Finding Slope from Two Points

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SWBAT calculate the slope between two given points on a line.

Big Idea

In this lesson, students build upon their understanding of slope by deriving the slope formula and then applying it.

Warm Up

10 minutes

To allow for additional practice for previous days' lessons, I have provided two problems in today's Warm Up. As students work, I circulate through the room redirecting students, as needed, while providing any support necessary.

Once the five minute timer sounds, I randomly call on students to share their answers and seek class confirmation or disagreement. Once students agree with answers presented, I highlight today's learning objective and move into the lesson introduction.

Lesson Intro

5 minutes

Today's Lesson Intro includes revisiting several representations of slope that students have previously experienced  on which we will build today's lesson. First, I showing several graphs and ask students how they would determine the slope of the given lines. I have animated lines for rise and run that appear when touched so students can see the change represented by the slope. Then, I show a table of values and remind students what they experienced in the "What's My Rule" lesson. I challenge them to find the rule for the given table and then isolate the slope from their equation. Finally, I share a  two-points slope question:  What is the slope of the line that passes through (6, -6) and (2, -4)? I tell students to discuss in their table groups strategies they would use to find the slope for two minutes and prepare to report out their ideas.

Deriving the Slope Formula

10 minutes

Once two minutes is up, I poll the class. The majority of groups typically suggest graphing the points, so I model this strategy on the SmartBoard. (I have the coordinate grid animated to appear once I touch the board so that I do not influence student suggestions prior to group discussions.) When I plot the given points, I label them on the graph. I select a volunteer to determine the slope from the points. I then direct students to notice the difference between the y-coordinates on the graph (-4 and -6) as well as the difference between the x-coordinates (2, 6) and ask them how it relates to the slope that was found. I then explain that they have just discovered a computational way of finding the slope of a line given two points called theSlope Formula. I introduce it as delta y over delta x and explain that the Greek letter delta is often used in math and science to indicate change.

We then practice a few examples so students can see how to use the formula.

Work Time

15 minutes

Once students have applied the slope formula few times, I introduce the Work Time task, which is to use the slope formula to find which pairs have the same slope of the equation y = 1/2x +3. I do this so that students not only have additional practice, but also so that we can discuss that points that share the same slope do not necessarily fall on the same lines, but are more typically parallel. This topic will reappear in future lessons, but I want to plant the seed early!

After the work timer sounds, I ask student volunteers to supply their found slopes. If any discrepancies appear, I ask a student volunteer to work it out on the SmartBoard.

Ticket Out the Door

5 minutes

To check for student understanding, I have created a Ticket Out the Door (TOTD) for today's lesson which asks students to do an error analysis of Joe's work on a two point slope question. Joe's work shows the incorrect use of the slope formula in that he uses change in x over change in y, a common error made by students. I will use the TOTD data to adjust future lessons, if needed.