Someone forgot his Pythagorean Triple

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And become SMARTER THAN HALF THE AUDIENCE!

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Properties of Arithmetic

I'm sure some of you have wondered "how does Mr. V. know all these tricks?"  One reason is because I have learned this set of arithmetic properties here:

http://www.coolmath.com/prealgebra/06-properties/

Many of you are already using these without knowing it.  The multiplicative inverse property is used in solving proportions through butterfly method.

The additive inverse property is used to solve for x in linear relationships when y is constant.

I just like the way the concepts are presented at coolmath. I hope you do too.

Oh, and if you don't learn them now, you will continue to struggle and will probably have trouble in the rest of your math career through high school and possibly beyond.

Planning

Image Source

If you don't understand the problem, creating a solution can be nearly impossible.

Word problems can be especially tricky, especially when they don't have accurate diagrams attached.

If you see a word problem that has to do with 2D or 3D shapes, one of the first things you should do is to draw a diagram using the information given.  That's why it's important to pay attention when Mr. V explains how to draw the shapes, especially 3D ones.  That's coming up in a video for next week.  Also watch out when a word problem starts slinging around a variable, as they might not always want to know what the variable stands for.  All of this has to do with understanding the problem.



Once you've done that, you can make a plan of what to do about it.  Perhaps your plan might include drawing the shape being described, or if the shape is on it's side, redrawing it so that it is on the base.  Or finding what the variable stands for so that you can test each answer choice.



Then you need to be extra careful about working your plan.  If your drawing is missing some information, you might need to adjust it.  Or if you aren't careful in finding the variable, your tests might say all answer choices were wrong.



In those cases, the reasonableness (meaning is it likely that the answer you got is the correct one) comes into question.  So you may need to look at the answer choices to see if you're close or way off.  Again, be careful about this, as there may be one close to yours intentionally placed there by the test giver.


At any rate, knowing what plans to use is a skill that can be practiced, and I intend for us to do that.



So, now that you've read the post, either put in your journal or take a sheet of paper and let me know where you think you might run into trouble when trying to solve word problems.

Caine's Arcade

Here's a few videos related to a project we'll be doing.

Video

Video 2

So when you're starting to get bored in math class, remember that we're working towards making a few of these.

That first weekend in October mentioned in the blog is really coming and our school is really planning to do something then.  This is the other reason we're starting to learn about 2D and 3D shapes right now, as opposed to later in the year.  Soon, I'll break you guys up into groups to figure out how to build a few of these.

This Game is Amazing!

Kerbal Space Program 101

Many of the concepts needed for rocketry require Calculus and Trigonometry, which both require a basic understanding of mathematics concepts in order to be clear. A strong understanding of ratios is also very important.

Quickly Solve Any Percent!

Understanding percents mostly require your multiplication facts.

Percentage Trick

Pretty nice, huh?  Here are a few more examples.

Percentage Trick 2

Hope this helps you when you look at percentages.  Especially when you're shopping or trying to figure out how much tax or tip is!

The Future Is Closer Than You Think

Science fiction is quickly becoming science reality.  Here's an example.

Mind Over Mechanics

Think this doesn't involve math?  You forget that anything involving a computer involves mathematics.

Cubism

 In Two Figures (1913-14), Liubov' Popova beautifully demonstrates the artistic possibilities of a Cubist reconstruction and, at the same time, her talent to transcend simple imitation.  http://myweb.rollins.edu/aboguslawski/Ruspaint/cubism.html

Sometimes students are incapable of seeing the art in mathematics.  Thus, I intend to display the mathematics in art.  There are two-dimensional and three-dimensional shapes in this painting.  Finding out how many and their dimensions might be a challenging group project.

Advanced Mathematics: Uses of Calculus

Another answer to the "When are we going to use math?" question.  Calculus provides mathematics answers to questions sometimes we didn't even know we were asking.  http://www.dummies.com/how-to/education-languages/math/Calculus/Practical-Applications.html has a whole list of problems that are answered with Calculus mathematics.

Sure, anecdotal or observational information could be substituted for the mathematics, but the mathematics will stay constant even when situations change.  For instance, calculus finds maximums and minimums very quickly, and thus will define the dimensions of a box based on the total area of a sheet of cardboard, through relating volume to surface area.

In this case, the math is faster and less expensive in time and materials than simply building boxes until you come to the maximum.  Thus, in order to understand this application, you must understand calculus and how surface area would confine volume, since both are related to the dimensions of the shape involved (rectangles).  So this is one example of how the math we learn in middle school relates to the math learned later in life.

Future Mathematics: Fractals

One thing my students tend to ask me, is "Mr. V? Where is math in our lives?"  Sometimes that answer has clear ties to what we're learning in class, but other times the mathematics are more advanced.  Fractals are a great example of advanced mathematics with current application.  Some examples follow:

Urban Planning:

http://www.nature.com/srep/2012/120724/srep00527/full/srep00527.html

Natural Patterns:

http://webecoist.momtastic.com/2008/09/07/17-amazing-examples-of-fractals-in-nature/

Chemistry/Physics:

http://www.wired.com/wiredscience/2010/08/superconductor-fractals/

Art

http://www.oneness4all.com/?cat=44

Crop Circles

http://www.cropcircleconnector.com/Bert/3dfractals.html

3D Graphics

http://www.profantasy.com/products/ft.asp

http://specialeffectsmoviesebook.blogspot.com/2013/02/1-fractals-in-special-effects.html

Technology

http://classes.yale.edu/fractals/panorama/ManuFractals/FractalAntennas/FractalAntennas.html

Sound and Music

http://www.tursiops.cc/fm/