We continue our work with Systems of Linear Equations.

Our opener will be Basketball Shots 2 (the sequel to their homework assignment)

Our lesson will include working through Atomic Weights (probably together), then the Types of Solutions activity builder, and then solving a couple of systems by both substitution and elimination for practice.

For homework they will decide when it might be best to use substitution and when it might be best to use elimination.

## Friday, June 10, 2016

### Day 16

Today's opener will be a short review of solving a system of equations by substitution.

Then we'll use this Activity Builder to start talking about solving systems by elimination. I tried combining (and tweaking slightly) two activity builders that I thought went well together, but I'm a bit worried it might be too much for the roughly 50 minutes I'm hoping to give for it. Your thoughts are appreciated.

Their homework will be a solving systems by elimination problem involving atomic weights. This might be a stretch for them, especially if we they don't have any class time to start on it (and I hope they do). That's partially why I'm not making this one a screencast (the other part of that partial is just to give them a break from making screencasts.)

Then we'll use this Activity Builder to start talking about solving systems by elimination. I tried combining (and tweaking slightly) two activity builders that I thought went well together, but I'm a bit worried it might be too much for the roughly 50 minutes I'm hoping to give for it. Your thoughts are appreciated.

Their homework will be a solving systems by elimination problem involving atomic weights. This might be a stretch for them, especially if we they don't have any class time to start on it (and I hope they do). That's partially why I'm not making this one a screencast (the other part of that partial is just to give them a break from making screencasts.)

**Update**: Changed the homework to Basketball Shots and moved the atomic weights to part of the lesson the next day. Just felt like it was a bit too complicated to give them that quickly.## Tuesday, June 7, 2016

### Day 15

We'll start with an opener that eases them into solving systems of equations by substitution.

We'll then complete the On The Road Again Activity Builder to learn more about systems.

Their assignment will be to record a screencast discussing solving a system by substitution.

We'll then complete the On The Road Again Activity Builder to learn more about systems.

Their assignment will be to record a screencast discussing solving a system by substitution.

### Day 14

We'll start with a short assessment over function notation and application.

We'll then begin looking at Systems of Equations using the Racing Dots Activity Builder.

Their assignment will be to complete the Playing Catch Up Activity Builder.

We'll then begin looking at Systems of Equations using the Racing Dots Activity Builder.

Their assignment will be to complete the Playing Catch Up Activity Builder.

## Monday, June 6, 2016

### Day 13

Today will continue to talk about best fit lines and learn the least squares regression equation.

The opener will again be practicing finding x and f(x), but in the context of a best fit line.

Our lesson will continue with the air travel situation but in a Part 2 of the Air Travel Activity Builder. We'll now focus on a "best" fit line over a "hey, it looks good" fit line, and talk about what the correlation coefficient means. I really think the idea behind this one is sound, but I think the execution of it still needs a lot of work. Suggestions appreciated.

For homework they will complete a linear regression application problem. I think this one is pretty good, but it may be a case of me really liking it and the students not so much. We'll see.

The opener will again be practicing finding x and f(x), but in the context of a best fit line.

Our lesson will continue with the air travel situation but in a Part 2 of the Air Travel Activity Builder. We'll now focus on a "best" fit line over a "hey, it looks good" fit line, and talk about what the correlation coefficient means. I really think the idea behind this one is sound, but I think the execution of it still needs a lot of work. Suggestions appreciated.

For homework they will complete a linear regression application problem. I think this one is pretty good, but it may be a case of me really liking it and the students not so much. We'll see.

## Sunday, June 5, 2016

### Day 12

Today we'll start talking about informal lines of best fit (soon to lead to correlation regression, and causation).

We'll start with an opener that practices solving an equation using function notation.

We'll then work two through Activity Builders, Line of Best Fit and then Air Travel (based on Dan Meyer's post from what seems a long time ago).

For homework I'll have them complete a short reading assignment (as well as look at some spurious correlations), then write a short summary of a second article (their choice).

We'll start with an opener that practices solving an equation using function notation.

For homework I'll have them complete a short reading assignment (as well as look at some spurious correlations), then write a short summary of a second article (their choice).

### Day 11

Today is all about learning function notation as well the difference between continuous and discrete functions.

Our opener will review figuring out whether a relation is a function from a graph of the relation.

Our opener will review figuring out whether a relation is a function from a graph of the relation.

Then we'll complete Function Notation on Activity Builder. My goal is to expose them to function notation, including solving when given either the independent or dependent variable, talk about continuous vs. discrete, and then do a couple of application problems.

For homework they will complete a similar application problem and record a screencast explaining it. In addition, I'll ask them to do a small additional amount of homework by gathering some data that we'll use in class on Friday (for an activity based on Dan Meyer's Air Travel).

## Friday, June 3, 2016

### Day 10

Today's topic is relations and functions. In the past I haven't felt good about this one, as I have trouble coming up with any creative ways to teach it yet, on the other hand, it just seems so straightforward to me that I can't figure out why students struggle with it so much.

We'll start with an opener that will review writing equations in slope-intercept, point-slope, and standard form, mainly because I do worry that the lack of repetitive practice I give students (i.e., not a lot of homework problems) compared to other teachers may harm their retention. We'll see.

Today's slides are most of the lesson, with basically just a rewrite of what I used to do with this topic, just updated with examples from activities I will have done this year. After we go through the basic definition of a function and some examples, I'll have them complete the Function, or Not Activity Builder (slightly remixed from the original by Daniel Henrikson).

For homework tonight I won't ask them to do a screencast but, instead, will ask them to see if they can "figure out" the vertical line test for functions. I'm curious to see how they'll do with this.

We'll start with an opener that will review writing equations in slope-intercept, point-slope, and standard form, mainly because I do worry that the lack of repetitive practice I give students (i.e., not a lot of homework problems) compared to other teachers may harm their retention. We'll see.

Today's slides are most of the lesson, with basically just a rewrite of what I used to do with this topic, just updated with examples from activities I will have done this year. After we go through the basic definition of a function and some examples, I'll have them complete the Function, or Not Activity Builder (slightly remixed from the original by Daniel Henrikson).

For homework tonight I won't ask them to do a screencast but, instead, will ask them to see if they can "figure out" the vertical line test for functions. I'm curious to see how they'll do with this.

### Day 9

Today we'll work more with point-slope form. We'll start with an opener that practices writing an equation in point-slope form, then substituting in for x and finding y, substituting in for y and finding x, then writing the equation in slope-intercept form.

We'll then briefly share some of their Des-Person creations.

The lesson will work through the How Long Does It Take To Sober Up? Activity Builder. I'm a little worried about the time it might take to do this, so still thinking if there's a good way to shorten it without skipping something important.

For homework, they'll do a modified version of Mathalicious's Domino Effect.

We'll then briefly share some of their Des-Person creations.

The lesson will work through the How Long Does It Take To Sober Up? Activity Builder. I'm a little worried about the time it might take to do this, so still thinking if there's a good way to shorten it without skipping something important.

For homework, they'll do a modified version of Mathalicious's Domino Effect.

### Day 8

Today is a PLC day, so we'll only have a 39 minute class.

Instead of an opener, we'll start with our first assessment over Graphing Stories. I'm not sure I like what I've come up with here. As I mentioned in the Day 7 post, I wanted to keep this relatively short (10 minutes or less) and have them demonstrate their knowledge of various parts of graphing stories (verbal descriptions, tables of values, linear equations with domain restrictions).

Well, I think what I have right now is perhaps a bit too complicated and will take a bit too long. I'm guessing this is closer to 15 minutes instead of 10. And, while I like the problem situation, I'm worried it's too "busy" for students. It's hard to tell, because after a week plus of working with these stories, maybe it will be as straightforward for them as it was for me (in my head) when I was thinking about this. If it is, then it's not too busy and they'll cruise right through it. But if they aren't feeling good about graphing stories at this point, I can see them getting lost in all the details. Your thoughts on this assessment would be appreciated as I think about this more.

After the assessment we'll briefly work on point-slope and standard form. I've never been enamored of standard form, but it's an expectation, so we'll touch on it. Point-slope form is trickier, because it's confusing for a lot of students but, once they understand it, it's useful in a lot of situations. Here are my slides for this quick overview. I'm not happy with these either, but perhaps a boring, straightforward quick look is all they need here. (We'll continue working on point-slope the next few lessons.)

For homework they will continue working on the Des-Person assignment they received the previous day.

This is the first day I don't feel pretty good about. I have questions and concerns about the other days (most notably with timing), but overall feel pretty good about them. This day doesn't feel all that good, starting with the shorter class period, the assessment not being quite right, and the lesson being less than inspired. I'm telling myself that not every day can be fantastic, but I'll be thinking about this one a bit more.

Instead of an opener, we'll start with our first assessment over Graphing Stories. I'm not sure I like what I've come up with here. As I mentioned in the Day 7 post, I wanted to keep this relatively short (10 minutes or less) and have them demonstrate their knowledge of various parts of graphing stories (verbal descriptions, tables of values, linear equations with domain restrictions).

Well, I think what I have right now is perhaps a bit too complicated and will take a bit too long. I'm guessing this is closer to 15 minutes instead of 10. And, while I like the problem situation, I'm worried it's too "busy" for students. It's hard to tell, because after a week plus of working with these stories, maybe it will be as straightforward for them as it was for me (in my head) when I was thinking about this. If it is, then it's not too busy and they'll cruise right through it. But if they aren't feeling good about graphing stories at this point, I can see them getting lost in all the details. Your thoughts on this assessment would be appreciated as I think about this more.

After the assessment we'll briefly work on point-slope and standard form. I've never been enamored of standard form, but it's an expectation, so we'll touch on it. Point-slope form is trickier, because it's confusing for a lot of students but, once they understand it, it's useful in a lot of situations. Here are my slides for this quick overview. I'm not happy with these either, but perhaps a boring, straightforward quick look is all they need here. (We'll continue working on point-slope the next few lessons.)

For homework they will continue working on the Des-Person assignment they received the previous day.

This is the first day I don't feel pretty good about. I have questions and concerns about the other days (most notably with timing), but overall feel pretty good about them. This day doesn't feel all that good, starting with the shorter class period, the assessment not being quite right, and the lesson being less than inspired. I'm telling myself that not every day can be fantastic, but I'll be thinking about this one a bit more.

## Thursday, June 2, 2016

### Day 7

Slightly shorter class period today (53 minutes) because it's an advisory day.

We'll start with an opener called Sloping Letters, which helps them review the idea of positive, negative, zero and undefined slope.

We'll start with an opener called Sloping Letters, which helps them review the idea of positive, negative, zero and undefined slope.

We will then go over a homework screencast and talk about their first assessment tomorrow. This assessment will be over Graphing Stories and will ask them to put together what they know about verbal descriptions, tables of values, linear equations with domain restrictions, and Desmos. I'll explain to them my assessment philosophy and how I will give them an adequate amount of time for the assessment, but not unlimited (therefore they should be prepared). The actual assessment will include a link to a Desmos graph (or possibly Activity Builder, haven't constructed it yet). Right now (may change after I construct it), they will complete the problem, then take a screenshot and upload that to formative. I anticipate giving them about 10 minutes for the problem, but we'll see.

Today's lesson will be a combination of Polygraph Lines and my version of Des-Person/Winking Man Part 1 (part 1 because I'm hoping to create a part 2 and maybe 3 after we do quadratics later in the year). I'm hoping this will be a fun way to reinforce what we've done, including having them focus on some vocabulary (slope, intercept, quadrants, etc.) as well as domain restrictions.

Their homework will be to prepare for the assessment tomorrow (so no screencast), as well as their own Des-Person assignment that will be due on Friday (if I'm on track, today is Tuesday, assessment will be tomorrow on Wednesday, we don't have class on Thursday).

## Wednesday, June 1, 2016

### Day 6

Today we revisit Graphing Stories and the MARS task Interpreting Distance-Time Graphs, but this time we will write linear equations for all the stories that have all linear components - even if they are piecewise.

The opener will review how to find the y-intercept when you aren't given it but, instead, are given the slope and a point, or more often two points and you have to calculate the slope first.

We will then discuss one of the student's homework screencasts from the previous class.

Today's lesson will work through the Activity Builder Graphing Stories Part 2. This will solidify our ability to connect descriptions, tables of values and graphs, and then to be able to write equations for those graphs (including domain restrictions for piecewise functions). As part of this we will need to utilize solving for the y-intercept since we won't always have that for the different pieces of our graph.

For homework they will complete one more graphing story and record a screencast with their thinking. The hope is that by the end of this lesson they are feeling very comfortable with everything related to graphing stories, including writing equations for linear data.

The opener will review how to find the y-intercept when you aren't given it but, instead, are given the slope and a point, or more often two points and you have to calculate the slope first.

We will then discuss one of the student's homework screencasts from the previous class.

Today's lesson will work through the Activity Builder Graphing Stories Part 2. This will solidify our ability to connect descriptions, tables of values and graphs, and then to be able to write equations for those graphs (including domain restrictions for piecewise functions). As part of this we will need to utilize solving for the y-intercept since we won't always have that for the different pieces of our graph.

For homework they will complete one more graphing story and record a screencast with their thinking. The hope is that by the end of this lesson they are feeling very comfortable with everything related to graphing stories, including writing equations for linear data.

### Day 5

Today I hope to to cement the connection between a situation, a table of values, the graph, and the equation. The will also begin to connect slope more explicitly with the idea of rate of change and specifically with speed for distance-time graphs.

We'll begin with an opener that reviews slope and connects it to rate of change and speed (screenshots below).

We'll then complete an activity that requires gathering some data on three people walking, entering it into an Activity Builder, then using the data to try to come up with equations to describe their motion. The first walker will start at 0 and walk at an even pace for 10 seconds. The second walker will start at 3 feet (for example) and walk at a steady pace (hopefully slightly different pace than the first walker, we'll see). The third walker will walk a piecewise graph. Starting at 2 feet (for example), walking at a steady rate for 4 seconds, standing still for 3, then walking at a steady rate back toward the starting point for 3 seconds.

The hope is that they will not only connect the actual walk to the data tables and the graph, but they'll get a better idea of how speed relates to the graph and the idea of a domain restriction and piecewise equations. In our next class we will then revisit Graphing Stories and the MARS activity, coming up with equations for any of the linear graphs (including the piecewise ones).

For homework students will take a piecewise table of values, graph it on Desmos and come up with equations, domain restrictions, and a verbal description of what may have happened, then record a short screencast of their thinking.

We'll begin with an opener that reviews slope and connects it to rate of change and speed (screenshots below).

The hope is that they will not only connect the actual walk to the data tables and the graph, but they'll get a better idea of how speed relates to the graph and the idea of a domain restriction and piecewise equations. In our next class we will then revisit Graphing Stories and the MARS activity, coming up with equations for any of the linear graphs (including the piecewise ones).

For homework students will take a piecewise table of values, graph it on Desmos and come up with equations, domain restrictions, and a verbal description of what may have happened, then record a short screencast of their thinking.

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