Crewton Ramone Two Shorts on Geometry

Remembering  complimentary angles and supplementary angles can be tricky. It also causes some people to think all math is, is memorization.

I always hear questions like, "can this do algebra, can this do geometry, can this do calculus?"...with "this" meaning Mortensen Math and the blocks. How do you apply manipulatives to Geometry or Trig? The basic concepts remain the same throughout the mathematics.

In cases like this all we are doing is learning vocabulary:



So there is a fast way to remember vocabulary. The problem is when you confuse vocabulary with understanding concepts or where you confuse memorization with conceptualization and problem solving. Some seem to think there is no difference between memorizing vocabulary words and memorizing formulae or addends or multiplication tables. Nothing could be further from the truth. We can "figure out" or use an algorithm that requires some thinking and doing to derive the quadratic, or even πr² or something simple like how to remember 9's times tables rather than just commit a bunch of facts to memory but with definitions there is no "figuring out" per se you either know it or you don't.

Although with reasoning and logic you may use induction or deduction to figure out a word's meaning it's not quite the same as knowing enough algebra to solve for x when given a second degree polynomial in standard form set equal to zero.

ax² + bx + c = 0 and coming up with the quadratic formula...and just memorizing the quadratic formula. With complimentary angles and supplementary angles it is very difficult to deduce which one means two angles which when added add up to 90 degrees and which one means two angles which when added add up to 180 degrees, unless you know quite a bit more English than the average highschooler has at their command...you either know what "table" means or you don't. Same with complimentary angles and supplementary angles. Don't confuse memorizing definitions of words or terms with wrote memorization of formula.

Now once we have the definitions down we can start to do some simple problem solving.



Turns out this stuff was super easy after all. We also covered distance formula which as just slightly advanced Pythagorean Theorem and a few or math terms and definitions that come with geometry like parallel and perpendicular, and then the names of angles, and poof, a few problems and the hour was over.

Just Playing Math With Base 10 Blocks

At my house this doesn't even qualify as "math time" anymore. It's just playing blocks. The fact that they are learning their addends and other math facts as well as refining their motor skills is an added bonus.



When we did do math we basically fooled around with factoring quadratics and distributive theory.

They multiplied problems like 5(3x + 2) = 15x + 10.

And factored problems like x² + 12x + 27...

They learned LOTS of math doing these and more problems like them. We laffed, we cried, we spent some time learning addends and multiplication and factoring via the algebra. Most places you are supposed to know your math facts BEFORE you get to algebra. If you want to watch the lesson you will need a password so you can go to the sample lessons page. If you click that link you will go directly to it or click the picture below...it will ask you for your password and should redirect you to the vid, or just click on the URL in the address window of your browser and hit enter, if not just scroll down until you see the video titled More Algebra for Basic Ops. Also check out the vids right ABOVE it.

Here is a super short sample of the 36 minute video.


Passwords are cheap and easy to get and don't change near as often as they should. # bucks will get you in for at leaste 60 days, and it will take you about that long to watch all the stuff I have up.

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More Everyday Math

Basically all we did was play with our food. By the time I thought about getting the camera out we were down to about 20 grapes...we had already eaten more than half. We practiced the all important concept "numbers are made of other numbers".

I was mostly focusing on addition and subtraction and multiplication he threw in division on his own at the end...so we covered all the basic operations. We could have easily gone down the fractions road...but we didn't. Main thing is to keep it simple and fun. Talking about math concepts as you manipulate real world objects helps them understand and add meaning to the abstract symbols they see.

Also the theme of late is math rich environment. That doesn't mean you have to be rich and spend a lot of money on manipulatives you can create a math rich environment pretty easily...just takes a little imagination and an idea of what you want to impart that day. Everyday math activities should be relatively short simple and fun.



You can't go wrong just play math. This is a great preschool math activity...or depending on where your child is and how late you started it could be a first grade math activity, or even second grade. I teach math concepts early using this method compared to public schools. By the end of second grade this boy will know his 45 addends and multiplication tables thru 12. Very little of it will come from drills with pencil and paper or math worksheets. Most of it will come from play. The worksheets and paper and pencil will reinforce what he already knows it won't be the primary tool for learning these math facts and concepts. He will also have tools and algorithms for figuring out problems he hasn't been exposed to and will quickly find there are quite a few patterns and rules that are immutable. A basic concept for teachers to understand is all math is IS COUNTING. So you can do adding or algebra, counting or calculus from day one. It's all just counting.

Seriously. Which way would YOU have rather learned?


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For new comers this may be a little hard to digest. Search this blog and my website you will see how we actually use algebra to teach counting and other basic concepts instead of the mindset where these concepts have to be mastered BEFORE we introduce algebra...