Thursday, August 28, 2014

Math problems of the week: Common Core-inspired algebra problems

From Free Common Core Math Standards practice, one of the first sites that come up when you google "Common Core math problems."

How clear are these problems  in their presentation, their terminology, and their solutions? You can submit answers and get your score on the original site.


Hainish said...

I don't think these are bad at all. (If you were to scrutinize other math standards as closely as common core, you'd be able to find faults with them, too.)

GoogleMaster said...

Ugh, another question designed to trip up the autistic. "Greater rate of change" when both slopes are negative, -3/2 vs. -4. Greater absolute value (-4)? Number that is greater than the other (-3/2)?

I'm going to assume that the NT test question author meant "greater absolute value" and doesn't see that there can be another interpretation.

Katharine Beals said...

@Anonymous ("There is no such thing as Asperger's..."),
This is the second time you've cut and pasted this comment onto this blog. You have also posted it all over the blogosphere. Finally, it is not relevant to this post. For all three reasons, I am deleting it, and will continue to delete it in the future.

Katharine Beals said...

@GoogleMaster--Yes! It turns out they mean absolutely greater rather than greater absolute value. I assumed the latter and got two questions wrong. I also found the first question hard to follow--again, for simple lack of perspicuity. If these sample questions exemplify what's on the new New York Common Core tests, this is a big problem. Standardized tests should be field tested for clarity (among other things) before they are inflicted on the general population.

Auntie Ann said...

They meant absolute? I never would have guessed that. They ask about "rate of change", and that sounds to me like a magnitude without direction.

Once again, they seem to be testing how well you can interpret the test writer's intentions, and not how well you can actually do the math.

Auntie Ann said...

This seems stupider the more I think about it. "Rate of change" is obviously a wordier stand-in for "slope". Has "slope" been outlawed in favor of new jargon?

If you rephrased the question: "which has the greater slope", I think it would be a bit less ambiguous. My guess is that it was written that way originally, but they decided "slope" was too technical and went with "rate of change" instead.

But they didn't stop to think that the words are not completely interchangeable. A "rate of change" can be great in a negative or positive direction. A line with a slope of -4 has a rate of change equivalent to a line of slope 4.

Anonymous said...

Am I missing something? They do mean magnitude. A slope of -4 has a greater "rate of change" than a slope of -3 because it is steeper. I used this logic on the problems and got them all right.

Katharine Beals said...

I'm cutting and pasting the explanation that the website gives for the "correct" answer to Question 1 after you submit your answers:


Question 1: Given the linear function f1 in the table below and the linear function f2 represented by the equation y = -3.2x +6, which of the functions has a greater rate of change?

x y
0 1
1 -3
2 -7
3 -11
4 -15

a) f1
b) f2

Solution: Function f1 has a rate of change of (-15 - 1)/(4 - 0) = -4
Function f2 has a rate of change or slope of = -3.2
In conclusion, function f2 has a greater rate of change than f1.