Middle School Math Tips
What are the secrets to understanding sines, cosines and tangents?
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.
How can I remember the functions of sine, cosine and tangent?
With middle school math's tips, one of the ways to remember sine, cosine, and tangents is to firstly, remember they only apply to right triangles, and here's the way to remember. SOH, S-O-H, CAH, C-A-H, TOA, T-O-A. So for the first part of SOHCAHTOA, S-O-H, sine equals opposite over hypotenuse. For the second part, CAH, C-A-H, cosine equals adjacent over hypotenuse. For the last part, TOA, T-O-A, tangent equals opposite over adjacent. So, just to review math's sine, cosine and tangents; the sine equals opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.
What are the most common algebra mistakes?
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.
How can I check my answers on an algebra test?
With regards to middle school math's tips, for an algebra test, students can check their work by plugging in the answer they got into the original equation. Here's an example: the answer here is X equals 16. So we can plug it back into the original problem or original test question and find out to check if it's the correct answer. Let's plug in this X for the X up here. So, 3, times 16, over 4, plus 10. Does it equal 22? We're going to find out. 3 times 16 is 48, divided by 4, plus 10, 48 divided by 4, is 12, plus 10, equals 22. The student now knows that they have the correct answer for this algebra problem up here.
How can I correctly multiply decimals?
In order to properly multiply decimals, you need to make sure that your working is done correctly as I'm going to show you here. You want to rewrite this decimal problem out as a vertical math problem. The most important thing is that these two decimal points are lined up. Now we have two extra spaces here which we need to fill with place-holding zeros. Now that our problem is correctly set up, we're going to go ahead and multiply the decimals. Zero times five is zero. Zero times three is zero. Zero times four is zero. Zero times one is zero. We do the same here. Next we have our one and make sure that every time you're going to put a place holder every time after you multiply. One times five is five. One times three is three. One times four is four. One times one is one. Without lining up your decimal points, this is all going to be incorrect work. So now we have one last piece to do, which is as follows. Zero. Zero. Zero. Zero. Now we're going to go ahead and add. Zero. Zero. Five. Now we have a total of one, two, three, four, five, six decimal places here. So one, two, three, four, five, six. So your answer is .1435.
What's an easy way to divide fractions?
Here are some tips for dividing fractions. Our first fraction will be 1/3 divided by 3/4. The first thing you need to know is you do not need to have a common denominator when you are dividing fractions. So, the way you divide fractions is you take the first one and you're going to multiply it by the reciprocal of the second term, meaning you are going to flip the second fraction. So, you're going to be multiplying the first fraction by 4 over 3. Once again what we did, the first term comes down as normal. The second one, you flip it, using the reciprocal, and then you multiply straight across. 1 times 4 is 4. 3 times 3 is 9. So, your answer is 4/9.
