Lesson plan

In this lesson, we will introduce the concept of finding the slope of a line from a graph for `8`th graders. We’ll review the different types of slope to activate students’ prior knowledge with slope. Students will then use what they already know about slope to try and find the slope of a graph. Strategies for teaching how to find slope of a line from a graph, like using prior knowledge and discussions, will help students learn how to find the slope of a line from a graph. You can expect this lesson to take one `45`-minute class period.

Grade 8

Linear Relationships And Functions

8.F.B.4

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Students will be able to find the slope of a line from a graph.

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Using prior knowledge can help when introducing how to find the slope of a line from a graph. Start the students off by having them identify each type of slope using the first slide in the slideshow.

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Encourage students to discuss how they came to their conclusions. Have students review the answers and justify their reasoning. You can consider using different explanations, such as a skier going uphill for a positive slope, or downhill for a negative slope, to help students remember these.

First have students identify the type of slope of the graph. Hopefully, students will be able to easily identify that this line shows a positive slope.

Talk to students about “rise over run”. Have students point out the two lattice points we can see. From there, draw a line for the rise and count “up `2`”. Then draw a line for the run and count “right `3`”. Sometimes it helps students if you write this as a fraction:

`\frac{\text{up 2}}{\text{right 3}}`

Then you can write the regular fraction to show the slope of `2/3`.

Allow students to write down this information so they can reference it as they are working later. Let students know that the points may not always be given on the line, so they will need to look for lattice points.

Let the students practice finding the slope with another positive slope example. Give students an opportunity to work with a partner to discuss how they would find the slope of the graph. Students may accidentally write the slope as run over rise, so it may be helpful to discuss that misconception with students if it arises.

With this example, students may struggle because it is a negative slope that can be simplified if they use the given points. Give students time to work with a partner to find the slope of the line from the graph and encourage students to justify their reasoning. As students finish, consider asking students to make sure the sign of their answer matches the type of slope it should be. This may help students who wrote their answers as a positive number to recognize it should be negative.

I find it helpful to tell students to always start with a lattice point on the left. So with a negative slope, they would go down and to the right. You can have them write a fraction again like:

`\frac{\text{down 4}}{\text{right 2}}`

The “down” will help them again to recognize that this is a negative slope. Remind students to always look for if they can simplify their fractions! The way I’ve used the lattice points here, I should simplify `-4/2` to `-2`.

This next example can help elicit discussions regarding the importance of the intervals when finding the slope of a line from a graph, even though the axes count by the same interval. Some students may choose to find the slope by counting the boxes; however, this only works because the intervals are the same. Pick two lattice points and show students how a slope of `-10/20`, which simplified to `-1/2` would be the same as if we counted the boxes and got `-1/2`.

For this __activity__, students can work independently or with a partner. The answer key is the sheet, so you will want to make sure you cut the slopes and graphs into individual cards before class time. Students should match each slope with its corresponding graph.

If students are grasping the slope of a line from a graph, ask them how they could find the slope of a line if they were only given the ordered pairs. It may help to give students specific points, like `(2, 4)` and `(-2, 12)`. This can allow you to see how students process the information when the graph is not given to them directly.

You can use ByteLearn assignments or worksheets as an exit ticket or homework assignment to help students practice finding the slope of a line from a graph on their own!

Finding the Slope of a Line from a Graph Practice

Problem 1 of 3

<LineGraph data-props='{ "options": { "x_min": -1, "y_min": -1, "y_max": 10, "x_max": 10, "cell_size": 20, "x_interval": 1, "y_interval": 1, "x_label": "", "y_label": "", "x_axis_name": "x", "y_axis_name": "y" }, "points": [ { "id": 0, "x": 0, "y": 2,"show_point": true, "highlight_point": true, "highlight_point_color": "black" }, { "id": 1, "x": 4, "y": 5, "show_point": true, "highlight_point": true, "highlight_point_color": "black" }, { "id": 2, "x": 8, "y": 8, "show_point": true, "highlight_point": true, "highlight_point_color": "black" }, { "id": 5, "x": -1, "y": 1.25 }, { "id": 6, "x": 10, "y": 9.5 } ], "line_segments": [ { "first_point_id": 5, "second_point_id": 6, "show_start_arrow": true, "show_end_arrow": true, "highlight_line": "black" } ], "legend_options": {}}'></LineGraph ><p>What is the slope of the line? <br><highlight data-color="#666" data-style="italic">Write your answer as an integer or simplified fraction.</highlight></p>

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