Of course there's no "Day in the Life" today. I will mention that the students are working on a packet on counting and adding money. They play soccer as part of "Unified Sports" with Best Buddies. And they read a packet on how weather changes the earth.
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.
Last year, I announced that my most popular posts were all in the summer. This year, the post with the most hits by far is -- an SBAC review post, just a few days after last year's announcement post:
SBAC Practice Test Questions 5-6
I'm not sure why this post is so popular. I assume it's because many teachers are searching for SBAC review material, but why these particular questions?
This post has as many hits as the next four combined:
Van Brummelen Chapter 5 The Modern Approach: Right-Angled Triangles
Music Post: More on 20EDL and Other Scales
Van Brummelen Chapter 4: The Medieval Approach
SBAC Practice Test Questions 21-22
It's interesting how my summer spherical trig and music EDL posts are also in the top five. And some of these topics overlap. (For example, I mentioned 14EDL and 18EDL music in the SBAC posts.)
Meanwhile, here's my top Geometry post (tied for #5):
Lesson 8-9: The Area of a Circle
Another Geometry post with many hits is Lesson 8-7, on the Pythagorean Theorem. Those lessons include two of my favorite activities, and apparently other teachers enjoy these activities as well.
Normally I like to reblog my most popular post -- and I will, on Thursday, when I was planning to reblog the SBAC Questions 5-6 worksheet anyway.
About a month ago, 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 last year 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 second 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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