Practice Session: Slope and Equations of Lines

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SWBAT create a linear equation in two variables by finding the slope and the y-intercept of a line, given either a graph or a pair of points.

Big Idea

The use of an online lesson allows students to approach this practice session from a variety of entry points.

Opener: Try This Delta Math Problem

5 minutes

Today we're back in the computer lab, where students will practice finding the slope and the equation of lines on Delta Math.  It's been a while since we've used Delta Math, because for the last few sessions in the lab we've done all sorts of different work.  It's also been a while since my students have studied slope explicitly.  Since September, we've laid all sorts of foundations for thinking about slope, but until today I haven't really said that word.

Here is what I post on the board as students arrive: it's a list of the Delta Math Assignments that they'll complete over the next few days (both in the lab today, and on their own time).  I tell everyone that they're going to do as much as they can today; the rest is homework.  Some students need help logging in and remembering how to navigate the site.  

Once kids are logged in, they should take a look at the first kind of problem, which looks like this:

In a few minutes, I'll give a mini-lesson how how to do this.

Mini-Lesson: Finding the Slope of a Graph, and Using this Applet

5 minutes

Once kids are logged in to Delta Math and they've had a minute or two to try the first module on their own, I give today's mini-lesson.  Check out this narrative for a description how I introduce this to students.  Here's a photo of what the board looks like when I'm done.

As a teacher, one thing that makes this mini-lesson fun is that I never know which problem Delta Math is going to randomly serve up.  I always love an opportunity to improvise.

Practice Time: Do As Much As You Can

30 minutes

It's been a while since we've done this, and I know that Delta Math engages a different subset of my students than a traditional lesson will, so it's great to see who gets involved today.  It's also great to watch my kids approach slope with confidence, some of them for the first time.

I try to emphasize the common sense behind slope.  I do not mention the formula (Delta Math takes care of that), but the words: "rise" or "change in y" and "run" or "change in x."  I guide students by saying, "What's the difference or change from this y value to this one?  That's called the rise.  Where does it go when we're writing slope?"

There are plenty of opportunities for kids to get their x's and y's backwards or to fill in the definition of slope upside down.  The immediate feedback they get from the computer program is great for that.  The same goes for reducing fractions and remember negative signs.  I could say these things all day, but they're easy details to overlook on a sheet of paper.  The computer doesn't allow for that, and although students will complain a bit about that, they'll also see the power of being forced to be precise.

Maybe a Mini-Lesson, Maybe Not

Depending on how this class moves, I might try to lead a class discussion about the second module of the Delta Math assignment, which asks students to find the slope of a line through two given points, without showing the graph.  

If the majority of the class gets here at about the same time, I'll put and example or two up on the board.  If kids are progressing at a wider variety of rates, I'll just talk to them individually to help them get going.

Debrief: Who Got it Done?

3 minutes

With a few minutes left in class, I use the teacher dashboard to post a list of students who completed the most work today, and I celebrate these students.  I make sure not to call anyone out in a negative way, but I want to positively show that it's possible to have gotten a lot done, and I give these kids some love.

As this happens, it's fun to see a few kids scramble to get from 80% or 90% to 100% on the first two modules in the final few minutes of class.  These buzzer-beaters are especially fun!