When I’m a teacher in the classroom, a lot of times students come up to me and say, “What’s my grade?” and I can tell them their grade and they say, “What do I have to get on my next test to keep my A or to keep my B or whatever?” This is the kind of process those students could use to figure it out by themselves. Let me show you.
In History your recent test scores are 95, 86, 78, 99, and 90. If you want your average to be 90, what do you need to get on your next test? Okay well let’s think about this. In my class 90 represents A- and anything above 90 is an A. 80 represents B- and between 80 and 89 is a B. So like if I were to look at this, I would say that’s an A test, B, C+ what happened here my friend, A+ all right and then A-.
This student wants to have an A- average, this is pretty real life right? Like you guys know how grades work. This is the kind of situation you might find yourself in during the school year. Well the way we can find out an average is by adding up all of our scores and dividing how many scores there are. It’s kind of tricky though let me show to you. First thing I’m going to do is write these guys out as a sum. These are current test scores, we’re going to add them up like so okay. This student has already taken 1, 2, 3, 4, 5 tests. He is going to take 1 more and we want to find out what should that value be.
I’m going to assign the variable x to represent that next test and the reason why I’m adding x is because we want his final average when we add up everything he’s done so far plus that new test to be equal to 90. The way to find the average is to add them all up, divide by how many you have. After the next test you’ll have 1, 2, 3, 4, 5, 6 tests total and we want that average to be equal to 90 that’s what it says. We want his average to be 90.
From here this is a solving problem that you guys might have already worked on. If not you can probably still figure it out. I want to go through and add up all of these things and when I do that on the calculator I get 448 plus whatever his next test score is divided by 6 should be equal to 90 and I want to get x all by itself. I want to isolate that variable.
Well right now this whole quantity is being divided by 6 and the opposite of dividing is to multiply right? So I’m going to multiply both sides by 6 so I’m left with 448 plus whatever his next test score is going to be equal to 90 times 6 which is 540. I’m almost there. 400, oops what happened to my x? Sorry guys I left you hanging there it is, don’t forget the x.
So I’m left with 448 plus his next test score needs equal 540. If you subtract 448 from both sides, you end up getting x equals 92. Let’s see if that makes sense. What I think this means is that in order to get an A- in the class, he needs to get a 92 on his next history test. That makes sense because in general his test scores are pretty good except for this day here when maybe he had a bad day. His tests are pretty much in the A- range. This guy and this guy, this high A+ kind of canceled himself out, so in order to keep the A- it makes sense that he needs to get 92.
So you guys can try this in your school year. Find out what your test scores are maybe you have them in your binder. Figure out what you want your grade to be, divide by how many tests they’re going to be and you can figure out what you need to get on your next test in order to keep the grade you want.
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M.A. in Secondary Mathematics, Stanford University B.S., Stanford University
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