Yesterday, I mentioned that I wouldn't post last year's Tic-Tac-Toe construction today, as it made more sense to post it yesterday as part of a post-PSAT activity. So instead, we move on to the next thing that I posted last year at this point -- which happens to be review for a test.
This should be the last time this semester that I'm switching my quizzes and tests -- what I posted last year as a test is considered to be a quiz this year. But this raises another issue -- should I even bother to give any sort of assessment so soon after the PSAT -- not to mention last week's quiz, now relabeled as a test?
I sometimes wonder whether it is wise to give tests the same week as any schoolwide standardized test -- whether it's the PSAT, high school exit exam, or Common Core test. In particular with the Common Core test, on one hand, we want students to do well on the test, and so I have no problem with giving students light work the rest of the week. And besides, part of the SBAC here in California is the Performance Task, and so we have no choice but to spend class time on that Performance Task, not giving lengthy assignments or preparing for a hard classroom test.
On the other hand, we know that many older students don't take the Common Core tests seriously. So some of these may just answer all the questions randomly in a couple of minutes -- and then still have the audacity to claim that they were working so hard on the test that they should have little to no work in all their classes the rest of the week!
My philosophy is that I'd rather give such students the entire week off than risk convincing the students who might have worked hard on the test that they're wrong to do so or that they should focus on classwork instead. So I will attempt to lighten the classwork during the week of any major standardized test.
Of course, the PSAT is not the Common Core test. Still, many students know that the PSAT is not the real SAT, and so they may fill in random answers such as they would on a Common Core test. I more effectively send the message that they should work hard on the PSAT by avoiding multiple quizzes and tests for which they must study so close to the PSAT.
And of course, the grade level matters. If I were teaching Geometry to classes of mostly sophomores (or freshmen), I wouldn't break for the SBAC because students in those grade levels don't even have to take the SBAC. In a PARCC state, I would still have to break for the PARCC though.
(BTW, notice that some states are starting to use the SAT as the Common Core test that all juniors must take, rather than PARCC or SBAC. This most notably includes Michigan, which is switching from ACT to SAT for this purpose. In Michigan, sophomores now take the PSAT and freshmen the PSAT 8/9 in the spring as part of their state testing requirements. I'd like this plan if it reduced the number of standardized tests students have to take, but unfortunately states like Michigan make the students take end-of-course exams on top of the SAT or PSAT.)
So you can see why I might not necessarily want to post a quiz today. Recall that when I first posted this quiz and test last year, it was on the Early Start calendar, and so it was still late September when I posted them. It's unfortunate that when I pushed this back to the Middle Start calendar, the quiz and test landed now in mid-October, close to the PSAT.
What would I post today instead of the quiz? All of yesterday's discussion about Levels 7 and beyond almost makes me want to post more levels of Euclid: The Game instead. But there are problems with Level 7 that might make it unsuitable for a high school classroom.
Let's recall how I solved Level 7 earlier. Our task is to construct a line segment with the same length and same direction as
But, as we found out, this construction is not valid in neutral geometry. We can't prove that
Then yesterday, we looked at the Second Theorem in Euclid's Elements, and we wondered whether we could use that construction to solve Level 7 instead. I will cut and paste the link for Proposition I.2., but first let me change the names of the points. The link calls the given point A and the given segment BC, while the game calls the given point C and the given segment AB. So I will change all the A's to C's and vice versa as I cut and paste the following information from yesterday's link:
And so I end up with nothing to post other than the quiz review. Of course, teachers can still give this review without actually giving the test: