Terry Butler - Lesson Plan 4 - Page 1

Terry Butler

Lesson Plan 4

Cooperating Teacher: Ms. Sheehan

Cooperating School: Northside High School

Date: October 27, 2009

Title of Lesson: Discovering Special Right Triangles Using Geometer’s Sketchpad

Audience: 10th grade Math II with Support Students

Content Objectives:

In a 45°-45°-90° triangle, the hypotenuse is times as long as each leg.

All 45°-45°-90° triangles are similar to each other.

Behavioral Objectives:

Students will use Geometer’s Sketchpad to discover a pattern in the data involving 45°-45°-90° special right triangles.

-What is the relationship between the legs of a 45°-45°-90° triangle and the hypotenuse?

-What is the relationship between two different 45°-45°-90° triangles?

Prerequisites:

Students should have basic knowledge of right triangles and their relationship to the Pythagorean Theorem. They should be familiar with the concept of similar figures.

Georgia Performance Standards (GPS) Objectives:

MM2G1. Students will identify and use special right triangles.

b: Determine the lengths of sides of 45°-45°-90° triangles.

MM2P1. Students will solve problems (using appropriate technology).

  1. Build new mathematical knowledge through problem solving.
  2. Solve problems that arise in mathematics and in other contexts.
  3. Apply and adapt a variety of appropriate strategies to solve problems.
  4. Monitor and reflect on the process of mathematical problem solving.

MM2P2. Students will reason and evaluate mathematical arguments.

  1. Recognize reasoning and proof as fundamental aspects of mathematics.
  2. Make and investigate mathematical conjectures.
  3. Develop and evaluate mathematical arguments and proofs.
  4. Select and use various types of reasoning and methods of proof.

MM2P3. Students will communicate mathematically.

  1. Organize and consolidate their mathematical thinking through communication.
  2. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
  3. Analyze and evaluate the mathematical thinking and strategies of others.
  4. Use the language of mathematics to express mathematical ideas precisely.

MM2P4. Students will make connections among mathematical ideas and to other disciplines.

  1. Recognize and use connections among mathematical ideas.
  2. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
  3. Recognize and apply mathematics in contexts outside of math.

MM2P5. Students will represent mathematics in multiple ways.

  1. Create and use representations to organize, record, and communicate mathematical ideas.
  2. Select, apply, and translate among mathematical representations to solve problems.
  3. Use representations to model and interpret physical, social, and mathematical phenomena.

In addition, standards originally addressed in the Middle Grades will be reviewed:

M7G3: Students will use the properties of similarity and apply these concepts to geometric figures.

  1. Understand the meaning of similarity, visually compare geometric figures for similarity, and describe similarities by listing corresponding parts.
  2. Understand the relationships among scale factors, length ratios...between similar figures. Use scale factors, length ratios...to determine side lengths... of similar geometric figures.

M8G2: Students will understand and use the Pythagorean Theorem.

Materials:

-Student Worksheet: Exploring Special Right Triangles Constructed from Squares

-Informational Sheet: Main Toolbar Keys in Geometer’s Sketchpad

-Lesson 5.1 Practice Worksheet, page 66 of Georgia Notetaking Guide, Mathematics 2

-Computers with Geometer’s Sketchpad

Procedure:

-Grouping–Students will attend the Computer Lab on the same hall as their classroom. Students will be grouped at Cooperating Teacher’s discretion.

-Launch # 1: How do you think we can explore special right triangles using Geometer’s Sketchpad? We discovered the relationship between the legs and hypotenuse of the 30°-60°-90° right triangle yesterday. Today we’ll look at another special right triangle that can be constructed from any square. Let’s get started.

Explore # 1:

  • DistributeStudentWorksheet: Exploring Special Right Triangles Constructed from Squares. (See attached.)
  • Guide students through the creation of a square and the creation of a 45°-45°-90° triangle using teacher notes/discussion guide entitled “Exploring Triangles Constructed from Squares.” (See attached.)
  • Observe students as they are constructing their squares and triangles. Help students who are having trouble with the process.

-Share/Summarize # 1:

  • Have students share results from their observations and calculations.
  • Does everyone agree?
  • What conjecture did you make about triangles whose angle measures are 45°-45°-90°? If no one came up with anything, ask them what the triangles had in common (Their relationship is a ratio of 1:1:.)
  • Allow students to volunteer a suggested Theorem for the relationships between the legs and hypotenuse for 45°-45°-90° triangles.
  • Write Theorem 5.1 on the board for students to record in their notes. In a 45°-45°-90° triangle, the hypotenuse is times as long as the legs.

-Apply:

  • Have students workLesson 5.1 Practice worksheet from page 66 in Mathematics 2 Georgia Notetaking Guide, in pairs. Discuss answers in class, have students show work on whiteboard.

Evaluation:

-Observe the students in their groups to see if they are participating

-Ask those students who seem uninterested questions about the activity and pull them into the class discussion

-Student Worksheet assignment will be used as a homework/daily participation grade

-Student Worksheets and Lesson Practice will be observed throughout for accuracy and completeness.

Key References:

Georgia Department of Education Frameworks, Math II, Unit 2

Mathematics 2 Georgia Notetaking Guide, McDougal Littell

Geometer’s Sketchpad

Modified from Lesson Plan by Ashley WallsmithFall 2009