Db Edu 598 Technology Lesson Plan

TECHNOLOGY INTEGRATED CLASSROOM LESSON Teacher Dan Bennett

Title “Exploring Ancient Ideas with Modern Technology: Using Web 2.0 Tools to Investigate the Pythagorean Theorem”.

Description of Activity In this lesson, students will use various websites and Web 2.0 tools to explore the proof of the Pythagorean Theorem. Students will practice using the Pythagorean Theorem in real-world situations and create a comic strip illustrating a real-world application.

Suggested grade level 8th grade

Pennsylvania Subject Area Standards 2.1.8.B Simplify numerical expressions involving exponents, scientific notation and using order of operations. 2.1.8.G Use the inverse relationships between addition, subtraction, multiplication, division, exponentiation and root extraction to determine unknown quantities in equations. 2.3.8.A Develop formulas and procedures for determining measurements (e.g., area, volume, distance). 2.5.8.C Justify strategies and defend approaches used and conclusions reached. 2.8.8.C Create and interpret expressions, equations or inequalities that model problem situations. 2.8.8.D Use concrete objects to model algebraic concepts. 2.8.8.E Select and use a strategy to solve an equation or inequality, explain the solution and check the solution for accuracy.

NETS Standards 1. Creativity and Innovation Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology. Students: a. apply existing knowledge to generate new ideas, products, or processes. b. create original works as a means of personal or group expression. 2. Communication and Collaboration Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others. Students: a. interact, collaborate, and publish with peers, experts, or others employing a variety of digital environments and media. b. communicate information and ideas effectively to multiple audiences using a variety of media and formats.

TECHNOLOGY INTEGRATED CLASSROOM LESSON 3. Research and Information Fluency Students apply digital tools to gather, evaluate, and use information. Students: a. plan strategies to guide inquiry. b. locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media. c. evaluate and select information sources and digital tools based on the appropriateness to specific tasks. d. process data and report results. 4. Critical Thinking, Problem Solving, and Decision Making Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources. Students: a. identify and define authentic problems and significant questions for investigation. b. plan and manage activities to develop a solution or complete a project. c. collect and analyze data to identify solutions and/or make informed decisions. d. use multiple processes and diverse perspectives to explore alternative solutions. 5. Digital Citizenship Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior. Students: a. advocate and practice safe, legal, and responsible use of information and technology. b. exhibit a positive attitude toward using technology that supports collaboration, learning, and productivity. c. demonstrate personal responsibility for lifelong learning. d. exhibit leadership for digital citizenship. 6. Technology Operations and Concepts Students demonstrate a sound understanding of technology concepts, systems, and operations. Students: a. understand and use technology systems. b. select and use applications effectively and productively. c. troubleshoot systems and applications. d. transfer current knowledge to learning of new technologies.

Learning objectives Students will: 1) Prove the Pythagorean Theorem using Internet resources 2) Find the missing side of a right triangle using the Pythagorean Theorem 3) Apply the Pythagorean Theorem to solve real-world problems 4) Contribute to a discussion board containing questions about the Pythagorean Theorem 5) Create a comic strip illustrating a real-world application of the Pythagorean Theorem

Materials required Computer lab (25 computers) Promethean board and video projector Class set of calculators Class set of scissors

TECHNOLOGY INTEGRATED CLASSROOM LESSON Class set of rulers Grid paper Copies of grid paper with triangle Copies of “Pythagorean Theorem Check-Up” Copies of “Pythagorean Theorem Application Problems” Copies of “Pythagorean Theorem Comic Strip” handout and rubric

Approximate number of class periods and length 5 45-minute class periods

Classroom management strategies: This lesson will be done individually and in small groups.

Warm up • •

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Print out copy of grid paper with triangle from http://www.pbs.org/wgbh/nova/proof/puzzle/papertriangle.html. Make copies for each class. Create discussion board for each class on school district web page (http://hub.colonialsd.org/Pages/default.aspx) *Access to the discussion boards requires a login and a password. Please contact me if you need these to look at the discussion board. It is assumed that students have a basic understanding of the terms leg and hypotenuse. It is also assumed that students understand the concept of “squaring” a number. Students will watch video on Pythagoras, chopped from YouTube with TubeChop: http://www.tubechop.com/watch/19728. This will give them a background on Pythagoras and his importance in mathematics.

Activities/ Procedures Day 1 • Students will watch “Pythagoras was a Square” video. Use the following link: http://www.tubechop.com/watch/19728 and teacher computer to project video onto Promethean board in classroom • After finishing video, instruct students that they will be using manipulatives to prove the theorem that Pythagoras popularized over 2,000 years ago. Explain to students that both the Egyptians and the Chinese knew about this idea long before Pythagoras, but he gets the credit because he was the first one to create a geometrical demonstration of the theorem. • Distribute copies of grid paper with triangle to each student along with a pair of scissors, a ruler, and a blank piece of grid paper. • To model the process, draw a triangle on the board and label the sides a, b, and c as seen on the grid paper. Ask students to think of each side of the triangle as also being the side of a square that is attached to the triangle. Draw squares on each side to help students visualize. • Tell students that we will each examine this relationship on our own. Instruct students to cut out their triangle then make three squares on a separate sheet of grid paper with sides that are equal

TECHNOLOGY INTEGRATED CLASSROOM LESSON

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to each side of the triangle. Begin with side a. Measure the length of side a. On the blank piece of grid paper, draw a square with sides that are the same length as side a. Label this square a2. Repeat these steps to create squares for sides b and c. Cut out the squares. Place each square next to the corresponding sides of the triangle. Ask students to guess the relationship between the squares. If a student guesses correctly, move on to the next step. If not, guide students to see that the area of the squares from the legs of the triangle is equal to the area of the square from the hypotenuse. Write the equation a 2 + b 2 = c 2 on the board. Ask students to prove this is true using the squares they drew. Students will need to overlap the squares to show the areas are the same and they will need to cut one of them into smaller squares to make it fit. After students have completed this proof, ask students if this works for other size triangles. After discussion, have students pair up with a partner and draw a different size right triangle. Have students repeat process from first activity to prove that this theorem works for any size right triangle. Discuss outcomes with class. When completed, ask students to see if this works for other types of triangles. In same pairings, have students draw non-right triangles and repeat process. Students should see that this theorem only works for right triangles. Discuss results as a class. Conclude with a statement of the Pythagorean Theorem: “The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.” Students should write this in their notes. Explain to students that there are many different proofs to this theorem and tomorrow we will be using the computer lab to investigate some of these proofs.

Day 2 • Class will be held in computer lab. Ask students to log on to computers when they enter the room. • Remind students that we will be examining other proofs of the Pythagorean Theorem. Instruct students to go to the following site: http://nlvm.usu.edu/en/nav/frames_asid_164_g_3_t_3.html?open=instruction s&from=category_g_3_t_3.html. Explain to students that these puzzles show other methods of proving the Pythagorean Theorem and allow students time to work through each puzzle. Students can move at their own pace and some students may need hints on where to start. Use the “Parent/Teacher” link at the top of the window for some hints to give to students. It is not crucial that every student finishes every proof, only that the students have completed at least one and have been exposed to others. • When majority of students have finished, use this time in the computer lab to introduce the discussion board and instruct students how to access it. The discussion board will be used to allow students to ask questions that were not answered during class time. This board will also be used for the teacher to pose questions to the students and give them time to reflect before answering. Explain that each class will have its own discussion board and each student will be required to make at least 2 posts over the course of the unit. Discuss with students the elements of a quality post (being specific, using more than one sentence, etc.) and walk students through the process of logging on to the discussion board through the Colonial School District website

TECHNOLOGY INTEGRATED CLASSROOM LESSON

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http://hub.colonialsd.org/Pages/default.aspx. (I apologize that it is only accessible with a district login and password). Here are the steps:  Log in by clicking link in very top right hand corner.  Go to “Our Schools”, then “Colonial Middle School” from the blue toolbar  Scroll down under the picture of CMS and click on the “Colonial Middle School Online Courses” link  Find your math class under the “My Classes” list and click on the link.  On the left, there is a gray box that has several options. Roll the mouse over “Discussions”, and then click on the “Class Discussions” option that comes up.  Click on the “Pythagorean Theorem” discussion. This will bring up the discussion board to post questions and comments. Give students time to post on the discussion board and finish any Pythagorean Theorem proofs that they were previously working on.

Day 3 • This class will be in the computer lab. Have students log onto their computer when they enter the room. • Using the whiteboard in the computer lab, demonstrate how to use the Pythagorean Theorem to find missing side lengths of right triangles. Use the following examples:  Legs have length 3 and 4, find hypotenuse length  Legs have length 5 and 12, find hypotenuse length  One leg has length 6 and hypotenuse has length 15, find length of other leg  One leg has length 10 and hypotenuse has length 22, find length of other leg • Students may need calculators; if so, have them available in computer lab. Students can also use calculators on computer. • Once examples are worked through, direct students to the Interactive Pythagorean Theorem Practice: http://www.shodor.org/interactivate/activities/PythagoreanExplorer/. This site will allow students to practice using the Pythagorean Theorem while keeping track of correct and incorrect answers. Students should be instructed to show all of their work on a separate sheet of paper. If students answer a problem incorrectly, they should turn to the student next to him or her and ask for his or her help in finding the mistake. Students should keep the work they do for these problems in their notebook for future reference. • This activity allows for differentiation since there are 3 levels of difficulty. Level 1 has all integer side lengths, while levels 2 and 3 use non-integer side lengths. This will let students practice according to their own abilities and move at their own pace. • Exit Slip: Pythagorean Theorem Check-In (attached at the end of this file) Day 4

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Prior to the start of this class, post the following question on the discussion board: “How does the Pythagorean Theorem relate to the real world? Specifically, how can you use it in your everyday life?” This class will be in the computer lab. Have students log onto their computer when they enter the room. Direct students to the NOVA website to investigate real-world applications for the Pythagorean Theorem: http://www.pbs.org/wgbh/nova/proof/puzzle/use.html. Discuss both the baseball and the ladder problem as a class. After working through these problems, have students log on to discussion board. Students should observe the new question posed to them and remind students that they must post at least twice per question on the discussion board. (Even if they have made two posts up to this point, they must post two more times in response to the new question.) Have students log off the discussion board and direct students to www.toondoo.com. Distribute assignment sheet and rubric to students (attached at the end of this file). Explain to students that they will be creating a comic strip illustrating a real world problem that requires the use of the Pythagorean Theorem to solve. Students will be given time in class to work on this assignment but will probably need more than just class time to complete the assignment. Walk students through registration on the site and make sure that each student is able to log in with their new username and password. Allow students time to explore the site and begin to work on their cartoon. Encourage students to ask questions or post questions on the discussion board if they come up after class. This assignment will be due one week from today. Distribute copies of “Pythagorean Theorem Application Problems” worksheet. This assignment is due tomorrow and will be reviewed in class. Students should also come into class tomorrow with an idea for their comic strip.

Day 5 • This class will be in the computer lab. Have students log onto their computer when they enter the room. • Review homework assignment with students. Discuss any problems as a class. • Students should use the period to create their comic strip. This is the only remaining class time they will have to work on the assignment so remind students to use their time wisely.

Assessment strategies • • •

Assessment on Days 1 and 2 will be based on teacher observation and student discourse. Since this is still in the discovery phase of the lesson, no formal grade is needed. Teacher observation and student performance on Interactive Pythagorean Theorem Practice will be used, along with the exit slip, for formative assessment on Day 3. For Day 4, homework from the previous night will be checked.

TECHNOLOGY INTEGRATED CLASSROOM LESSON • •

Discussion boards will be checked to make sure that each student has made at least 2 comments. Comic strip will be graded according to attached rubric.

Related Web Sites www.toondoo.com (Creating comic strips about Pythagorean Theorem) http://nlvm.usu.edu/en/nav/frames_asid_164_g_3_t_3.html?open=instructions&f rom=category_g_3_t_3.html (Pythagorean Theorem proofs using puzzles) http://www.pbs.org/wgbh/nova/proof/puzzle/papertriangle.html (Paper triangle for proof) http://www.shodor.org/interactivate/activities/PythagoreanExplorer/ (Online practice using the PT) http://hub.colonialsd.org/Pages/default.aspx (Discussion board through CSD HUB) http://www.pbs.org/wgbh/nova/proof/puzzle/use.html (Real-life applications of PT) http://www.pbs.org/wgbh/nova/proof/puzzle/pyramid.html (Enrichment problem)

Back-up plan: (if the technology fails!) • • •

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The first day of the lesson can be done, for the most part, without the technology if there is a problem. The video at the beginning can be replaced with an explanation by the teacher about the history of Pythagoras and his importance to mathematics. The demonstration part of day 2 can be done through the projector and Promethean board if needed. The lesson will be more teacher-driven than student-based discovery but we can still accomplish the same goals. Day 3 can be changed to a cooperative activity using the homework worksheet. Students can pair up and use the “Pairs Check” cooperative structure. Student A does a problem, talking out loud the process. Student B watches, coaches, and praises. Students then switch roles. After every 2 problems, pairs should compare answers with another pair. Continue until all problems are completed. If the technology does not work for days 4 and 5, the comic strip can also be made by hand.

Branching out Enrichment: Students may attempt the challenge problem on the NOVA website about pyramids located at http://www.pbs.org/wgbh/nova/proof/puzzle/pyramid.html Remediation: Students can work on more Pythagorean Theorem practice problems on the “Pythagorean Theorem Extra Practice” worksheet (attached at the end of the lesson).

TECHNOLOGY INTEGRATED CLASSROOM LESSON

Grid Paper with pre-drawn triangle (Day 1)

TECHNOLOGY INTEGRATED CLASSROOM LESSON

Name___________________________ Date____________________________

TECHNOLOGY INTEGRATED CLASSROOM LESSON Pythagorean Theorem Check-Up For each of the triangles below, please find the length of the missing side. Express the side length in decimal form, rounded to the nearest hundredth. Please show all of your work! 3 in. 1)

2) 6 in.

10 in.

7 in.

Name___________________________ Date____________________________ Pythagorean Theorem Check-Up For each of the triangles below, please find the length of the missing side. Express the side length in decimal form, rounded to the nearest hundredth. Please show all of your work! 3 in. 1)

2) 6 in.

10 in.

7 in.

TECHNOLOGY INTEGRATED CLASSROOM LESSON Name________________________________ Date________________________________ Pythagorean Theorem Application Problems 1) A telephone pole support cable attaches to the pole 20 feet high. If the cable is 25 feet long, how far from the bottom of the pole does the cable attach to the ground?

2) Frank Rd and James Rd. make a perpendicular intersection. The state wants to build a new road. The new road will intersect 3 miles north of the intersection on Frank Rd. and 4 miles west of the intersection on James Rd. How long will the new road be that intersects Frank and James Rd? The new road would cost $10 per foot to pave. What would be the cost of the new road?

3) The mobile phone company is anchoring wires to the top of their 1200 ft high communication towers. The cable for the support wire comes in a roll that is 3900 ft long. The company requires you to use the entire roll. The cable can only be cut twice to ensure its strength. All cables need to be equal. How long will each cable be and how far from the base of the tower do they need to be anchored?

4) In the city planning meeting, a scale drawing of a park was drawn. The park fills inside a square city block. The scale was 3 inches equal 3/10 miles. One side of the city blocks was 4 inches in the drawing. One member of the city planners said, "There needs to be a short cut through the park from the corners." How long in miles will the short cut be? Round answers to the nearest tenth of a mile.

TECHNOLOGY INTEGRATED CLASSROOM LESSON 5) You are planning to put a new digital flat TV on a wall that is 12 ft long and 9 ft high. The digital TV has a diagonal of 72 inches. The length of the TV is twice the width of the TV. How much of the wall will still need to be decorated around the TV?

Over the past several days, we have explored the Pythagorean Theorem and its many uses. Now, it’s your chance to be creative and show me what you’ve learned! You will be required to make a comic strip illustrating a real world problem that can be solved using the Pythagorean Theorem. This should be an original problem, not a copy of one that we have seen in class. Your comic will be graded on 4 categories: text, attractiveness/organization, graphics/pictures, and (most importantly) mathematical accuracy. The rubric for this assignment is included with this handout. You should be using the site www.toondoo.com to create your comic strip; however, you are also permitted to make the comic strip by hand if you choose. You created your account in class so you should have your own login and password to use. Please see me if you have any difficulty with the site or your comic strip. Lastly, be creative and have fun!

TECHNOLOGY INTEGRATED CLASSROOM LESSON

Pythagorean Theorem Comic Strip Rubric Text

4

3

Speech relates to the illustration, and clearly communicates in detail the action in the scene. Few grammatical errors are present. Speech relates to the illustration and clearly communicates the action in the scene. Some grammatical errors are present.

Attractiveness and Organization

Graphics/Pictures

Mathematical Accuracy

Comic strip is well organized, strip is eyecatching, and color and graphics enhance the strip.

Graphics go well with the text and there is a good mix of text and graphics. All graphics are mathematically accurate.

All components are present and mathematical information is complete and accurate.

Comic strip is well organized, strip is appealing, and color and graphics are apparent.

Graphics go well with the text, but there are so many that they distract from the text. All graphics are mathematically accurate.

All components are present and mathematical information is mostly accurate. A few mistakes may be apparent.

TECHNOLOGY INTEGRATED CLASSROOM LESSON

2

Speech relates to the illustration, however not enough information is given to clearly identify the actions of the scene. Some grammatical errors are present.

Comic strip is somewhat organized, strip is simple, and there is a limited use of graphics and color.

Graphics go well with the text, but there are too few and the comic seems "text heavy". Graphics are mostly mathematically accurate.

Most of the components are present and mathematical information is partially accurate. Some mistakes may be apparent.

Comic strip is unorganized, strip is forgettable, and there is little to no color or graphics.

Graphics do not go with the accompanying text or appear to be randomly chosen. OR Graphics are not mathematically accurate.

Only some of the components are present, many mistakes are apparent, or the comic strip is incomplete.

1

Speech sometimes relates to the illustration. Scattered information is given in the speech bubbles, often leaving the reader wondering what is going on. OR Frequent and severe grammatical, spelling, or punctuation errors that interfere with understanding.