Here you will see students as young as 4 and 5 years old doing algebra and "advanced" math, without ever knowing it's supposed to be hard. You are invited to learn how to use this method...
Showing posts with label 5 Minute Lesson. Show all posts
Showing posts with label 5 Minute Lesson. Show all posts
Here is a quick video showing various ways of factoring a quadratic. Using the the blocks to show what we are talking about with each factored expression of
3x² + 17x + 24
Can be factored several ways. The most common way is a great example of economy of symbol.
Note how we are still all positive...keeping in mind degree of difficulty. Lets understand some basic concepts before we start adding negatives coefficients to the mix. Most text books just dive right in instead of taking it one step at a time.
The blocks take the fear out and make the symbols relate to something tangible in reality. They can actually see it.
Then when you show your students the other forms it's obvious. Then when it's time to start graphing these bad boys finding zeros and more points and the vertex and y-intercepts and such is easy because they already have this much under their belts instead of being inundated with it all at once.
The student in this video is shy and as soon as the camera goes on he chokes up...had the camera not been on he would have had an easier time answering my questions. Anyhow the action figures or lego men or whatever you have are handy to help get the point across.
Got the Star Wars effect going on here...a long time ago in a galaxy not far enough away they were still teaching math like idiots. Then suddenly math was cool...and the kids could see it and the symbols made sense because they could decode them and everybody was laid back and groovy.
For more get a password and head over to the house of math.
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.
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...
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.
Getting to know a little about CUBES is important. Children need to have experience with numbers. Square numbers are good to be familiar with too and so are cubes. The problem with a lot of base 10 blocks is they represent cubes as...well, cubes. Which makes sense except that then the manipulatives are limited to the third power then. How do you show powers past 3? Simple you don't.
Here are the first 12 written out. But certainly DON'T just write them out as a drill until AFTER you have built them and talked about them and played with them a bit first. Here is a vid called Crewton Ramone Squares, Cubes and Division because it's about squares cubes and division. I'm creative like that.
Mortensen Math keeps it in two dimensions. Arithmatic not physics. (x)(x²) = x³ or (x²)(x) = x³ instead of (x)(x)(x) = x³ this is a subtle but important distinction which allows me to teach very young students higher powers and so called more advanced mathematics.
Before you get to cubes might be a good idea to play with squares and square numbers. My students will write them out several times during a course of lessons. So they see the numbers and have some experience with them. This will stand them in good stead when they take standardized tests. Many students get through high school without ever knowing their squares and cubes and at Crewton Ramone's house of math we go all the way to 25 with these. (And out to 20x20 on the multiplication tables.) Seriously, your kids know the names of the Pokemons but they don't know the name of 17² or 17³...or maybe it's all the characters in Harry Potter...or they can recite lines from Twilight, but you get the idea.
Squares and cubes should be familiar and easy and part of their instant recall just like 2x2 or 10x10x10...and make sure you eventually go out to 25. You have 12 years to get this accomplished. Here is a short video where Sarah and I are studying for her GED and cubes make their appearance...we only go to 12 here.
My favorite part about this vid is the comments: people just don't know what to make of me or it. This is a proof of concept vid...needs more work but I want to make math music vids that are current. Like Weird Al Yankovic except for math...change the lyrics of popular songs to explain math concepts...and then have puppets and good looking kids and base ten blocks dancing around to the beat.
This is just a proto-type if you will. I need a small crew to do camera, song covers and puppets and most of all editing.
Anyhow this one was designed for little kids...three to five. And it was designed to be watched more than once...the concept is multiplication by twos...and getting to know the names of the base 10 blocks.
Unconventional. Odd. Different. People not sure what to think. No pocket protector. No nerd glasses. Multiplication by two's for the little kids.
No. This ain't your grandma's mathematics. It's Crewton Ramone for the wee ones. Just a few math concepts at a time. Math needs to be cool again...currently it is the domain of nerds who do not reproduce...
You need more than one example but this is a quick 3 and a half minute lesson on how to find the inverse of a function.
In this case what is the inverse of
y = -4x² + 2 ?
Due to my math experience I looked at the multiple choice answers and knew which one it had to be...however due to my carelessness when I tried to show him why I got the wrong answer because I left off a negative when I copied down the problem. We did the problem more than once and this vid shows the last time we did it.
Two principals here:
One: NEVER TRUST THE TEACHER.
Two: You aren't wrong you are just getting more information.
Too many parents (and some teachers) are afraid to work with their kids because they might get it wrong and be embarrassed or what have you. Just get to work and see if you can get the answers...sometimes it's good to get the answer first and then look at the problem. I have had more than one student say it's easy when you know the answer. That's true and then with the thought this is easy you can see how to solve the problem and you know where you are going.
Another thing with some multiple choice tests: you can see answers that reflect common mistakes or misunderstandings of concepts that would lead you to pick the wrong answer. Talk about them. Talk about why they would put that answer as a choice on the test. This often helps deepen understanding.
Now in order to learn how to do these it requires more than on 3 and a half minute video. They can get the rule "just switch the variables and solve" but they will forget the rule in just a few weeks...
You need at leaste three examples of which this would be one of the last ones. They should have also spent some time understanding the basic concepts of Hero Zero and No Fun Get Back To One. (HZ & NFGBT1)
Here is the first example I showed this particular student:
y = x² therefore the inverse would be y = ± √x
First we "swap" the variables: x = y² which is the same as y² = x and solve (NFGBT1) by "square rooting" both sides: y = ± √x
Then you just make them slightly more complex: y = x² + 1 etc...
Then you get two thumbs up because they "get it."
"Example isn't another way to teach, it is the only way to teach." ~AE
Here is a quick screencast, less than five minutes showing two problems.
6x + 2 = 14
There are 6 Girl scouts with some cookies. I have two cookies. Together we have 14 cookies do we all have the same amount? (...or how many does each girl scout get?)
9x + 3 = 21
Nine kids have 21 apples divided among themselves, they have three left over...how many apples does each kid get...?
There's a lot more I would have said on the first one by way of explanation...but it was on the fly unrehearsed one take...the problem solving page goes into more detail because I'm sure after watching these which are NOT beginner problems you will have questions.
For a more complete explanation on problem solving go to Crewton Ramones House of Math.
Some times it feels like 10 minutes and two hours fly by.
Really.
Here are two 5 minute screencasts covering a two hour session with a student who is 11...his friend did not show up so it wasn't quite as much fun and we did not go as fast because as he said, "it's no fair trying to beat you, you already know all this stuff."
We did cover a lot of ground though. We had fun and two hours do go by FAST.
If you see my add on Face Book (those who live on Maui) don't be afraid to click "like" or click through to my webpage...I am not paying per click but per thousand impressions...I did the math, PPC did not make any sense at all.
