P&R+Exploration+with+Pythagorean+Theorem


 * P&R: Exploration with Pythagorean Theorem **

** TEACHER CANDIDATES: ** Graciela Rios, Anna Nu ñ ez, Tami Davis, Noemi Bazan, Natasia Brooks


 * DATE & TIME: **** 3/9/11 **


 * GRADE LEVEL & SUBJECT: ** 8th Grade Geometry

· __ 8.2.F: __ Demonstrate the Pythagorean Theorem and its converse and apply them to solve problems. · Students will draw a triangle with GSP. Students will complete worksheet using the Pythagorean Theorem.
 * LEARNING TARGETS: **

Plan for formative and summative assessment of outcomes for individual students The beginning problems on the worksheet will assess the students’ basic understanding of the Pythagorean Theorem. We will perform our formative assessment of individual students by walking around the room, checking that the students are working, and going over the problems as a class. The last problem on the worksheet is purposefully made difficult in order to provide an accurate summative assessment of outcomes for the individual students. This will be determined by how well and how quickly the students are able to solve the last problem. We will also use a rubric to grade the problems on the worksheet
 * ASSESSMENT STRATEGIES: **

Students will be working individually or in groups depending on their preference for the majority of the class period. In the end, have students get into group of three when worksheet indicates.
 * GROUPING OF STUDENTS FOR INSTRUCTION: **

Geogebra, calculators, computers, Doc Cam, projector, whiteboard, and provided documents Prerequisite Knowledge and skills · Basic algebra · Simple unit conversions · How to use Geogebra Prerequisite and new vocabulary · Right Triangle · Legs · Hypotenuse · Perimeter
 * INSTRUCTIONAL MATERIALS, EQUIPMENT, AND TECHNOLOGY NEEDED: **
 * PRIOR KNOWLEDGE AND SKILS: **


 * LEARNING EXPERIENCES: **

Timeline: 11:00—Review vocabulary and log onto computers 11:05—Introduce GSP 11:10—Students work on worksheets on their own 11:25—Let group volunteer to solve problem on board 11:40—Show video and collect worksheets for grading

Lesson Plan: 1. Start the class period by instructing students to log-in to computers. 2. Once this has been completed, review the vocabulary from previous lesson, to ensure comprehension: a. Right triangle i. 90 ° angle b. Legs – sides of the triangle c. Hypotenuse i. How do you determine what side of a triangle is the hypotenuse? d. Examples

3. Use the slideshow to make students identify right triangles in the real world. Pull the projection screen to let the students draw on the whiteboard tracing the projection on it.

4. Introduce the Pythagorean Theorem and ask leading questions about solving for unknown sides. 5. Pass out worksheet, which has instructions for basic Geogebra actions such as turning on a rectangular grid and plotting points. Have students work individually or in groups of three by rows.

6. Students will then use Geogebra as a tool that will help verify the conjectures they make and the answers they produce. 7. Let students attempt to work on their own for a couple minutes then go through the worksheet problems with them in order to make sure they understand. Repeat until at the end of worksheet (type up solutions for worksheet problems here—easy application: missing sides, incorporate story problems). a. Solutions for problem 1 (Slide) b. Solutions for problem 2 8. For the last problem on the worksheet, have students get in to groups of three by rows if they are not already in groups. They will work together and use each other’s names in the problem. 9. After about 5-10 minutes, ask for volunteers to demonstrate their understanding of Pythagorean Theorem by coming up to the white board and solving it in front of the class (this should be an interactive process and should engage all students). a. Solutions for problem 3 i. Have students present their solutions 10. Once done with the worksheet, collect students’ work and dismiss after playing the Pythagorean Theorem Rap video on YouTube. 11. Grade worksheets using rubric provided.


 * Potential Guided Questions: **
 * What's the shortest distance between points A and B?
 * Given a triangle, what would segment AB represent?
 * What are some real-world examples?
 * In a square, how many right triangles are there?
 * How many degrees are in a right angle?
 * Given the Pythagorean Theorem, how can you solve for any given side?

** Extension: ** The lesson can be altered so that only the first two questions on the worksheet are used. The third problem can be a challenge or extra credit problem since it is a more advanced application of the Pythagorean Theorem. Once the students have mastered this theorem, you can apply this concept to find the diagonals of 3D objects such as boxes and pyramids. There are examples on the following website: [|GoGeometry]

** Teacher Reflections: ** We started the lesson with real-world connections to engage the students’ interest. Also, by giving the students something to do hands-on (drawing on the white board) we were able to assess the students’ understanding of the main principles on right triangles. The worksheet and rubric provides a summative assessment of how well students comprehended the theorem. This lesson can be made stronger by making the connection between the lesson introduction with technology, shortest distance between two points, and vocabulary of right triangles. We can do this by planning our questions and formative assessment methods to keep students thinking without giving them the answer. We could also plan for a way to require all students to present their answers.