Geometry For Beginners - How To Label Figures, Understand Area And Its Label, And Learn Formulas

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As a life-long Algebra enthusiast, the idea of even wanting to write about Geometry is a shock to me. Recently, I was given the challenge of writing about daily uses of Geometry, and straight through that research process, I discovered that it is truly impossible to exist without at least a basic insight of Geometry--it truly is everywhere you look. While my high school days, my Geometry instructor scared me to death and I easily blanked out straight through much of his class out of fear he might call on me. Even though I went on to come to be a math major in college and a high school mathematics teacher, I worked very hard at never having to teach Geometry naturally because my basic insight of Geometry was weak from my high school experience. I don't want that to happen to you!

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How is Geometry For Beginners - How To Label Figures, Understand Area And Its Label, And Learn Formulas

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I did, in fact, teach Geometry any times since new teachers seldom get to pick what they want to teach; so I do know what sorts of things give Geometry students trouble. (Fortunately, you don't need to be afraid of me--I'm not nearly as gruff as my Geometry instructor was.)

The three concepts that give students strangeness in Geometry with seeing areas of any of the shapes are: (1) labeling figures, (2) remembering the acceptable formula, and (3) insight the view of area and the conjecture it has such a strange label.

Labeling Figures: Geometry probably uses formulas more than any other math class, and if you don't understand formulas and haven't memorized them, you are, as they say, up a creek without a paddle. So first, I am going to give you some tips for helping you understand and learn formulas.

Each time you are introduced to a new topic with formulas, be sure you copy this facts in you notes, drawing the figure as accurately as potential with labels on each part of the figure--and I don't just mean labeling sides as x, y, z. Use the names of the parts as well as the symbols. Use words and symbols on your labels and if they haven't already given fastener names, then furnish your own, like hypotenuse h, side s, base b, diameter d, etc. Speaking out loud in class probably isn't a good idea for this next part, but when you get home, immediately open your Geometry notes and go over those new formulas Out Loud. And also speak in faultless sentences and say formulas both as symbols and words. (I will come back to this.)

For example: Today, we are going to learn to find the area of a rectangle. We are going to first photo in our minds a rectangle. Look around you and find three or four rectangles. (Just to be sure we are all picturing the same thing--four sides with opposite sides equal in distance and all angles are right or 90 degree angles. Right?) You might have found a plain sheet of paper, or your desk top, or a poster on the wall, or the cover of a book, or the screen on a Tv. Now draw a rectangle (it doesn't matter if the short or long side is the bottom) in your notes. Now label the sides: the bottom is base b and so is the opposite side (bases don't have to be just on the bottom); and since the corners are right angles, the left side can be labeled as height h and so can the right side. (I'll stop the recipe in a moment, but I want to mention now how area is easily measured.)

Understanding Area and Its Label: You already know that the sides of these figures are straight lines and, thus, get measured with straight line tools, like rulers. The units of portion will be things like inches, feet, meters, miles, etc. Let's pretend our rectangle is 4 inches by 6 inches. On your diagram, under the word and fastener label add the value with its label. (Under height h, add 4 inches.)

Area is Not a straight line measure. Area refers to the space inside the figure. Area is easily measured by placing squares inside the figure. Since our sides are measured in inches, we need squares that are each 1 inch by 1 inch. Technically we should easily cut out these squares and place them inside to see how many squares are needed to fill the rectangle. Instead, we just draw these squares on the diagram, and soon see that we can reconsider this rectangle as having four rows of 6 squares or 6 rows of 4 squares. Therefore, our rectangle has an area of 24 squares that are each 1 inch by 1 inch. The words after 24 are prominent to know, but writing all that is time-consuming; so we use abbreviations. We could say 24 sq. In., or 24 in^2. Always remember that area is measures with squares, and this is why the labels for area Always involve the word "square" or the abbreviation sq. Or the exponent 2 for squared.

Area Formula: From our rectangle example, we can easily see that the area could be found by adding all those squares together, or more easily, just multiplying the two numbers together. This produces the recipe (in symbols) A = bh. In words--remember to use faultless sentences--the area of a rectangle is the goods of the base and height. Once you have mastered saying and insight the long version of the sentence, you can use the shorter version: The area of a rectangle is base times height.

I cannot stress to you enough the importance of studying formulas by saying them out loud and by Always studying the sentence version at the same time or even first. If you know the sentence version of a formula, substituting the symbols is simple.

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