Applying Distance to Perimeter and Area on Coordinate Plane

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Objective

Students will be able to apply the Pythagorean theorem to answer other geometry questions such as perimeter and area.

Big Idea

Applying the Pythagorean Theorem to other types of geometry questions increases the difficulty and helps make connections.

Lesson Rational

5 minutes

Beginning the New Activity

45 minutes

Applying the Pythagorean Theorem to perimeter and area can be somewhat challenging for students, which is why I like for them to work with partners on this activity during class.  I move from group to group questioning students about their work and answering questions they have for me.  If my groups seem to be figuring out the work with perimeter without too much difficulty, then I let them work until all groups have finished questions one and two before I pull the class together and allow a few groups to present their work underneath the document camera.  I want all the groups to check their work as the group presents and I choose who will present as I move about the room formatively assessing everyone.  If two or three groups worked differently but effectively, then I might ask more than one group to present their thinking for the same for similar questions.  Then I allow groups to get back to work on questions three through six and then again a few groups present work at the board.  Questions seven and eight are typically the most challenging but a good discussion as you move towards the volume unit later in the year.

Lesson End

5 minutes

When students spend the entire class period working through challenging examples, it is usually difficult to have a lengthy wrap-up.  I usually close days like today with a short class discussion on the usefulness of the Pythagorean Theorem in finding length and sometimes multiple lengths.   Let students verbalize that perimeter is no different than finding the length of a single line, only the process is repeated for every line segment graphed.  Usually the realization that perimeter is different from area happens during this lesson.  Somehow, students still seem to struggle with understanding the difference between these two vocabulary words. 

Homework: Study for Test