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Often students get confused when they are dealing with sines, cosines and tangents because they see them as words on a page in the middle of a bunch of numbers. It's important to that remember sines, cosines and tangents are actually numbers. Look in your math book and often you'll find a chart that says, “the tangent of 45 degrees is …” and there's a certain number there. Then that helps them to realize that it's not as scary as they think it is. It's actually a number just like 2, 4, or 6.
Some of the most common mistakes kids make when they're doing algebra is that they do not show enough working or they aren't showing every step of their working when they're writing the algebraic solution down. Another of the problems they make in algebra is they confuse signs. So I'm going to do an algebraic problem and talk you through it right now to show some of those common mistakes. So first of all, this is a negative sign here, and many times kids will not distribute the negative sign if they need to. So what they should do in the next step is write 2x - 3x, because the minus distributes over into the parentheses, and this minus and that minus become a positive. So it should be + 4 equals 2. Many of the kids can do that step in their head, but to physically write it down, now they show that they have distributed their signs, and they know they won't make a mistake.So next we'll go ahead and solve through. 2x - 3x is -x + 4 = 2. Now, just to make sure you're being complete and showing all your work, you do -x + 4 - 4 = 2 - 4. These cancel out and you get - x = 16. Divide both sides by -1, another step that many kids would just do in their heads but it needs to be written out, x = -16. Once the algebraic problem's done, the student should also box their answer, just to make sure that they kept everything clean and concise, and now they have their algebra problem solved.
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