Description
What our Pythagorean Theorem lesson plan includes
Lesson Objectives and Overview: Pythagorean Theorem introduces students to the pythagorean theory, used to find the length of a side of a right triangle. The lesson provides several illustrated examples demonstrating how to use the pythagorean theorem, as well as activities for students to attempt on their own. At the end of the lesson, students will be able to understand and apply the Pythagorean theorem to solve problems. This lesson is for students in 5th grade and 6th grade.
Classroom Procedure
Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand. The supplies you will need for this lesson include crayons or markers, grid paper or graph paper, scissors, and tape.
Options for Lesson
Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. One optional addition to the lesson activity is to have your students use colored triangles that have been cut out to find the missing side. You can then tape the triangles around the classroom in right angle areas. For an additional activity, you could have your students research Pythagoras and make a video about his discovery of the theorem.
Teacher Notes
The teacher notes page includes lines that you can use to add your own notes as you’re preparing for this lesson.
PYTHAGOREAN THEOREM LESSON PLAN CONTENT PAGES
Pythagorean Theory
The Pythagorean Theorem lesson plan includes two content pages. Pythagoras was a Greek philosopher and mathematician who developed a mathematical theorem that we still use today to find the length of a side of a right triangle. This theorem only works on right triangles (triangles with a 90-degree angle).
The Pythagorean Theorem is a² + b² = c². The variables a and b are called the legs, while the variable c is called the hypotenuse. The hypotenuse is the side directly across from the right angle in a right triangle. The lesson includes a helpful drawing with labels for the legs, right angle, and hypotenuse.
Let’s look at some examples. In the first example, a = 3, b = 4, and c = x. To solve, plug the values into the formula: (3)² + (4)² = x². Then solve: 9 + 16 = x² becomes 25 = x², which becomes x = √25 = 5. The length of the missing side (the hypotenuse) is 5 units.
In the second example, a = 8, b = x, and c = 17. In this example, you have the length of one leg (a) and the hypotenuse (c), but not the second leg (b). To solve this problem, first plug the values into the formula: (8)² + x² = (17)². Then solve: 64 + x² = 289. Next, subtract 64 from each side: x² = 225. This becomes x = √225 = 15. The length of the missing side (b) is 15 units.
Sometimes, the value of the missing side is not a whole number. That’s okay! Your answer can be a decimal.
It’s very useful to know how to find the length of a missing side. You might ask yourself how far you should extend a ladder up against a wall or how long your shadow is at 2:00 in the afternoon. You can answer these questions, and more, using the Pythagorean Theorem!
PYTHAGOREAN THEOREM LESSON PLAN WORKSHEETS
The Pythagorean Theorem lesson plan includes four worksheets: an activity worksheet, a practice worksheet, a homework assignment, and a quiz. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.
COLORING ACTIVITY WORKSHEET
For the activity worksheet, students will color the grids or graph paper on the worksheet with the corresponding set of squares. Each student will color the squares a different color and cut out a triangle with the two smaller lengths as the legs. Next, they will position the squares around the triangle to see how each component relates to the theorem.
MISSING LENGTH PRACTICE WORKSHEET
The practice worksheet asks students to find the missing side length for eight triangles, showing their work.
PYTHAGOREAN THEOREM HOMEWORK ASSIGNMENT
For the homework assignment, students will cut out six right triangles from a piece of paper. They will then measure the two legs and find the hypotenuse of each triangle. For each triangle, they will sketch a drawing and show their work.
QUIZ
This lesson also includes a quiz that you can use to test students’ understanding of the lesson material. For the quiz, students will first answer a question about the Pythagorean theorem. They will then label a triangle using the terms “leg,” “right angle,” and “hypotenuse.”
Worksheet Answer Keys
This lesson plan includes answer keys for the practice worksheet and the quiz. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.
