Today I subbed in a high school self-contained special ed class. It's in my first Orange County district -- and indeed, I've subbed for this class several times before, most recently in my February 23rd post. Since it's an unrepresentative class, there's no need to do "A Day in the Life" today.
As is typical in classes like this, I don't have much opportunity to sing. The aides do take the students for a walk, but I must stay in the classroom to exercise with one guy who has opted out of hybrid. I show him several Jack Hartmann videos, one of which is involved with rhyming and the other with counting by twos or fives. I do try to count/sing along with Hartmann, so this sort of counts as my song for the day.
And indeed, this takes us directly into math. I show the students a BrainPop Jr. video on telling time -- specifically elapsed time. There's a toy clock that I use to help the students. Most of them appear to figure it out, although some are confused with when to count by one, five, or ten minutes on the clock.
As usual, I pass out candy and pencils to these students. And since this is most likely my final visit to the class for the year, I also hand out some graduation greeting cards to the seniors.
Unfortunately, one guy doesn't appear too grateful for my gift. At the end of the day, he's supposed to take a Chromebook and practice typing on the TypingClub website. But he doesn't want to type, and so he slaps me in the face twice -- after I gave him his graduation card. (It's inappropriate for me to post any more details on the blog -- all that matters is that I leave his name/actions for the regular teacher.)
Today is Saturday, the second day of the week on the Eleven Calendar:
Resolution #2: We make sacrifices in order to be successful at math.
I do teach them math on the clock, but it's tricky to explain making sacrifices for learning to a class of special ed students.
This is what I wrote two years ago about today's lesson:
Question 17 of the SBAC Practice Exam is on inscribed angles:
Use the circle below to answer the question.
The circle is centered at point C. Line segment PQ is parallel to SR. What is the measure of angle QPS?
(Other givens from the diagram: angle QRS = 68, quadrilateral PQRS is inscribed in the circle.)
A) 68
B) 112
C) 136
D) 158
For this Geometry question, This is a job for the Inscribed Angle Theorem. (Now you can see why I said that the Inscribed Angle Theorem is the only part of Chapter 15 that actually appears in any SBAC or PARCC questions.)
Angle QRS is 68, so arc QPS is 2 * 68. Since a full circle is 360 degrees, arc QRS is 360 - 2 * 68. So by using Inscribed Angle again, angle QPS is (360 - 2 * 68)/2 = 180 - 68. This is 112 degrees, and so the correct angle is B).
By the way, I intentionally avoided arithmetic until the last step, 180 - 68. If angle QRS had been x, then QPS would be 180 - x. The opposite angles of an inscribed quadrilateral are supplementary, and this is essentially the proof. The givens that two of its sides are parallel (i.e., that the quadrilateral is a trapezoid) and that SR is a diameter are irrelevant.
Both the girl and the guy from the Pre-Calc class correctly answer B) for this question. But neither of them show their work completely. It appears that both students are simply assuming that PQRS is an isosceles trapezoid -- a correct but unproven assumption. (We're given that PQRS is a trapezoid, but not that it's isosceles.)
Question 18 of the SBAC Practice Exam is on graphing equations:
Choose the ordered pair that is a solution to the equation represented by the graph.
(The graph shows the equation y = (2/3)x + 2, but only the graph is given, not this equation.)
A) (0, -3)
B) (2, 0)
C) (2, 2)
D) (-3, 0)
Since only the graph is shown, we must look at the graph to see which of these points appears to lie on the graph. The first three choices clearly miss the graph. Point D) is difficult to tell since the step size on the graph is 2 rather than 1, but since none of the others are correct, D) is the answer.
This reminds me of the awkward method that Lesson 3-2 of Glencoe and the first lesson in Edgenuity use to solve equations. We're given an equation like (2/3)x + 2 = 0, and we're asked to solve it by graphing the function f (x) = (2/3)x + 2 and seeing where it crosses the x-axis! I'd argue that it's easier just to solve the equation algebraically than to graph it. And suppose the answer wasn't -3, but something like -2.5 or -3.5. That would be hard to discern on the graph! At least here on SBAC, the equation is already graphed, as opposed to being given a (one-variable) equation and expected to solve it by graphing in the coordinate plane.
Both the girl and the guy from the Pre-Calc class correctly answer D) for this question. But the guy appears to have crossed out A) before marking D).
This worksheet was originally considered to be an activity -- as usual, I'll post a Desmos link at the end of the week instead. I choose Exploration Questions from the two sections (Geometry Lesson 15-3 and Algebra I lesson 3-7) f the U of Chicago text listed below. The Geometry question isn't much (about camera angles), but Algebra I contains some interesting questions. One is about calendars -- which I just happened to write about earlier this week.
SBAC Practice Exam Question 18
Commentary: The Inscribed Angle Theorem is in Lesson 15-3 of the U of Chicago Geometry text, and it's the only Chapter 15 Theorem that appears on the SBAC. Meanwhile, Lesson 3-7 of the U of Chicago Algebra I text is arguably related to this standard. This standard might be confusing if students are required to learn about this before solving equations algebraically, which, unfortunately, is the way Edgenuity presents this material.
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear....
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