Monday, August 22, 2016

Benchmark Testing Week (Days 5-6)

Here is today's Blaugust topic:

22. Be the Change.. what will you do this year to impact the culture of your school and/or classroom?

Well, I want the culture of my classroom to be one in which every student knows that he or she can be successful in math and science. The first step in establishing this culture is to determine the students' level of previous understanding as part of the current Benchmark Testing Week. Only after I find out what the students already understand can I help them expand their knowledge.

The Benchmark Tests have been provided by Illinois State, since as I've said before, we are currently using the Illinois State text. In the past, I've posted tests and other materials that I've developed on the blog, but in order to avoid copyright issues, I don't post Illinois State material on the blog...

...that is to say, I don't post correct Illinois State material on the blog. I can and will post questions that contain errors -- and I found so many all over the middle school tests.

Most of the sixth grade errors involve the lack of an accompanying picture that contains information necessary to solve the problem. The following are given using the Illinois State Database ID number:

68. 24 science books are shown as what percent of books on a shelf?
a) 10%
b) 15%
c) 20%
d) 50%

79. What is the ratio between fruit and nuts in this chart?
a) 1:2
b) 2:1
c) 1:4
d) 2:4

81. What would the next number of cups and ounces be in the chart?
a) 6 cups, 48 ounces
b) 48 cups, 6 ounces
c) 4 cups, 32 ounces
d) 32 ounces, 4 cups

If you couldn't solve any of the above problems -- don't worry -- neither could I.

32. A student is trying to see if 3:15 is equivalent to 12:60. Complete the missing number and confirm if they are equivalent or not.

a) 55, Yes
b) 60, Yes
c) 60, No

Notice that it's possible to show that 3:15 and 12:60 are equivalent without a picture -- it's only required to "complete the missing number." According to the key, the "missing number" was 60 (most likely, it was to complete a proportion like 3/15 = 12/??). Fortunately, hardly any of my sixth graders tried to mark a) 55 as the answer anyway.

200. The opposite of the opposite of 3 is:
a) 0
b) -3
c) 3

This problem is a classic -- "the opposite of 3" is -3, but "the opposite of the opposite of 3" is +3. I am not surprised that many of the sixth graders (who are new to integers) would be confused and choose b) -3, but I am surprised that Illinois State would give -3 as the correct answer!

On the first day, the eighth grade Benchmark Test contains 32 questions given from the first two strands of the Common Core Standards -- The Number System and Expressions and Equations. And just as with the sixth grade test, the eighth grade test contains errors!

1202. Which of the following is an irrational number?
a) 1/10
b) 1.75
c) 0.001
d) pi

Obviously the correct answer is d) pi -- yet believe it or not, Illinois State gives b) 1.75 as correct!

1262. Evaluate x^3 = 21
a) (+ or -)2
b) 2
c) (+ or -)3
d) 3

First of all, the students aren't supposed to evaluate the equation -- they're to solve it. But much more importantly, Illinois State gives the solutions as d) 3 -- but none of the answers are correct. (And ironically, the very next question on the test asks students to find the cube root of 27.)

The plan is for the eighth graders to answer questions about Functions, Geometry, and Statistics and Probability during the rest of this week. Still, this doesn't give me faith in the Illinois State text when my very first interaction with the text involving correcting numerous errors. (Fortunately, there appears to be no errors with the seventh grade test.)

Going back to my Blaugust prompt -- well, I don't impact the culture of my classroom and convince the students to be successful by handing them tests riddled with errors.

By the way, here is the song that I played for my students:

Benchmark Tests -- by Mr. Walker

Verse 1:
Why do we take Benchmark Tests?
It's the start of the year so let's
See how much we know, know know!

It's much new stuff on Benchmark Tests.
If we don't know it, we take a guess.
We leave none blank, oh no, no, no!

The teacher sees our Benchmark Tests,
Knows what to teach more or less.
That's the way to go, go, go!

This counts as the first verse of this song. I'll write and play the second verse in January for the second Benchmark Test, and the last verse in May for the third Benchmark Test.

This is a song that I made up myself. I mentioned back in my Pi Approximation Day post that I would invent songs by choosing a random number and then assigning digits to each note, as Michael Blake did with pi and a few other irrational constants (not including the "irrational" 1.75, though).

The number I chose at random was:


I decided to use the key of C major. On the guitar, certain other keys are often easier to play, such as G or D major, or if we want to go minor, A or E minor. But for this song, all the chords are easy to play in C major.

I use Michael Blake's trick -- 1 = C major, 2 = D minor, 3 = E minor, 4 = F major, 5 = G major, and Blake uses 0 to denote a rest. This gives the chord progression as:


I then add a melody that seems to fit these chords, and then finally lyrics that fit the melody and describe what the students are doing today and tomorrow -- the Benchmark Tests, of course.

Elsewhere in the MTBoS, I notice that Elissa Miller uses a Benchmark Test system similar to ours, where she gives the same test three times during the year:

We ended the week by taking our end of course exam which will be given again in December and May. I spent my time making answer keys and updating my spreadsheet data.

Lucky her -- she uses a spreadsheet, but we're expected to put our Benchmark Test data into student folders (then again, there's nothing stopping us from placing the data onto a spreadsheet anyway).

Meanwhile, I found something interesting written by Sarah Carter, one of the most famous members of the MTBoS:

Tomorrow's our last PD day before kids start on Monday.  Having kids come in and out of my room helped to make the fact that school is starting soon actually sinking in.  It also reminded me of how much I have missed interacting with my students.  I've enjoyed my break, but I'm ready to get back to teaching some math.  And physical science.  That part is going to be an adventure.

In other words, Sarah Carter -- just like me -- finds herself teaching a science class! She's a high school teacher and I'd thought that something like that would never happen in high school. But, as she explains, she teaches in rural Oklahoma, and so the issues that occur at my small charter school can also happen in small rural high schools like Carter's.

So I'll definitely be looking at Carter's blog more often for hints on teaching science. But here's something on Carter's blog that I'm able to use right away:

I had posted a number line on the wall in my classroom, with the words "forever" printed on either end of the number line. One student asked my why the word "forever" was printed there -- apparently she must be a Buzz Lightyear fan because she thought "infinity and beyond" would make more sense than "forever."

And that very same day, Carter posted Infinity Posters on her blog. So of course I had to put the infinity signs up on my own wall. So far, that student hasn't reacted to them yet, since she was so busy with the Benchmark Tests.

My next post will be on Day 7, which is Wednesday, August 24th.

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