It's now the time of year when I post my annual SBAC review. But first, I like to start with my most popular posts of the year -- going back exactly one year to last year's announcement post.
As usual, my most popular post of the year was in the summer:
https://commoncoregeometry.blogspot.com/2020/07/stewart-chapter-8-off-on-comet.html
I'm not sure why my July 6th post had the most views of any post. Maybe it's because so many interesting things are happening in that particular post -- the traditionalists' debate (where a commenter named Alex Loftus stands up to the traditionalists), Shapelore and the tangent function (with a Numberphile video), music and guitar tuning (back before I fixed my broken D string), and graphics in Java. Most of my summer posts contained lots of topics, but so many fun ones landed on July 6th.
The next two most popular posts were both during my long-term:
https://commoncoregeometry.blogspot.com/2020/10/go-formative-unit-2-review-day-39.html
https://commoncoregeometry.blogspot.com/2020/11/lesson-331-writing-linear-functions.html
In both my October 12th and November 4th posts, I focused on my eighth grade classes. Both of these were just before unit tests in APEX (Units 2 and 3 respectively), and so much of my discussion was about the Go Formative assignments that we used for prepare for them. I wrote about which questions I thought my students would excel on and where they would struggle on the actual tests. In my October 12th post, I also wrote about Fawn Nguyen and Eugenia Cheng.
Today is Thursday, and so it's time for my weekly series on COVID-97 and high school Track. This week, my alma mater participated in the fourth dual meet of the season -- the third league meet. It was held on the opponents' home track.
Unfortunately, I was unable to attend this week's dual meet, but I do know how well our distance runners raced this week.
But the biggest thing happening on the track isn't this dual (or triangular) meet. It's the fact that according to the schedule, our school is entered in an invitational -- the Irvine Distance Carnival. This refers to Irvine, a city in Orange County (home to UCI). The host of the race is Irvine High School.
Unlike Cross Country where there were no multi-school meets, apparently invitationals are now being allowed in Track. In an earlier post this month, I mentioned subbing for a Track coach, and the other coaches told me that this school was about to participate in such an invitational.
Invitationals in XC are straightforward, but in Track they are trickier. Some invites don't contest all events -- often they are called "Relays" where every event is a relay, even the distance races (so you might see a 4 x 800 race there). Other invites are only for premium runners -- for example, the most prestigious invite here in California is the Arcadia Invitational. There are no JV races -- just Varsity races, and a qualifying time must be met. For example, this year, the qualifying time for entry into the boys mile is 4:28. (Apparently there is now a Frosh Soph Mile, but even for that race, the qualifying time is a mere two seconds slower, 4:30.) Obviously, I've never qualified for Arcadia.
According to this link, the "Distance Carnival" is on Saturday.
The whole purpose of this exercise is to map this to the COVID-97 world. That is, we assume that on these same dates in 1999 (that is, on May 8th), our school enters an invitational, and I must figure out what race, if any, I would have participated in, and what my times might have been.
First of all, not only did my school not participate in the Irvine Invites in 1999, but the meet didn't even exist back then (as this is only the tenth annual race). So instead, under COVID-97, we should replace Irvine with a meet that really existed back then.
Here's a link to an old archive of 1999 Track meets:
http://archive.dyestat.com/9out/states/ca/week403.html
For example, instead of Irvine, we might consider the Covina Invitational, which is specifically listed as being the week before Arcadia. It's uncertain whether there will be a Covina Invite in 2021 -- a link to the Covina website suggests that it was originally planned for this weekend, but it will be either delayed or cancelled altogether. Thus arguably, an authentic What If for COVID-97 should also cancel this meet, but if I do, then I'm left with no actual race for this weekend.
On May 6th, 1999 (fourth dual meet, third league meet), my 800 time would have been 2:25.
I must admit that for my actual school this week, the slowest upperclassman time in the 800 was 2:21 (although some Frosh Soph runners were slower). I believe that my best career 800 time was around 2:25, but if I were in this week's 800, my competitive juices might have kicked in, and I would have tried to hit 2:20 in order to beat my teammate.
Oh, and before we leave the COVID What Ifs, I must revisit the COVID-93 What If based on new information from the district I attended as a young K-8 student. The secondary schools announced that they would return to four days per week (Level 4) starting the week of April 26th. Mapping this to the 1995 calendar, it makes sense to make this May 1st. This is due to Easter on April 16th and the week after being spring break -- most schools don't make the expansion right after the break, but usually have at least a week of transition.
This means that under COVID-93, I attend two days per week in April and four days in May. This also corresponds to the long-awaited move of LA County into the yellow or least restrictive tier.
Let's get to the SBAC. Some readers might wonder whether it's worth blogging about the SBAC this year during the pandemic. But once again, while the state test is cancelled for Grades 3-8, high school juniors must still take the test since it's often used for college placement. I haven't heard from my LA County district yet on when it plans on giving the SBAC -- if it hasn't yet, then this year's SBAC review will be useful. (Last year I only posted some of my SBAC review questions.)
In past years, I wrote about how one class I subbed for had an SBAC review packet. I forgot to tell the students not to write on the packets -- and unfortunately, two of them did. I decided to keep those two packets and save it for this month's SBAC review for the blog.
Here's how this will work -- when I cover the two daily questions on the blog, I'll write how the two students (whose packets I have) fared. These are one guy and one girl. Both are taking Pre-Calculus as juniors, so they should be doing well on these SBAC questions.
OK, here it goes. This is what I wrote two years ago about today's SBAC review:
By the way, you might wonder how beginning my test review today actually fits the district whose calendar the blog is following. Well, in all high schools, this is the first week of AP testing, and the tendency in most schools is to avoid giving the SBAC during AP time. Thus, unfortunately, most high schools have already given the SBAC. I would have needed to given the last tested lesson (Lesson 15-3) by Day 139 in order to beat the SBAC. (The English test is given even earlier -- it was still the third quarter when it was given.) Reaching Lesson 15-3 by Day 139 is a bit tricky -- but of course I would have tried much harder to reach it if I were teaching a class with many juniors (the tested grade).
Also, notice that following the digit pattern with the new Third Edition of the text might prepare students for SBAC better than my old Second Edition. There are only 14 chapters, and the Inscribed Angle Theorem appears much earlier in the text (Lesson 6-3). And most of what remains in Chapter 14 on circles doesn't appear on the SBAC, so it can be saved for after state testing. Anyway, let's begin our SBAC review.
Question 1 of the SBAC Practice Exam is on factoring:
1. Select the equation that is equivalent to (m^2 - 25).
A) (m^2 - 10m + 25)
B) (m^2 + 10m + 25)
C) (m - 5)(m + 5)
D) (m - 5)^2
Yes, this is an Algebra I question -- but it's not a first semester Algebra I question. As a rule of thumb, the first semester of Algebra I is linear and the second semester is nonlinear. Thus as soon as we see an exponent, we know that it's from the second semester of Algebra I (if not Algebra II).
Notice that two of the answers, A) and B), aren't even logical. All we did there is add an extra term, either -10m or +10m, for no apparent reason. So I hope most students will choose either C) or D).
And of course, the key is factoring the difference of squares. Choice D) isn't a correct factorization of the difference of squares -- in fact, choice D) is the factorization of choice A). And so the correct answer is C).
Both the girl and the guy from the Pre-Calc class correctly answer C) for this question.
2. Select an expression that is equivalent to sqrt(3^8).
A) 3^(1/4)
B) 3^3
C) 3^4
D) 3^6
Again we have an exponent, so this isn't a first semester Algebra I problem. Indeed, I suspect that rational exponents -- the idea that the nth root of x^m is x^(m/n) -- doesn't appear until Algebra II.
Once we define rational exponents, the question is easy -- sqrt(3^8) = 3^(8/2) = 3^4. Therefore the correct answer is C).
Both the girl and the guy from the Pre-Calc class correctly answer C) for this question.
We know that the SBAC tests up to Algebra II. The idea is that most freshmen start with Algebra I, which gets them to Algebra II by the year of the test. Of course, traditionalists are upset that there's no Calculus on the test (but even if Common Core encouraged eighth grade Algebra I, that's only Precalculus by the time of the 11th grade test). Some traditionalists take it a step further and don't even accept the level of Algebra II on the SBAC, calling it "pseudo-Algebra II."
Anyway, our first two questions are beyond first semester Algebra I. Oh well -- let's hope that first semester Algebra I appears in tomorrow's questions.
SBAC Practice Exam Question 1
Common Core Standard:
Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).
SBAC Practice Exam Question 2
Common Core Standard:
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Commentary: In Question 1, students are likely to confuse the difference of squares with a perfect square trinomial. These special factoring methods are studied in Lessons 10-7 and 10-9 of the U of Chicago Algebra I text. In Question 2, students are likely to forget the definition of rational exponents and how it can be used to solve the problem. Also, they might forget that a root without an index is a square root, with index 2.
By the way, let me mention one more closely related Common Core Standard:
CCSS.MATH.CONTENT.HSA.CED.A.4
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
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