
Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
At the end of this lesson, students will be able to explain a proof of the Pythagorean Theorem.

Prior Knowledge: What prior knowledge should students have for this lesson?
Students should be able to:
 multiply variables.
 find the area of a rectangle and a triangle with variables assigned to sides lengths.
 simplify an algebraic equation by canceling terms by using the inverse operation.

Guiding Questions: What are the guiding questions for this lesson?
 How can the Pythagorean Theorem be proven?
 What is the relationship between the sides of a right triangle and its hypotenuse?
 How can you use areas to prove the Pythagorean Theorem?

Teaching Phase: How will the teacher present the concept or skill to students?
After the formative assessment, introduce the class to the famous Greek mathematician, Pythagoras. One way to introduce the class to Pythagoras* is to play a small clip from Disney's Donald Duck in Math Magicland. If you do not have the DVD, you can find the clip on YouTube at (The video should automatically start at 1:57 and the segment ends at 3:48.)
*NOTE: This video is not intended to be directly relevant to the Pythagorean theorem being studied in this lesson, but it does illustrate Pythagoras' ways of thinking and applying mathematical practices to understand the world around him.
Tell the class something like the following:
"Pythagoras did many things in the areas of mathematics, music, philosophy and science. He is most known for a mathematical theorem named after him. The Pythagorean Theorem allows you to find the length of any side of a right triangle, if given the other two sides. For example, the Pythagorean Theorem can be used to find the length of missing side xÂ in the figure below." Display the figure from Example 1
"Tomorrow we will learn how to solve for the unknown length, but today we will discover for ourselves, the Pythagorean Theorem."

Guided Practice: What activities or exercises will the students complete with teacher guidance?
Put students into groups of 3 or 4. if they are not already. Hand each group one of the following assignment sheets. Guided Practice
Assign members to a group,Â so that there are an even number of groups. Half will receive page one and the other half will receive page two.
Explain to the class that each group will find the area for the figure given. They will do this by find finding the area of each section. Then they will combine the sections to find the total area of the figure.
Explanation of each page:
Page 1: The large square contains a smaller square with the area of c^{2}. The larger square also contains 4 congruent right triangles, each with the area of .5ab. Thus the total area of the figure is c^{2} + 4(.5ab) = c^{2} + 2ab.
Page 2: The large square contains two smaller squares with areas of a^{2} and b^{2}. ThereÂ are also two congruent rectangles, each with an area of ab. Thus the total area of the figure is a^{2} + b^{2} + 2ab.
When each group has finished, have the groups pair up to a make larger groups. Each larger group is made up of one group with page 1 and one group with page 2. A suggestion to make the transition easier is to print eachÂ set a different color. For example, print one set on blue paper, another set on yellow paper. This way you can ask each group to find the other group with the same color.
Tell groups that they each had the same figure. This means that the total area expression found by each group is equal. Give groups time to explain how they found the total area. After that, ask groups to set both expressions equal to each other and ask what they see. They should have the equation written below:
a^{2} + b^{2} + 2ab = c^{2} +2abÂ Â Since each side of the equation contains 2ab, we can subtract 2ab to arrive at the Pythagorean Theorem; a^{2} + b^{2} = c^{2Â Â Â Â }
Have each group report out what they found. There may need to be discussion on how a^{2} + b^{2} + 2ab = c^{2} +2ab becomes a^{2} + b^{2} = c^{2}. It might help to show this :

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Have students go back to their original seats. Hand out the following attachment: Independent Practice
Note: You may need to do an example to help students. It would be recommended to use a 51213 triangle.
Have students draw squares from each leg of the 6810 triangle (similar to the image below).
Next they will calculate the area of each square and verify that the Pythagorean Theorem works. Go from student to student to be sure thatÂ each understands.

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Have each student write a short letter to a hypothetical student who was absent and have them explain how they proved the Pythagorean Theorem.

Summative Assessment
Have each student write a short letter to a hypothetical student who was absent and have them explain how they proved the Pythagorean Theorem.

Formative Assessment
At the beginning of class, have students find the area of the following figures:
 a rectangle with sides of length a and b
 a square with sides of length a
 a right triangle with a base of length a and a height of length b
It is recommended that you also ask students to draw figures for each one of the items above.
This formative assessment will be valuable when students are calculating two different ways to find the area of a square within a square. Have students go back to these examples, if their groups have difficulty in the finding the area of the square two different ways.

Feedback to Students
Feedback will be given thoughout the lesson.
The first time will be during the formative assessment given at the beginning of the lesson. The feedback will confirm that students have the prior knowledge of calculating the area of rectangles and triangles with variable side lengths.
The teacher will monitor the students' work and dialogue; then ask guiding questions to probe their thinking and extend their conceptual development.
Students will also get feedback after their groups calculate the area of a square two different ways in the Guided Practice activity. One way is to calculate the area of the square by multiplying the sides [(a+b)(a+b)]. The other way is to find the area of the center square (c X c) and add it to the area of the 4 triangles [4 X .5(a)(b)].
Students will also receive feedback from other students, when they present their findings to the class. (See Guided Practice activity)