*Mathematics Calendar 2018*, Theoni Pappas writes:

sin 67 = cos

*theta*

*theta*= ?

Well, this is where the definition of cosine as

*complement's sine*comes into play. The correct answer must be the complement of 67 degrees --

*theta*= 90 - 67 = 23. Therefore the correct angle is 23 degrees -- and of course, today's date is the 23rd. This is covered in Lesson 14-4 of the U of Chicago Geometry text.

Today was the special training day for the upcoming summer Algebra I class. So naturally I have plenty to say about it.

Much of the training concerns the software we'll be using for the class. Last year, my charter middle school used PowerSchool to keep track of grades. This year, the district is using Edgenuity for the summer school classes. There's a huge difference between PowerSchool and Edgenuity though -- while PowerSchool was used only for attendance and grades, Edgenuity actually has videos of all the content we'll be teaching.

My own experience with educational technology is mixed. I've written much last year about grades on PowerSchool, as well as IXL and Study Island for content -- and the Illinois State text also had an online component. None of those programs had any videos, however.

But I don't believe I used that technology to its fullest last year. For example, I tried to use Study Island for

*science*with my eighth graders last year. I often assigned the students some questions to answer, which failed because they hadn't learned the lessons yet. Then I handed out worksheets for them to study, which they lost before it was computer time -- if they even read the worksheets.

That's not how Study Island was supposed to work. I was supposed to have the students read the information

*on Study Island*, then answer the questions. In other words, it's a

*complete lesson*on Study Island -- which would have been useful in my science-starved classroom. The real problem was that I -- with my mind still stuck in the 1980's -- never considered the idea of having an entire lesson be online.

Well, Edgenuity is taking the idea of online lessons a step further. The students can log in, play videos, and answer the questions online. No textbook is needed. All I must do is monitor the students and help them whenever it's necessary.

The first three hours are training on the software itself. Then after lunch, the next three hours are for us to collaborate with those who are teaching the same subject to make plans. There are about twenty of us teaching math or science thus summer. I am one of seven who is teaching Algebra I, and one of three who is teaching the first semester of Algebra I. One is currently a science teacher, while the other is a fellow sub who is also a student teacher. In fact, right now she and her master teacher are finishing up their own regular Algebra I classes.

Because she is the most experienced and most recent Algebra I teacher, we guys simply let her be in charge of planning the curriculum. Here are her plans for the class:

- The Edgenuity lessons are rearranged to conform to the order established in the Glencoe text.
- Only the first five chapters of Glencoe are taught. Chapter 6, on systems, was formerly a first semester topic, but now it's been pushed back to the second semester.
- Our class lasts for three weeks. The first week corresponds to the first two chapters, the second week to Chapters 3-4, and the last week is Chapter 5 followed by the district written final.

Chapter 1 of the Glencoe Algebra I text is called "Relationships Between Quantities." All of the content of this chapter appears in eighth grade (or below) in the Common Core Standards, and thus there is no Edgenuity video on any Chapter 1 content. The idea, then, is for the three of us to teach Chapter 1 material on the first day as a traditional lesson, and then have the students start using Edgenuity on Chapter 2 material on the second day.

Two chapters a day might seem fast, but that's the nature of summer school. I used to tutor students in math for three years (but I didn't create this blog until my third year of tutoring). Five years ago was my busiest summer of tutoring. Several students took classes, including an entering freshman taking Algebra I in order to move ahead and take Geometry the following fall. His teacher used the Glencoe text and covered two chapters per week, just as we're doing this summer. (Then again, his class didn't use Edgenuity or any other software.)

The student teacher showed me the pacing plan she's using during the school year. Some of the lessons in Glencoe are labeled "mastery" -- just like MC (major content) in last year's pacing. We expect that during the summer, we'll only have time for the "mastery" lessons.

Here are the lessons labeled "mastery" in the first five chapters of Glencoe:

1-2. Order of Operations

1-4. Distributive Property

2-3. Multi-Step Equations

2-4. Equations with Variables on Both Sides

2-6. Ratios and Proportions

3-1. Graphing Linear Equations

3-2. Solving Linear Equations by Graphing

3-3. Rate of Change and Slope

4-1. Graphing Equations in Slope-Intercept Form

4-2. Writing Equations in Slope-Intercept Form

4-3. Writing Equations in Point-Slope Form

4-4. Parallel and Perpendicular Lines

5-2. Solving Inequalities by Multiplication and Division

5-3. Solving Multi-Step Inequalities

5-4. Solving Compound Inequalities

5-5. Inequalities Involving Absolute Value

The student teacher showed me the pacing plan she's using during the school year. Some of the lessons in Glencoe are labeled "mastery" -- just like MC (major content) in last year's pacing. We expect that during the summer, we'll only have time for the "mastery" lessons.

Here are the lessons labeled "mastery" in the first five chapters of Glencoe:

1-2. Order of Operations

1-4. Distributive Property

2-3. Multi-Step Equations

2-4. Equations with Variables on Both Sides

2-6. Ratios and Proportions

3-1. Graphing Linear Equations

3-2. Solving Linear Equations by Graphing

3-3. Rate of Change and Slope

4-1. Graphing Equations in Slope-Intercept Form

4-2. Writing Equations in Slope-Intercept Form

4-3. Writing Equations in Point-Slope Form

4-4. Parallel and Perpendicular Lines

5-2. Solving Inequalities by Multiplication and Division

5-3. Solving Multi-Step Inequalities

5-4. Solving Compound Inequalities

5-5. Inequalities Involving Absolute Value

Edgenuity allows us to log in as a student and start watching the videos. When I watched the first video for solving equations, the lesson kept returning to graphing functions -- that is, we solve an equation

*f*(

*x*) =

*g*(

*x*) by graphing

*f*and

*g*and finding the

*x*-value of their intersection. But this requires students to learn

*graphing*linear equations before

*solving*them. Neither the U of Chicago nor the Glencoe texts teach equations this way (and it's awkward, since, for example, students can't solve an equation in standard form for

*y*in order to put it into slope-intercept form). But apparently, this is how Edgenuity teaches it. We reordered the lesson so that solving equations comes first, but we can't change how the speaker in the video introduces equations. (Lesson 3-2 of Glencoe also seems to use this approach, but this is after Chapter 2 on solving equations the usual way.)

Like PowerSchool, Edgenuity allows grades to be weighted. Last year, the administrators told us what the weights were, but this year, teachers are allowed to choose the weighting. The only requirement is that all seven of us teaching Algebra I must agree. So far, there is disagreement between us first semester teachers and the second semester cohort. We want to weight it as 20% each for quizzes, tests, and the final exam, with 40% for assignments (which, since they're on computer, could be classwork or homework). But the second semester teachers don't want the assignments to count at all, so that students can focus on the quizzes. Next Wednesday, there will be a two-hour meeting after school so that we can continue to discuss the grading (as well as the Edgenuity approach to solving equations).

This is the reason I was trying to hold off writing much about summer school until after I attended today's training. As much as I want to start making plans for the summer, I can't truly plan until I know more about the class I'm going to teach. The revelation that this will be a computer-based class means that this class will be very different from the class I taught last year.

For example, notice that the grade weights are for quizzes, tests, the final, and assignments. So there's no room for participation points. Last year my Warm-Ups and Exit Passes were part of participation grade, and so there's no room to start or end classes with Pappas-like problems either. Fortunately, this also means that I won't be lulled into the trap of deducting participation points as a punishment, which as I found out last year, doesn't work.

I'm also wondering what to do about music break. If the students are spending most of the period watching videos and answering questions online, does it make sense to have music break at all? And now suddenly, all of those posts on EDL scales are unnecessary if I can't play any music in class.

Moreover, I was planning on beginning the summer with "The Dren Song," the same song that I started with last year. But of course I won't have any Dren Quizzes this summer, since this is something else that I won't be able to grade. Edgenuity requires all grades to be for the online assignments unless we override them (which we'll do only for the district-mandated written final).

Also, should I even continue to post SBAC Practice Exam questions on the blog? The idea behind posting SBAC questions is to get me thinking about how I'd like to teach certain topics. But now the Edgenuity videos take instruction-related decisions out of my hands.

For now, I've decided to continue posting SBAC review anyway. Ironically, both of today's SBAC questions are on systems -- a topic I'd thought would be part of first semester Algebra I until this morning, when I found out that they're actually second semester topics.

Question 15 of the SBAC Practice Exam is on systems of equations:

A store sells new and used video games. New video games cost more than old video games. All used video games cost the same. All new video games also cost the same.

Omar spent a total of $84 on 4 used video games and 2 new video games. Sally spent a total of $78 on 6 used video games and 1 new video game. Janet has $120 to spend.

Enter the number of used video games Janet can purchase after she purchases 3 new video games.

Here is the system to solve:

4

*u*+ 2

*n*= 84

6

*u*+

*n*= 78

Using the substitution method:

*n*= 78 - 6

*u*

4

*u*+ 2(78 - 6

*u*) = 84

4

*u*+ 156 - 12

*u*= 84

-8

*u*= -72

(By the way, if we use elimination instead, multiply the 2nd equation by 2 to obtain -12

*u*- 2

*n*= -156 which also leads to -8

*u*= -72.)

*u*= 9

6(9) +

*n*= 78

54 +

*n*= 78

*n*= 24

So Janet purchases three video games for $72, leaving her with $48, enough for five used games. And therefore, the number students must answer with is 5.

Question 16 of the SBAC Practice Exam is on systems of inequalities:

Click on the region of the graph that contains the solution set of the system of linear inequalities.

*y*

__<__(-1/2)

*x*+ 3

*y*

__>__2

*x*- 2

The correct graph must be below the (-1/2)

*x*+ 3 (or the downward-sloping) line and above the 2

*x*- 2 (upward-sloping) line. These intersect in the region to the left -- the correct answer to shade.

**SBAC Practice Exam Question 15**

**Common Core Standard:**

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

**SBAC Practice Exam Question 16**

**Common Core Standard:**

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

**Commentary: In the U of Chicago Algebra I text, systems appear late -- not until Chapter 11, with systems of inequalities in Lesson 11-10 as well as systems of equations in the earlier parts of the chapter. In the Glencoe text, however, systems appear in Chapter 6. Nonetheless, systems are considered a part of second semester Algebra I. After today's summer school training session, I am ready to take on the challenge of teaching this lesson to my students.**

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