If you want to do well in Geometry, learn the terminology first.
There's a lot of it. Terms build on previous terms. And most importantly, there are advantages of familiarity with terms:
- no surprises on tests
- quicker applications (because you will remember mathematical aspects of terms)
- easier to move from one subject to the next
- easier to find your way around the textbook
- easier to show your work even when you can't find the answer
- easier to work your way through to an answer when you completely forgot how it's done
I'm serious! Don't whip out the calculator until you're sure you know what they're talking about. Read the definitions before you start on the problem-solving. You might even have a scratch pad handy to do some sketching of shapes.
Terminology for geometry includes
- Parallel and normal/perpendicular (lines)
- Congruent and similar (triangles and other shapes)
- Hypotenuse and leg (right triangles)
The biggest issue I run into in training others in PowerPoint is that people don't realize that PowerPoint is there ONLY to assist you in making a presentation. YOU are the one with the knowledge; PowerPoint is just there to help you organize that knowledge.
The real issue in making presentations is your connection to the audience. So don't make the mistake that knowing PowerPoint better will make that connection better. THAT has to come from YOU. Once you come to terms with that knowledge, you'll really begin to see the limitations of PowerPoint - if you don't work around those limitations, PowerPoint will get in your way. There is, for example, an e-book out there entitled "How PowerPoint Makes You Stupid." Because if we don't use PowerPoint rightly, we can't be anything but, no matter how well we know the program. So here's what your presentation skills must encompass apart from PowerPoint:
(1) You must have information to present besides what's on the slides....
The role of assumptions is to simplify a problem, so we can solve it faster – sometimes so we can solve it, period. You are very likely to do this for a research paper, and you'll have to present them up front because they affect everything else you write. Assumptions are a sign that we don't know everything, and we want to move forward based on what we do know. For instance, in a business plan you estimate how much your company is worth now (in which case your assumptions explain where the value comes from) and how much you will make, say, in your first year of business (your assumptions say where the sales are coming from)
The best assumptions are either true or they don't kill you (i.e. leave your audience mocking your stupidity). The worst assumptions are the ones you use again and again until you use them automatically (i.e. assumptions about political opponents, who must be wrong because, well, they're opponents, see?). In the business world, bad assumptions lead to lost...
If I had a dollar for every time a student in a math class has asked me "how do I use this in real life?" I'd have a paycheck. But, like it says in the song, "if I had a million dollars, I'd be rich."
I'm asked this most often by Algebra 2 and Geometry students, so here are three things I can show them.
(1) The Rule of 72. Which states, in probably over-simplified form:
"If you take the number 72, and divide it by your interest rate, the result is the number of years it takes for the principal to double."
That's a pretty good simulation of compound interest there, especially for rates around 15% or less. This way students can see how fast a credit-card balance can balloon up, without their having to fool around with the formulas. Once they get the idea, the formulas don't seem so bad.
(2) The break-even point. This is a simulation of a system of two linear equations:
- One is for the money a company brings in via sales. You assume...
They say that people fear public speaking more than anything other than death.
Guess what? "They" spread that fear by saying it. Forget I said it just now!
The audience is on your side. They're in your corner. Know why? Because they're already there. If you fall on your face, they've wasted their time, and they do NOT want that.
So here's what the audience wants - practically craves - from you:
- To be entertained.
- To be inspired.
- To have something to share.
They want to be entertained. Listen: the beginning of your speech is the critical moment, the point when mumbling will lose them forever. So what you want is a funny story, or a shocking statistic, or a question they can't help but answer. Whatever you choose, make it relevant to your topic, practice it again and again, walk out there with a swagger, and launch right into it without any notes. It's your moment! Grab 'em right away!
They want to be inspired. You want them - no, you EXPECT...