#3042. Pythagorean Theorem

Mathematics, level: Middle
Posted Wed Jan 28 19:06:56 PST 2004 by J. Samick (jensamick@yahoo.com).
Johnstown, USA
Materials Required: Chalk, Chalkboard, Erasers, Computer, Projector, Projector Screen, Calculators, Handouts
Activity Time: 50 minutes
Concepts Taught: Reason and Measurement

Teacher J. Samick Date October 22, 2003
Class Pre-Algebra Grade Level 7
Unit Reasoning and Measurement Lesson Pythagorean Theorem
PA Academic Standards: 2.1.8.E, 2.2.8.A, 2.3.8.A, 2.5.8.B, 2.5.8.D
2.1.8.E - Simplify and expand algebraic expressions using exponential forms.
2.2.8.A - Complete calculations by applying the order of operations.
2.3.8.A - Develop formulas and procedures for determining measurements.
2.5.8.B - Verify and interpret results using precise mathematical language, notation and representations, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs and diagrams.
2.5.8.D - Determine pertinent information in problem situations and whether any further information is needed for solution.
Goal of this lesson:
The goal of this lesson is for students to be able to calculate the unknown side of a right triangle, given the lengths of the other two sides.
Materials:
„X Chalkboard
„X Chalk
„X Erasers
„X Computer
„X Projector
„X Projector screen
„X Calculators for groups of students
„X Handout for in class work
„X Handout for homework
Clerical/Administrative Tasks:
„X Take roll
„X Report any absentees to the office
„X Make copies of all handouts
„X Have answer key prepared for both handouts
„X Confirm that there are an adequate number of calculators
„X Arrange desks so that all students can see the projector screen clearly
„X Get PowerPoint ready on the computer
„X Pull down the projector screen
„X Turn projector on
Instructional Objectives:
„X The students will be able to describe and define the Pythagorean Theorem when asked from memory.
„X The students will be able to identify a right triangle and the corresponding sides that fit the Pythagorean Theorem.
„X The students will be able to recognize the Pythagorean Theorem and read it out loud properly.
„X The students will be able to identify the difference between the legs and hypotenuse of the right triangle.
„X Given two sides of the right triangle, the students will be able to solve the Pythagorean Theorem for the missing variable.
„X The students will be able to define and differentiate between when they are and are not supposed to use the Pythagorean Theorem.
„X The students will be able to cooperate with group members during the handout.
* I used the Cognitive Apprenticeship model *
Introduction:
„X Briefly explain that we are going to be discussing the Pythagorean Theorem and that we believe it was developed by the Pythagoreans. (1-2 min)
„X Transition: Distribute handouts and give directions to instruct the students on what to do. (2-4 min)
Developmental Activities:
* Modeling *
„X Start the PowerPoint slide show, go through each slide in detail and explain the Pythagorean Theorem. (6-8 min)
„X We will go through examples on the board of how to write numbers in radical form, which is necessary in order to prepare the Pythagorean Theorem. (2-4 min)
„X We will go over where the square root key is on the calculator and how the students should use this key. (1-3 min)
„X We will go over the definitions of inductive and deductive reasoning and the students will be able to understand these terms fully. (2-4 min)
„X Onto the handout, explain to the students that you are going to do number one and number two with them, but they should also do it at their seats on their handout. (1 min)
„X Write the Pythagorean Theorem on the board, a2 + b2 = c2.
„X Read the first problem out loud to the students. Let a = 24 and c = 25, find the other leg of the triangle, b. (2-3 min)
a2 + b2 = c2
242 + b2 = 252
576 + b2 = 625
b2 = 49
b = 7
„X Ask students if there are any questions. (1 min)
„X Read the second problem out loud. Let a = 4 and b = 5, find the hypotenuse, c, of the triangle. (2-3 min)
a2 + b2 = c2
42 + 52 = c2
16 + 25 = c2
41 = c2

„X Ask students if there are any questions. (1 min)
„X Make sure to let the students know that their answers aren¡¦t always going to come out to an exact number; they may find a side of the triangle to be a square root.
* Scaffolding *
„X Read the third problem out loud and have them do it at their seats with other students. I will walk around and monitor to make sure that they all understand the concept. Have one student come up to the board and demonstrate how to do the problem. (2-3 min)
„X Problem number three: Let b = 5 and c = 13, find the other leg of the triangle using the Pythagorean Theorem.
a2 + b2 = c2
a2 + 52 = 132
a2 + 25 = 169
a2 = 144
a = 12
„X Ask the students if there are any questions. (1 min)
* Coaching *
„X Announce to students that they should try to complete the fourth problem on their own. I will walk around the room and monitor to make sure that everyone understands the concept. Have a student volunteer to come up to the board and complete the problem for everyone to see. (2-3 min)
„X Problem number four: Let a = 3 and b = 4, find the hypotenuse of the triangle using the Pythagorean Theorem.
a2 + b2 = c2
32 + 42 = c2
9 + 16 = c2
25 = c2
5 = c
„X Ask students if there are any questions. (1 min)

* Fading *
„X Tell students that they all did a very good job in learning and practicing the Pythagorean Theorem.
„X Ask if there are any questions, and tell the students that they are going to have a worksheet to complete for homework on this material. (1-3 min)
„X Transition: Distribute the homework handout and ask the students to put it away. (1-2 min)
Assessment/Evaluation:
„X Ask for a student to volunteer to tell you what the parts of the right triangle are called. (Answer: a = leg, b = leg, c = hypotenuse)
„X Formally assess when grading homework handout.
Conclusion:
„X Transition: Have students clean up their tables and return to their regular seating arrangement. (1-3 min)
„X Ask the students again when they are allowed to use the Pythagorean Theorem? (Answer: only in right triangles)
Accommodations/Adaptations for Students with Special Needs:
„X Billy, who has ADHD, will be seated towards the front of the classroom so that I can be sure to pay close attention to him.
„X When the students are working on the handout, I will check with Billy several times to make sure he is on track.
„X I will pay close attention to see if Billy seems confused or distracted, so that I can answer any questions he may have in a reasonable amount of time.

Reflective Notes:
„X ¡§How was my timing?¡¨
„X ¡§Did the students understand the material?¡¨
„X ¡§Did I get to cover all the material in my lesson plan?¡¨
„X ¡§Am I satisfied with the way I planned the lesson?¡¨
If Time Permits:
„X ¡§If Time Permits:¡¨ Students will be allowed to work in groups of two on their homework assignment. I will be walking around the room to monitor and make sure that everyone understands the concept of the Pythagorean Theorem.
Technology Integration:
1. I will place the PowerPoint on the overhead screen and go through it will all the students in the class.
2. Since there is a 1:4 ratio of computers to students in the classroom they will have to take turns using them. We will use a rotation system, where there will be 4 different groups of students and they will be permitted to use the computers one assigned day from Monday thru Thursday. On Friday, all students will be incorporated into the classroom using the original teaching setting. When on the computers, the students will be required to make up an appropriate worksheet dealing with the mathematical concept that we are talking about that specific week. This will count as a graded assignment.
3. When the entire class enters the computer lab, they will be required to log in as usual. Based on the topic that we are discussing in class at the time, I will have various puzzles, games, and worksheets created on math websites that I belong to as a teacher. I will have a list of websites for each student to have at their computer, such as: www.coolmath.com, www.mathpower.com, www.funbrain.com, and www.algebrahelp.com just to mention a few. These websites will also be very useful for the students to have to use on their time when they need help with their mathematics. As we go along the websites, I will monitor by walking around to assure that all students are with me and not doing other things on the computer during my class time.