Here is another challenge problem from the *NEW* 2014 GED Test, let's try to figure this one out together so that we can be ready to help our learners achieve their educational goals!
Add one number to each column of the table so that it shows a function. Do not repeat an ordered pair that is in the table. Here are the numbers you may choose from: 2, 5, 7, 9, 12, 18
| x | y |
|---|---|
| 5 | 5 |
| 2 | 18 |
| 9 | 12 |
Let's have fun and discuss this problem so that we can help each other grow mathematically. As you tell your students in the class, there are no dumb questions or answers. So please - chime in with your thoughts and responses.
Happy Discussing - I will post the answer to this problem the 2nd week of June since we may need additional time to talk about functions.
Brooke Istas
Comments
... knowing what a function is (and what it doesn't have to be) helps here... There is more than one answer.
Sue,
Correct this is more than one solution to this problem and yes knowing what a function is is extremely helpful here. Do you have a creative way of helping your learners understand what is and isn't a function?
If so, please share.
Brooke
One analogy that works is to explain that my "input values" -- my x values -- are like items in a store. Each item has a price. Pickles are a dollar. Ping pPong balls are 4.99 ... etc.
Now, every item has a number, a unique number just for it. And, every item has a price -- and it is the same price, all over the store.
You can't have one item with two prices.
So in my table, I can't say (2,0) and (2,2) are points... and have it be a function.
However, I *can* have two things with the same price. I can have 2,2 and 8,2 as points on my table.
Some graphs have a pattern and a formula (like y = 2x) ... but functions don't have to have a pattern. They're a function as long as all the x's have one y apiece.
... now, that's the "you're given a table" verbal version. The "vertical line" test works peachily as well.
... I would have thought it would be a bit more of a "reasoning" question if you had to place *all* the numbers in a spot and have it be a function, tho' it wwould still have lots of possible answers since the y values are totally interchangeable.
This problem has a 50/50 chance of being right if the student doesn't repeat a value; as long as the x chosen is not one that is on the list already, s/he'll have a right answer.
As questions go, this one doesn't really require much reasoning; I'd think most students who had no idea (or who got frustrated with trying to figure out an equation for the function) would have chosen a number not already represented and then just stuck any of the other numbers in there... and that would be a right answer... so there's probably lots of folks who'll get this right...
I would reason that I cannot use any number for x that has already been used. This limits the available values to 7, 12, & 18. Given the definition of function, y can be any of the values, but I would look for a value that would give me a "nice" function. (7, 5) fits the bill because it and the other points all lie on a parabola y = x2 - 12x + 40. I presume this is the intended (though not actually only correct) answer.
... okay, I'm not well-caffeinated but
I must be having a bad arithmetic day.
x = 2
y = 18
18 = 2 x 2 - 12 x 2 + 40
18 = 4 + 40 - 24
18 = 20 ?
y = 12 and x = 9
12 = 9 squared - 12 times 9 plus 40
12 = 81 - 108 + 40
-27 + 40 = .... 12?
Heading for the teapot ... but starting to understand "GED Math" and how it's different from the math I learned.
That's what I get for trying to do math after a long day....
(My fear is that you're right -- that students were expected to use a calculator and do some "best fit" moves -- and, somehow, just supposed to 'know' to do that. After all, it was awfully close!)
Every student can follow the instruction to add one number to each column in the table, and to only use numbers from 2,5,7,9,12,18 -- even if they know nothing about what restriction is implied by wanting the result to be a function table. There are 6*6 = 36 pairs they could choose from. But if they followed the second instruction as well, then they would eliminate from consideration 3 pairs and so have only 33 pairs to choose from. Exactly 3*6 = 18 of these pairs work for extending the function, so if they chose pairs at random their chance of getting the problem right are 18/33 = 6/11 = .55.
Since they only asked for one extra row of numbers to be entered, why did the test makers include two empty rows of boxes?
Why do the test writers say "shows a function" rather than the standard "is [or 'is part of'] a function table"?
Is there an official right answer?
Is the test given as a multiple choice one?
I've got somebody coming in for help this week with a Kaplan GED test prep book... Is there a way I can discern whether it's for the old or the new test? The questions from my glance-through seemed a tad easier to comprehend than the ones we've been challenged with, but that could be 'cause "challenging" questions were chosen on purpose.
We use the new Kaplan GED book with our students. The new books have a good-sized green circle on the cover that says, "Fully Updated for the 2014 test change."