Feb 22 2012

New York State Tests: 5th Grade Math 2010

As I’ve looked through the state tests for questions that I considered ‘bad,’ I should mention that there are other things I object to besides ‘bad’ problems that are included on the test.  What I’ve noticed is a lack of ‘good’ problems too.  If you want to see all the full tests, I found them all on the state website.  I’ve also seen way too much emphasis on certain topics at the exclusion of others.

Though there are plenty of questions involving rulers and protractors on this test, I found just one question on perhaps the most important fifth grade topic of all:  percentages.  I think all 5th graders should know that 50% is the same as half and that 90% is almost all and 10% is just a few of something.  I’d like to see them be able to calculate that 16 out of 20 is 80%.  I could even imagine a very good multiple choice question that would enable students to estimate.  Something like:  15% of 40 is A) 1 B) 6 C) 20 D) 30.  Of all the potentially ‘good’ questions about percents, they chose to include just one question.  This question, ironically, doesn’t really test a knowledge of percents at all.

The answers, .71 and 29/100 can be gotten right by someone who merely memorized a few manipulation rules and could be gotten wrong by someone who has a good feel for the concept of percents.

One problem I have with this question is that they say ‘The pencils are divided evenly among 9 classrooms’ which is not possible since 9 does not go into 935 evenly, unless you break some pencils up and give 8/9 of a pencil to each class.  And, yes, I do know what they are getting at in this question, but will the kids?

The amazing thing about this question is that on the 3rd grade and 4th grade tests they had to demonstrate the ability to recognize congruent (though rotated) figures without a ruler or protractor, but in 5th grade they are told to use a ruler and protractor.  To do this question with those tools would take quite some time as they would have to measure all 3 sides and 3 angles of the original triangle and then do the same with the others until they verify an exact match.

The problem is that there are 21 angles in this picture.  And it is not clear if the 4 actual right angles ‘count’ since they also look like they are just the coordinate axes.

They had to recognize similar figures on the 4th grade test, and now they are supposed to use a ruler and protractor.  Of course they should be able to pick out the best choice without any of those tools, but if a student wants to take the directions literally, and thinks she has to use those tools, this question would take some time.

Knowing the geometric definition of ‘corresponding’ just doesn’t seem to be worth a question on this 34 question test.

This is a type of question I’ve noticed on a lot of these tests and also in modern textbooks.  Locating someone’s error and being able to correct it is a skill that is probably worth developing.  But this one is so contrived.  Cal got it wrong because his answer is not right.  Not much more to analyze.  “Cal got this wrong because if you add 65 and 45, you get 110, and if you subtract that from 180, you get 70 degrees for the third angle, not 60.”  Finding the missing angle of a triangle is a fine ‘recall’ question, but when you turn it into a little writing assignment, I think that it is overkill.

 

 

3 Responses

  1. Cal

    After you do New York tests, you should check out California ones. See if you think they are better or worse.

    Did you notice–in a question that tells them to use a protractor, the right angle is marked.

  2. Fran Chase

    I had a student who did just as you said. The interesting thing is for our district the test is given at the beginning of 5th grade and students aren’t taught how to use a protractor until well after the test is given. My student spent a lot of time using the protractor to answer one of those questions therefore she didn’t finish her test and she was highly upset for the rest of that week. I tried to comfort her but to no avail.
    I have often thought why isn’t math more relevant to our everyday lives. How to figure out compound interest and what 25% off means. A lot of the story problems don’t seem very relevant. I would love to send you some of the POTD that my students are expected to solve in 10 minutes. Problem of the Day.

  3. This was kinda easy …. i will not say that because some other people think its hard so i will not blam them :)

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By a somewhat frustrated 1991 alum

Region
Houston
Grade
High School
Subject
Math

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