Friday, July 24, 2015

Math problems of the week: more Common Core-inspired 4th grade test questions

From the Smarter Balanced Assessments, a Common Core-inspired, standardized test consortium now consisting of about 12 states: the next three problems on the sample 4th grade practice test.

Extra Credit:

Discuss the 21st century challenges posed by these problems in terms of verbosity (problem 7), clarity (problem 8: the meaning of "gives each student 1 card"), and understanding the user interface as opposed to understanding addition with regrouping (problem 9).


FedUpMom said...

I get stuck at the very first line. "A student claims that all fractions ..." followed by "show this is only sometimes true." A claim that all x are y is either true or false. It isn't sometimes true. If you find a counter-example you have proved the claim false.

Auntie Ann said...
This comment has been removed by the author.
Auntie Ann said...

FUM: exactly. Mathematics and logic have traditionally gone hand-in-hand. I guess, not anymore!

Also, since the set up is only that larger fractions have a smaller denominator, 4/7ths, 5/7th, 6/7ths or 1348766/7ths should all be correct answers, yet the rest of the problem does not seem to include those answers as part of the solution set.

I'd also note that on problem #9, no carrying is required. Do any of the problems on the exam require carrying? Do the subtraction problems require borrowing? Considering the input method runs left to right, it makes doing math right to left difficult, which suggests that they don't have that on the actual test.

I wonder how some of the problems are graded. There are several on the whole test which I think you could fill in at least two different ways, and if the test preparers didn't take that into account, the student will have done it right but gotten the wrong answer. (I'm thinking of the chip bag problem, which doesn't explicitly say you have to put one bag on the left and the other on the right--if a kid filled it out the other way would it be counted correctly?)

It also takes forever to go through the test. The problems would only take a couple of minutes on paper, but take a great deal longer on the screen.