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...
Improper Fractions are easy to understand, if you have some one who can explain it in a way that you can understand.
"No concept is beyond the child if it is explained at the child's level."
This lesson can go a lot of ways, it can be a fractions lesson, it can be combined with a measurement lesson, it can be in introduction to more fractions concepts, it can be an introduction to algebra concepts, it can be a lesson on division and multiplication....in the video I was accompanied by a peanut gallery consisting of a 4 and 5 year old and the lesson was for an Autistic child so I kept it simple and we did fractions, measurement and multiplication and division....but above all all we did was COUNT and that's the way we always start.
The fraction has the what kind part and the how many part all in one place, the top tells how numerous the numerator and the bottom tells d'nom, the nom, the name of it: the denominator. When the denominator is bigger than the numerator we call this an improper fraction because there are whole numbers hiding in there...our job is to find out how many. Let's start with 7/2 = ?
It's easy for the student to count how many twos are contained in 7 or to measure 7 with 2's. They can see that we are counting 2's and there are four of them of them...but wait we only can count THREE whole ones and we use a part of the fourth one, one out of two parts and we call that one half...
In this problem we ended up using 3 of 6 and so we did a couple of lesson on reducing fractions. There are several ways to explain it.
We can look at the relationship, it's one to two, one three on top two three's on the bottom.
We can expose the common factor of three by turning them on their sides, and counting the edges 1 x 3 / 2 x 3 and see 3/3 is ONE.
We can still see the ratio of one to two if we look. You need to do many problems like this for them to be able to do these easily but start off small so they get the CONCEPTS under their belt first.
Here is a short vid explaining these concepts with comments and button pushing by the four year old:
Continuing down the algebra path with a 6th grader who is getting math enrichment.
Right off the bat we went to identifying the pieces we were going to use to do a "problem" with
2x4 + 7x3 + 10x2 + 7x + 2.
Use a three period lesson to make sure the student is comfortable with the terms and pieces we are going to be playing with.
Note how we stay in arithmetic not physics when we move to the 4th power explanations, staying in two dimensions keeps otherwise unwieldy problems EASY. Here the student labels the parts and gives their factors.
Then doing problems like this are easy and fun:
You can teach little kids, and I mean little kids like 4 and 5 year olds, all kinds of math using 4th power algebra. This student happens to be 12.
Here is a bright 6th Grader who is coming for math enrichment. The screen casts and pictures are from his 2nd and 3rd sessions.
It is quite enjoyable for both teacher and student when we are not panicked because we have to pass a test or make up a bunch of homework, or try to get the grade up from "F" to "A".
Here we see the 12 year old student who is in 6th grade doing math that many high school students have trouble with, and he is doing them with ease. It's fun.
This is his second time seeing them but his first time where he has to do everything by himself. Below you can see him using both symbols and drawing AFTER he has "built" them with the base ten blocks. You will find that without the blocks students have a hard time drawing them on their own. They need to get their hands on them. I know many people look at this blog and website and wonder how little kids find this easy when just by looking at the pictures or even the videos they do not find it so simple, especially if they are unfamiliar with the method or manipulatives. You need the blocks to play with, it's very important for learning. As I mention in the screencast the emphasis is not so much on algebra as on multiplication, factoring and addends...they learn to factor polynomials at this age as a bonus.
The drawings lead naturally to the symbols. Start in the concrete with manipulatives move to drawings and last go to the symbols. Since math is a language based on 5 basic concepts, we can go from algebra to fractions easily in the same lesson...all we are doing is counting different things.
Here you see the easy way and the hard way. You don't see the blocks or drawings but the student did.
Here are drawing and manipulatives being used to illustrate this story problem.
Ben takes 4 hours to clean the yard. Bob takes 2 hours to clean the same yard, how long do they take working together? And another problem, Ben takes 5 hours to clean the yard. Bob takes 3 hours to clean the same yard, how long do they take working together?
Math brains need good food to power them...not processed sugarfied cereal dowsed in artificial food coloring.
Oatmeal is always good but black rice is even better.
Simple: cook black rice.
Put it in bowls.
Handful of raisins.
Two tablespoons of coconut milk.
I use a Vita Mix to make rice oat and cashew milk.
A teaspoon or two of honey and mix it up...
"Just a spoonful of black rice bran contains more health promoting anthocyanin antioxidants than are found in a spoonful of blueberries, but with less sugar and more fiber and vitamin E antioxidants," said Zhimin Xu, Associate Professor at the Department of Food Science at Louisiana State University Agricultural Center in Baton Rouge.
"If berries are used to boost health, why not black rice and black rice bran? Especially, black rice bran would be a unique and economical material to increase consumption of health promoting antioxidants," added Dr Xu.
Coconuts are seen by some as a miracle food, helping protect and cure the body of internal and external ailments. Coconut milk has many uses, most of which build up the immune system and the body's defenses. You can find coconut milk in the ethnic foods section of a local grocery store.
Nutrients
1. Coconut milk contains many vitamins, minerals and electrolytes, including potassium, calcium and chloride. Saturated Fat
2. The saturated fat in coconut is made up of short-chain and medium-chain fatty acids the body quickly turns into energy instead of storing as fat. Therefore, even though it's high in saturated fat, coconut can aid in weight loss. Lauric Acid
3. Half the medium-chain fatty acids in coconut milk are composed of lauric acid, which is anti-viral, anti-bacterial, anti-microbial and anti-fungal. Coconut milk can help boost the immune system. Dairy-Free
4. Coconut milk is a dairy-free alternative for those who are lactose intolerant or allergic to animal milk. This vegan drink is also soy-free, gluten-free and nut-free. Relief of Ailments
5. Coconut milk is known to relieve the symptoms of sore throats and ulcers.
Here is a blog post about the Elenco Snap Circuits SC-500 kit we have. As you can see they REALLY, really like playing with it.
School Lunch. The importance of food for healthy kids and healthy minds:
Speaking at the 2007 EG conference, "renegade lunch lady" Ann Cooper talks about the coming revolution in the way kids eat at school -- local, sustainable, seasonal and even educational food.
A sample of a lesson with a 4 and 5 year old. You can see their progress with skip counting. Soon you will also be able to see their progress with Algebra...over all their understanding of math concepts increases weekly.
The point is not to just teach little kids little math with little numbers...play and have fun and all kinds of math concepts can be discovered.
Always tell them what they have and make them count it, if they give you a wrong answer. Remove the "no" from the lesson and remember they don't get it wrong they just get more information...
Here are a few vids on the Quadratic Equation itself. How to derive it and why it looks like it does. There will be a couple of more short vids on this topic, but for now here are three.
This first vid really needs redoing because you can't always see the symbols and I left off the x in the middle term when I copied it at one point...but good enough for now...
Playing with addends. A lesson on combining. If you listen carefully you will hear addition and subtraction together.
Here the younger boy is loading up the tray so we can play with it. He is building tens and seeing and touching the pairs, complements or in mathematical nomenclature: addends for TEN.
This is an "Addition Subtraction kit" from Mortensen Math. Very useful for putting a child in a situation where they cannot fail, they build ten and learn all 45 addends. They can't help but learn some subtraction too. Do you need this kit? It's nice but if you have a combo kit you don't really need it...some parents want to have everything and it is nice to have. Meantime you have everything you need in a combo kit.
Note they changed clothes for the video...
Here is a quick video showing two boys fooling around with addends. They have become camera aware and now ham it up a little for the camera by pretending they don't know the answers.
Years from now when shown these videos I'm going to be interested in their response. Anyhow, note there is no "no" in the lesson, they are simply told what they have and they are not wrong they just get more information...
Many people use these powerful tools to teach addition at this age and that's about it...and maybe some place value but they can learn so many more concepts.
