fast, and since all math is, is counting plus some reasoning and critical thinking skills getting the counting down will make the computation portion of the mathematics a non issue.  The thinking skills can then be concentrated on and mastered. Again, once you understand the concepts all they can do is change the numbers...but the "problems" are all the same.

Righty tighty lefty loosey...of course had to throw some math in there but they popped out of bed first thing this morning and have been at it ever since.

They really got a sense of satisfaction out of building their own toys. I help them when asked but for the most part they did it themselves. Next week they build the bad guys which look a little more complicated.  But they have some experience now and confidence. In the future even more complex sets can be obtained and built...and then one day we can work on cars together.

Playing With Electricity Some More

Playing with Snap Circuits Pro:

Using "snap circuits pro" all by themselves, Dboyz make a fun little device. The 4YO did most of the work, and the 6YO completed the circuit and we went into a dark bathroom to test it out. Great activity, they came up with lots of uses for "their invention..."

They are learning to follow instructions and copy pictures or plans to make things in physical reality...a skill required in science and engineering.

Also note that the smoothie ingredients are "coconut sugar" not coconut, sugar...

Exchange between the older boy and myself:
"So when you were my age there were no computers or electronics?"
"There were electronics and computers, but only big corporations and the government had them.  There were no laptops or smart phones...certainly no youtube or ability for me to make video's and put them on the internet because there was no internet."
Eyes widen, mouth drops open as he contemplates...

K-Mart Counting

We were in K-Mart and we came across cases of bottled water. My little boys decided to count water bottles by 6's and then by 4's. We could count way past twelve 6's!!

Then we figured out each case had 24 bottles...and each row on a pallet had 12 cases and each pallet had rows stacked 6 high...that was more math than they could do but they did understand that 12 x 24 was one row and 12 x 6 was the number of cases on a pallet...that they could do counting by 6's and then it took a little reasoning to figure out that 72 was the number of cases on a pallet and we would have to multiply by 24 to get bottles of water.  There are lots of ways to count that, we talked about 24 and 24 to get 48, and ten 24's to get 240 and then 240, 7 times plus the 48...but the 240 times 7 was more than they could handle in their heads.

For older kids you could figure out how many ounces and then how many gallons of water...and then how much each pallet weighed in water alone at 8 pounds per gallon...

Math is all around you and math time is anytime. It's fun to count.

Playing With Electricity

I bribed them; told them they would get chocolate covered goji berries if they came up with a better project than just turning on a light or turning the motor. So they did. Here is what they built:

4 year old: The snap circuits pro is easy to make for you and you can make what ever you want BUT you have to make a circuit.

6 year old: Circuit means it has to circulate. That means go in a circle. The circuit has to be complete. It will turn out the way you want, just look for the numbers and letters and follow the instructions.

Capoeira

Getting a solo lesson because nobody else showed up. I look at these pictures and realize what a little boy my little boy still is even though he's grown quite a bit in the last few years.

Blurry but we put it in anyway.

BI says: Capoeira is fun.  Capoeira is a mix of fighting and dancing.  I like to move my body.

I am stretching to get ready for practice.

Play Math, Feed Brains...

Little boys playing with cars is as natural as summer following spring...just add a tiny twist and they add some math knowledge too...I was quite surprised when I asked  the older boy what 7 plus 3 was and he responded 9...took him a bit to realize it was 10.  More practice.  They get more than math out of it too, they get to refine their motor skills, and of course a place to park their cars...they have more than 5 times this many cars...when we were playing with them we also counted wheels. Which means counting by fours. For you adults, the wheels are the multiplicand and the cars are the multiplier, and we would write it 4 x 6 = 24, multiplicand, multiplier, product.   That is 4 taken 6 times NOT 6 x 4 which is the same product but we didn't have 4 cars with 6 wheels each did we.  The 5 and 6 year olds (and even the 7 thru 12 year olds don't care and you don't need much of a lesson on this at this age. I mention for the confused adults...soon we will tackle why we invert and multiply too, but not today.



The "milk" is made in a vitamix, soon we'll have a vid on that too. It's pretty easy to make, just stick the stuff in and put it on high...nutrient dense food, in liquid form.

Putting Pictures On The Blog.

Today I am learning how to put pictures on the blog. First we have to get them from the camera to the computer hard drive. Then we can get them to this website! Once they are here I can tell my dad what to type about them.

Ants on a log is fun thing to make, if you have holiday coming up ants on a log is a fun thing to make.

Your kids will love it. It's a great snack. I can eat 4 in one day.

I'm not going to say anything about that.

I'm playing cars with my dad and my dad is cookoo and my brother is cookoo, but I'm not! I'm just making a face!


*the captions were dictated to me by the older boy...

Is 29 Prime?

This came at the end of a long discussion about numbers. First we did some simple multiplication problems for the 4 year old. We had just woken up from naps and were laying on our backs, them using me as a pillow.

"What's 3 x 3?" I ask.

"6!" No look of approval. Older brother is bursting at the seems.

"Count by threes! 3, 6...." He says. His brother doesn't answer. "NINE it's nine! Everybody knows that!"

We played with multiples of other small numbers like 2, 3 and 4 and 6.

We talked about square numbers and identified square numbers up to 36 which took a bit of thinking and work, then for the older boy I asked him factors of numbers.

"What are factors of 12?" I ask. This is a degree of difficulty higher than just multiplication.

"Three 4's." Without hesitation.

What else?

[As I type this I hear from the other room "There's popcorn everywhere!"]

"2's...."

"How many 2's?"

"5...?" Again no look of approval. "No wait..." Begins counting. "6, I meant 6."

Count with your kids. We go on to factor 18, 20, 30 and more. No blocks no symbols, just talking about numbers and counting. Instead of story time, we had number time. Next time we play blocks they will see in the concrete what we were talking about. 29 made them count by 2, 3, 4, 5, 6, 7, 8, 9, before they decided it was indeed prime.

I hear "read with your kids" all the time. I never hear "count with your kids."

Count with your kids.

Dboyz Start Blogging

There was quite the debate over what to call this blog. "Dragon Vrs Man", "7657", "Math Dragon Genius", "Math Dragon 7657" and a host of others were bandied about. This blog will be about math and video games and stuff.

From the point of view of the child...as they get older less me more them. Why 7657?

http://www.m0ar.org/7657

Pirates. Dinosaurs, these are just two of their favorite things...