Today is the first day of the traditional five-period schedule. This counts as a special day, and so I'm doing "A Day in the Life" today:
8:45 -- First period arrives. On the new schedule, this is now the first of two seventh grade classes, and the first of two classes with the aide.
Last night, I noticed that the regular teacher and department chair were working hard to make the scale drawings worksheet assignment accessible on Canvas. And so I begin the class by asking the students to try to access it -- and as it turns out, they still can't reach it.
Meanwhile, today's lesson is a study guide on APEX. And as it turns out, APEX has also been changed due to the new schedule -- my old first period was an eighth grade class, and since they're no longer in first period, APEX lists my first period class as having no students. I assume that the regular teacher has been listed as the teacher for the second semester class -- I could inquire as to how I can get added as a second semester teacher, but it isn't worth it since I'll be gone in a week.
So I can't unlock APEX lessons or quizzes, but I can open the first semester class and look at Lesson 6.1.1, for myself only. The regular teacher has made sure that the students can see the lesson. I can also see the printed study guide for it since he's attached it to the weekly agenda on Canvas.
The lesson begins with some vocab questions ("scale factor," "scale drawing"). Students learn how to write a scale factor as the ratio of lengths on the drawing to lengths on the actual object. Then they must decide whether to multiply or divide by this scale factor in order to find certain lengths.
The weekly agenda takes into account that students now attend each class in person three times, including twice in person. Today's plan is to get through the study guide today, so that the students can complete APEX Quiz 6.1.5 on their last meeting of the week. But after wasting so much time checking whether the Canvas assignments are accessible, there isn't enough time for me to get through the full lesson. I see that the next question on the study guide is on area and the fact that the ratio of the areas is the square of the scale factor -- and I figure that there just isn't enough time to introduce it.
9:40 -- First period leaves and second period arrives. On the new schedule, this is now the first of two eighth grade classes, and the second of two classes with the aide.
The Math 8 classes are starting to solve systems of equations. There is a worksheet on Solving Systems by Inspection -- that is, comparing the slopes and y-intercepts of the two equations to determine at a glance whether there is a unique solution, no solution, or infinitely many solutions.
Fortunately, unlike the seventh graders, the eighth graders can access their assignment. Indeed, they can access it twice -- directly from Canvas and on Go Formative. The trickiest part of this lesson is now they must convert linear equations from standard to slope-intercept form. Indeed, there is a second Go Formative lesson on this conversion.
As the second semester begins, there are a few new students in my classes. In particular, there is a new guy in today's class. Tomorrow, I will meet a pair of siblings (one in Math 7, the other in Math 8) who moved in from Northern California.
10:35 -- It is now time for tutorial. This week, tutorial is tied to second period, and so the students remain right where they are.
I take advantage of this time to have the students continue working on Go Formative -- many of these students are special ed and can use the extra time. Most of them at least complete the Solving by Inspection on Go Formative, but I'm not sure how many actually get the one on Slope-Intercept Form.
11:05 -- The students leave for snack break.
11:15 -- Third period arrives. On the new schedule, this is now the second of two eighth grade classes.
This time, I don't have the benefit of tutorial, but as these are stronger students, we're still able to get through Solving by Inspection on Go Formative. Once again, we don't get to Slope-Intercept Form.
12:10 -- Third period leaves and fourth period arrives. On the new schedule, this is now the second of two seventh grade classes.
I don't waste time asking about the assignment on Canvas because I know they can't access it. And so I use the extra time for at least mentioning area, since I see that area will indeed appear on the upcoming APEX quiz on Thursday.
1:05 -- Fourth period leaves for lunch.
1:45 -- Fifth period arrives. Math Skills is the one class that doesn't change on the new schedule. As usual I have these students work on ST Math and Dreambox.
2:35 -- Fifth period ends, and so does my day of teaching.
3:00 -- I go next door to speak to the department head. I thank her for trying to set up the Math 7 assignment but tell her that many of my students see only "Access Denied." She insists that she's fixed it since I can see it on my computer. She wonders whether the students have since refreshed their browser tabs -- but I'm still not sure.
Then she tells me that she's having trouble getting through Lesson 6.1.1 as well -- and can't believe that APEX would insist on teaching area here. She's strongly considering throwing out this week's quiz, just as we've done so many times before when APEX proves to be too difficult. We might replace it with another assignment -- possibly a Slides activity similar to the one we did for inequalities in December.
Over the past 24 hours, I've been receiving emails from seventh graders who complain that they have an assignment due today but can't access it. At 5:15 and 5:40, two girls email me that they can't submit (as opposed to access) the assignment. That's an easy fix -- and something I can do. I change it so that it accepts submissions, and I extend the due date to tomorrow since there are so many problems.
But then at 7:55, another seventh grader tells me that she's still seeing "Access Denied." So I repeat what the department chair tells me -- perhaps she should refresh her browser. I also notice that she's sending me the email through Canvas for her third period class, but third period is no longer one of my Math 7 classes. So I suggest that she switch to the newly numbered fourth period class. Perhaps changing to the right period might make a difference. Then again, she acknowledges that the due date is now tomorrow, not today, so somehow she can see the new due date but not the assignment itself.
I want to use today's post to discuss this geometry unit on scale drawings, but my success in teaching this unit is tied to the accessibility of this worksheet assignment. Today's Tuesday, soon to be Wednesday, and yet we're still not sure whether the students can access Monday's assignment.
In fact, here's what I'm considering doing tomorrow. In fourth period, I plan on asking a student to do me a favor -- try getting to the assignment, and if "Access Denied" still appears, I'll march with that student straight next door to the department head's room so she can see "Access Denied" for herself. I'm hoping that this way, she'll be better able to diagnose and fix the problem.
As for the lessons itself, the problems with APEX are rearing their ugly head again. The department chair and several other teachers have badmouthed APEX for giving so many complex lessons and squeezing so much content into a single lesson.
On this blog, I've avoided criticizing APEX, mainly because I've seen worse -- namely the Illinois State text from the old charter school. We've seen how that curriculum isn't really divided into units, chapters, or lessons -- instead, it naively follows the Common Core Standards, with a section corresponding to each individual standard.
I was hoping that APEX, with its division into ten units, would avoid these pitfalls and be organized more like a pre-Core text. Instead, while APEX did put some thought into the Math 8 curriculum and placed the F (functions) strand just before the EE standards on linear functions and slope, its Math 7 curriculum has shown almost blind adherence to the Common Core. The RP, NS, and EE standards were all covered in first semester, and now the second semester begins with the G (geometry) strand.
Once again, let's look at the specific standard being addressed:
CCSS.MATH.CONTENT.7.G.A.1
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
And we do see the word "areas" mentioned in this standard, which explains why APEX jumped on this mention and included area in this unit, even though it might confuse students.
Notice that the only Math 7 standard that teaches area is on the area of a circle. The areas of triangles, parallelograms, and so on are taught in Math 6. A pre-Core text would have had a full chapter on area, reviewing the figures taught in Math 6 and then culminating in the area of a circle. The Illinois State text, on the other hand, would teach only circle area, since that's all that's mentioned in the standards.
Here's what I suspect APEX will do -- have a single "lesson" on area and then squeeze in triangle, parallelogram, and circle area and expect us to cover the lesson in a single day. And in today's scale lesson, APEX throws in the areas of triangles even though the area lesson hasn't been reached -- its justification would likely be that hey, the kids learned triangle area in Math 6 and should already be comfortable with it.
One way to solve this problem, if we insist on covering the lesson on scale drawings and area before the lesson on area itself, is to give only the most trivial figures to find areas of -- namely rectangles. All that's needed is a brief reminder that area equals length times width -- no reason to bring in triangles or explain what that 1/2 is for. It might even be possible to use only the areas of squares -- and using only square area could reinforce the fact that if a scale has factor k, areas are scaled with factor k^2.
Notice that I did teach scale drawings to my Math 7 class at the old charter school. Just as at my current school, I covered it in a week -- the first week after a long break (albeit Thanksgiving, not winter). But I didn't write much about it on the blog -- instead, my posts were dominated by what I was teaching in my Math 6 and 8 classes. (I'd always focused on Math 8 on the blog that year -- but that week, the song I performed was from the Math 6 lesson.) And when I did mention my seventh graders, it was more about their bad behavior that week rather than the lesson.
I do remember giving the students a test at the end of the week, and Math 7 did OK on it. I don't recall how I taught the lesson that week except that I did avoid proportions. This week, the Powerpoint that I showed them on Monday used proportions, the key for the assignment (for some reason, students can access the key but not the assignment itself) multiplies or divides by the same number on top and bottom, and APEX directs students to write an equation that's not a proportion (scale factor * actual length = drawing length). Seeing three different ways to solve one problem is bound to lead to some confusion among the students.
Today's song is based on the Math 8 lesson. It's the Slope Song I mentioned last week -- since the students are reviewing Slope-Intercept in preparing for Solving Systems by Graphing, that song I rediscovered is surprisingly relevant now. I'll repost the lyrics:
Delta-y over delta-x,
Rise over run and,
Use it if you need, but,
Try in head just for me.
y minus y all over,
x minus x, and,
Calculator,
Use it if you need, but,
Try in head just for me.
On the guitar, I played the song in the key of A minor (well, it's based on the 12EDL scale, but that definitely sounds minor) and used only Am and D chords. In fact, I got lazy and played an Am7 chord, since that uses only open strings (in my current EACGAE tuning). The D chord was more like D/A in order to hide the problems I've been having with the D string.
(In Math 8, this week also reminds me of a past week of teaching -- at the school I started to do student teaching before I argued with my master teacher. In Algebra I, the class fell behind, and so solving systems was covered in only a week -- and all we did was solve systems by graphing! At least I got to substitution at the old charter school.)
Tomorrow will be the only day I don't post on the blog -- I'll send out a tweet, and then I'll spend the rest of the night entering second quarter grades. The blog will resume on Thursday.
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