Lesson plan

In this lesson, students will learn how to find the distance between two points. Students will review the Pythagorean Theorem. Then, through student discussion and problem solving, students will learn how the Pythagorean Theorem can help them find the distance between two points. You can expect this lesson with additional practice to take one `45`-minute class period.

Grade 8

Triangle Theorems

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Students will be able to find the distance between two points.

- Teacher slideshow
- Blank coordinate grid sheet
- Online Practice

Students should review the Pythagorean Theorem before applying it to a coordinate grid.

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Give students an opportunity to work on the problems together, and review the theorem and its importance before moving on. For today’s lesson, it may be easiest to provide students with a __blank coordinate grid sheet__.

Ask students to consider what they already know that could help them find the distance between the two points. Students can plot these points on their own graphs on their __blank coordinate grid sheet__. If students are not sure where to start, ask them to draw a line to represent the distance. To help struggling students, you may need to draw the rest of the right triangle. Once students recognize that the distance represents the hypotenuse of the right triangle, they should recognize that the Pythagorean Theorem can help them find the missing side length of a triangle, which would represent the distance between the two points.

Once students draw the legs of the right triangle, ask them what the lengths of each leg would be. It’s helpful to write in the measurements of the legs so students can associate them with the right triangle on the graph. Then, as a class, solve `3^2 + 4^2 = c^2` to find that `c`, or the distance between the two points, is `5` units.

With the next example, give students a moment to plot the two points on their graphs on the __blank coordinate grid sheet__. To support student discussions, give students a couple of minutes to attempt this problem with a partner or table group. Students should be able to explain how they found the lengths for each leg of the right triangle and then how they solved using the pythagorean theorem.

- Struggling students: It may be beneficial to use different colors so that it is easier for them to see the difference between the sides of the triangles they will need to draw.
- Advanced students: Consider asking them how they would approach the problem if they did not have a coordinate grid given to them.

For this example, students will likely have to plot the points on their __blank coordinate grid sheet__ or create their own open coordinate grid with only the `x`- and `y`-axis. Students’ misconceptions related to coordinate grids may appear, like plotting the ordered pairs as `(y, x)` instead of `(x, y)`. Depending on students’ readiness, check that they plotted the points in the right areas. This can help prevent students from miscalculating with the wrong values. Another option is to have students check the leg lengths they find before giving you an answer.

Depending on the amount of time left in class, you may be able to do multiple rounds of this activity. Students should use their __blank coordinate grid sheet__. Let students know that they can use a new graph for each problem they do.

On the first blank grid, students should pick `2` points to find the distance between. Then, they will calculate the distance. Students will then find a partner. Each partner will plot the points the other chose and find the distance. Partners should then check to see if their distances between the points they chose matched. If student answers do not match, encourage students to look through their work to figure out where the error may have been.

After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of practice problems for finding the distance between two points. Check out their online practice and assign to your students for classwork and/or homework!

Distance Between Two Points Practice

Problem 1 of 5

<p>Find the distance between `(``-7,9)` and `(``-2,``-3)`.</p><LineGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 15, "x_interval": 1, "y_interval": 1 }, "points": [ { "id": 0, "x": -7, "y": 9, "show_point": true, "point_size": 5, "highlight_point_color": "#000000", "x_coordinate_highlight": true, "y_coordinate_highlight": true }, { "id": 1, "x": -2, "y": -3, "show_point": true, "point_size": 5, "highlight_point_color": "#000000", "x_coordinate_highlight": true, "y_coordinate_highlight": true } ], "line_segments": [ { "first_point_id": 0, "second_point_id": 1, "show_start_arrow": false, "show_end_arrow": false, "dash": true, "line_width": 2, "dash_length": 5 } ]}'></LineGraph >

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