Apply the Pythagorean Theorem to a Broken Telephone Pole and an Isosceles Right Triangle.

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SWBAT find the exact and approximate original height of a broken telephone pole, as well as recognize the pattern of an Isosceles Right Triangles.

Big Idea

The purpose of this lesson is to solve a multi-step problem using the Pythagorean Theorem and understand when to apply it.

Warm Up

10 minutes

I intend for this Warm Up to take the students about 10 minutes to complete and for me to review with the class.  The purpose of this Warm Up is to use students' prior knowledge from the previous lesson on perfect squares to introduce a review on applying the Pythagorean Theorem. My students have been introduced to the Pythagorean Theorem in previous grades, so my focus for this lesson is to dig deeper.  I will do this by having students provide reasoning with their answers (MP2).

There are four problems in the Warm Up.  Students have to draw a picture to represent the first three problems.  Problems one and two are both squares, and students are asked to find the length of the diagonal.  Problem 3 is a rectangle and students are asked to find the diagonal.  In Problem 4, I hope that my students recognize the pattern of the length of the diagonals of the squares in Problems 1 and 2 and apply it to 45-45-90 degree triangles. I demonstrate reviewing the Warm Up in the video below. 

Real World Problem

15 minutes

After the Warm Up is complete, I provide a real world application for the students to work with partners.  Each student has an assigned partner in class.  Sometimes I change partners for certain lessons, but I did not for this lesson.  I do my best to assign students homogeneously, unless I feel a different partner is needed for a student to be successful.

In this lesson pairs work to find the original height of a broken telephone pole.  It is a multi-step problem that requires students to persevere.  First, finding the length of the broken part of the pole that has fell over using the Pythagorean Theorem.  Second, finding the original length of the pole by adding it to the standing part.  Finally, writing the  length in exact form and approximate form, a skill that students learned in the previous lesson.     

Once I collect the application problems from all students, I review the problem with the class.  I focus on the exact and approximate answers.  I expect that some of my students will struggle with Problem 2.  I show a few student samples in the reflection, Interpreting my Students' Work

Independent Practice

20 minutes

My purpose in giving my students the Pythagorean Theorem Problems is to provide them with time to practice and to gain more confidence in their ability to apply the Pythagorean Theorem.  I ask my students to approximate their answers to the nearest tenth.

Students are instructed to draw a picture from the given information, and then solve the problem. Most of the problems form a rectangle. It will take my students about 20 minutes to complete the independent practice and for them to self- grade their paper, as I go over it.  I post the answer Key for them to grade, but I question students about number three and four because I want to reinforce that the diagonal or hypotenuse is easy to see the exact measurement using the 45-45-90 degree triangle.   The diagonal can easily be found by the length of the leg times square root of two.  Students still have to enter it into the calculator to get an approximate answer to the nearest tenth.  

I anticipate that my students will have to most difficulty with number eight because it is a multi-step problem.  As I walk around to monitor during the practice, I will prompt some students with questions to help them to persevere.  Some possible questions are:

  • What given information do you have about the table?
  • What given information do you have about the door?
  • What do you need to find to see if the table fits through the door?
  • What explanation can your provide  to support your answer? 

Exit Slip

10 minutes

I hand students the Exit Slip with five minutes of class remaining.  This Exit Slip is a quick reinforcement of knowing the Pythagorean Theorem, and when to apply it.  I restate that the Pythagorean Theorem cannot be used to find the measure of angles of any triangle, and can only be used to find the length of the sides of a right triangle.  

Students sometimes think you can apply the Pythagorean Theorem to solve for missing angles, so I want to clear up any misconceptions about when the formula is used.