You're sitting in Geometry class staring at a monstrosity of lines when the following question comes out of your teacher's mouth in a language closely resembling Greek:
Line segment AB is parallel to line segment CD. Line segment EF is perpendicular to line segment CD. Line segment GH intersects both line segments AB and CD at points M and N, respectively. Solve for angles x, y, and z.
"Gesundheit," you reply. Your teacher looks you in the eye. Before you can go on to suggest some excellent throat lozenges, your teacher says, "Please come to the board and solve this problem for the class."
You take a deep breath and walk toward the board. Everything you just learned about angles rushes through your mind. "Complimentary angles add to ninety. Supplementary angles add to one-eighty..." your thoughts race as you grab the blue marker. The marker remains hovering above the board. "I... I don't know where to start," you stammer.
"What do you remember about opposite angles?" your teacher hints. You stare back at her and realize how dry your mouth has gotten when you reply, "Angles across intersecting lines are equal?"
"That's right!" she says and draws the following picture on the board:
"There's a relationship you missed," your teacher replies while picking up the green marker, "Let's redraw what we were given using the relationships described in the problem."
"Now what do you see?" she asks.
"Angle y equals forty," you say, starting to feel less flustered.
"Exactly!" your teacher explains, "We knew that line segments AB and CD were parallel. That means if they are intersected by the same line you can relate the angles. Now, let me show you something else using Angle Addition." She grabs a purple marker and writes quantities in some of the blank spaces.
You immediately see it. "Angle z equals twenty!" you exclaim.
"Can you explain it to the class?" your teacher asks.
"Well, angle y is opposite of angle z and the given angle. So you could write it like this," you say while you write the following equation: 40 = z + 20. "Solving for z, we find that z equals twenty degrees."
"Perfect!" your teacher smiles. "Just one unknown left."
On a roll you say, "Since line segment AB is a straight line we know that these top angles have to equal one-eighty. They are supplementary angles." You write on the board:
"So angle x is sixty degrees!" you say triumphantly.
"Well done!" says your teacher. "Class, do you see how redrawing the problem helps prevent yourself getting overwhelmed by a flurry of lines?"
"Does this only work for opposite angles?" a classmate asks.
"No, you can use this on any question. Check this out."
The class is buzzing. You smile because looking at all of those lines made you dizzy.
"Looking at the whole problem can sometimes distract you from the simple relationships," your teacher explains. "Try working through tonight's homework problems using this method. You may have to draw a few different simplifications before you find one that works, but don't give up! After enough practice you won't need to draw the simplifications, but they start to jump out at you."
A popular fundraiser is to guess how much of a certain object are in a container. Often this object is sweet, sweet candy. The person with the closest guess wins the candy-filled container. Increase your odds of winning by making an educated guess! An educated guess is simply an estimate.
Let's say there is a jar filled with jelly beans. How many jelly beans does the jar contain?
First, estimate the size of the jar to determine its volume. You pull out the cell phone in your pocket that you guess is about six inches tall. Using it to estimate the dimensions of the jar, you determine the height is about one-and-a-half cell phones and the diameter is one cell phone. Using the volume of the cylinder you calculate the volume of the jar to be about 254 cubic inches. Using the same logic you intuitively estimate that a jelly bean has a diameter of 0.5 inches and a length of 0.75 inches. Estimating the volume of a jelly bean using a cylinder you find the volume of a single jelly bean to be 0.15 cubic inches.
Then it is a simple matter of dividing the volume of the jar by the volume of a single jelly bean to find that about 1,693 jelly beans could fit in the jar. But what about the gaps between the jelly beans? Great point! Various sources estimate the jar contains 20% air by volume . Use proportions to calculate how many jelly beans would take up 80% of the jar by volume.
How sweet is that? Give this technique a whirl at your next fundraiser. Who knows, your math wizardry may help you walk away with a jar full of jelly beans!
 "How to win a guess the number of jelly beans contest". How Tutorial. WordPress. 18 April 2011. Web. 31 July 2016.
 "How to Win a Jellybean Guessing Contest". Cleverness: Getting Diggy with It. WordPress. 07 March 2007. Web. 31 July 2016.
There are two scenarios when one looks back on their high school experience: you either loved or hated math class. Many people will extrapolate from there and say, "I hated math class. I wasn't any good at it, I just don't think that way." People don't really argue with this thought. It almost seems logical. Who hasn't struggled with a math concept over the course of their educational career?
We use math every day. When you are trying to determine if a sale is worthwhile, spacing pictures equally on the wall, or calculating how much longer a trip will last if you are going the speed limit. Now the question becomes, did your distaste for math stop you from figuring those problems out? No. What will keep you from figuring out those problems is your level of math proficiency.
Proficiency is tied to practice, not enjoyment. You become better when you practice. Want to hit a baseball? Practice. When you first started to practice hitting a ball there was a lot of failure. Failure isn't fun. This is where the final piece of the puzzle pops into place. Your desire to learn created persistence. It's that persistence that made you practice even when you hated it.
You use math every day. It's important to have adequate skills so that you can navigate the math problems of every day life. Like when learning to hit a baseball, it is helpful when you have a coach that already knows how to hit a baseball. Same goes for math. If you are having trouble it can help to work with a tutor and keep practicing.