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Detailed Lesson Plan Student Intern’s Name: Malynta Masby Lesson Title: Pythagorean Theorem Lesson Planned Time: 2 days (50 minutes) Objectives Upon completion of the lesson, the students should be able to: Objective 1: Identify the Pythagorean Theorem formula and prove it using the areas of squares to find the sides of a right triangle. Objective 2: Use the Pythagorean Theorem to find the hypotenuse of right triangles. Objective 3: Make observations of the use of right triangles in architecture. Objective 4: Recognize that the hypotenuse of a right triangle is always the longest side, and be able to compare imperfect squares to other integers. Georgia Performance Standard Alignment 8.NS The Number System - Know that there are numbers that are not rational, and approximate them by rational numbers. 8.EE Expressions and Equations - Work with radicals and integer exponents. 8.G Geometry -Understand and apply the Pythagorean Theorem. Essential Questions, Knowledge & Skills What is the Pythagorean Theorem and what Students will know how to round numbers to polygon is it used with? the nearest hundredth. How can the Pythagorean Theorem be proven Students will know how to solve equations that and used? involve several steps. Differentiated Instruction Discuss alternate or additional strategies, resources, or activities to engage students at varying levels of readiness, modalities and/or interests. I will use different stations that all require students to practice using the Pythagorean Theorem to solve problems. The stations will include board games, manipulatives, and online activities to appeal to the diversity of interests. Some activities will also have extension questions to challenge those students who have advanced knowledge of the content. Materials/Preparation What materials will you use? -The Pythagorean Theorem Board Game (dice, tangrams, question cards, and computation table) -Prove It! Worksheet -candy (skittles) -Smart board & tablet - 120 drinking straws -graphing paper -masking tape -electrical tape or duct tape How will you arrange the desks? The desks will be arranged in groups of approximately four students per group. Students will rotate through each station remaining in their cooperative teams. Warm-up Exercise: 10 minutes How will you get the students’ attention? I will employ a kinesthetic activity to get the students’ attention. Students will begin the warmup by drawing a number line diagram using only positive integers. Once this is drawn, I will ask students to rewrite each integer on the number line as the square root of a perfect square. For example, students will write √1 below 1 on the number line, √4 below 2 on the number line, √9 on the number line below 3, and so on. Once this is completed up to 17, I will tell students that oftentimes the hypotenuse is not a perfect square, but we can estimate what two numbers it falls between based on the conversion of whole numbers into the square root of perfect squares. I will then give a few examples and see if students can estimate what two numbers it falls between. For example, students should be able to position the √40 between 6 and 7. Afterward, I will ask a student to draw and label the type of triangle used for the Pythagorean Theorem. I will then write the lengths of each leg and hypotenuse, and ask students if the triangle was not drawn could they determine which number is the hypotenuse. Students should be able to answer that the hypotenuse is the longest side; and therefore, it is the greatest number. Select students will be given numbers then asked to locate their position on a number line taped to the floor. Once positioned, I will tell the class that these three numbers represent the two legs and hypotenuse of a triangle. I will then ask the class which number represents the hypotenuse and have them explain their reasoning. After a few rounds, students should realize that the hypotenuse is the length of the longest side of a right triangle and should be able to identify the hypotenuse when three numbers are presented without the diagram of the triangle accompanying them. How will you connect this lesson with their previous knowledge and/or the real world? This lesson will be connected to student’s previous knowledge and real world applications through the type of word problems presented. For example, during the online game station, students will be asked a question involving a television and entertainment system. Within this question, students will determine if the television will fit within the entertainment system. Students will also answer a real world question for their ticket out the door. Students will compute the quickest route to return home from their friend’s house using actual street names within the McNair community for relevancy. One station will also present real-world buildings and architectural structures. Body: 30 minutes How will you present the new content? I will use stations to present the Pythagorean Theorem. The Pythagorean Theorem was introduced at the beginning of the week, so through this lesson students will receive ample practice using the Pythagorean Theorem during different activities. Playing cards will be used to divide students into four groups. Students will rotate through each station in groups of 3 or 4 students. One student in each group will be the designated leader of the group. They will be responsible for coming to me with any questions the group has while I am assisting other stations. I will rotate through each station in a clockwise cycle, spending three minutes at a time at each station. Students will spend 15 minutes at each station, completing two stations the first day, and rotating through the other two stations the following day. What examples will you use? There will be four separate stations. At the first station students will work at the Smart Board and use the tablet to complete different online activities. Students will review some of the Pythagorean Theorem concepts and compute the length of the hypotenuse using the following website: http://jmathpage.com/middleschoolmath/jmsmpythagoras.html . More advanced students, once having received adequate practice, will have the option to play a Jeopardy game of the Pythagorean Theorem at the following website: http://www.math-play.com/Pythagorean-Theorem-Jeopardy/Pythagorean-Theorem-Jeopardy.html At the second station students will play the Pythagorean Board Game. Students will roll the dice and use those two numbers to represent the lengths of the legs of a triangle. They will then use the Pythagorean Theorem to find the hypotenuse, rounded to the nearest whole number. Students will progress forward the number of spaces that is equivalent to the length of the hypotenuse they calculated. Students may also land on a space that requires them to answer a trivia question about the Pythagorean Theorem and the history of Pythagoras. Students will show their work on the worksheet provided. At the third station students will use round sized pieces of candy as manipulatives to illustrate one method of proving the Pythagorean Theorem. They will take the candy to cover the squares made using the sides of the two legs of a right triangle. They will then only use those pieces of candy to cover the area of the square made using the length of the hypotenuse of the triangle. This activity should help students to further conceptualize the fact that the Pythagorean Theorem states that the sum of the area of the two squares made from the length of the legs of the right triangle is equal to the area of the square made from the length of the hypotenuse of the right triangle. Students will answer the questions on the Prove It worksheet to further guide their understanding. At the fourth station students will construct towers using straws and masking tape. The group will be given 30 drinking straws and will be required to use right triangles in their design to construct the tallest, sturdiest tower that will remain standing for at least one minute (long enough to measure its height). Prior to construction, students will sketch their designs on graphing paper and identify right triangles in different historical architectural buildings including the pyramids that Pythagoras observed when formulating his theorem. Transitioning to the Abstract What potential questions or problems do you anticipate? I anticipate students having difficulty understanding why the theorem uses the areas of squares instead of the lengths of the sides of the triangle. I anticipate students having questions about which numbers to plug into which part of the formula for the Pythagorean Theorem. I anticipate students having difficulty performing multiple step equations and showing their work in an orderly fashion. I anticipate students having difficulty rounding numbers to different specified place values. I anticipate students having difficulty articulating the inverse operation of squaring a number or variable, which is taking its square root. I also anticipate students having difficulty estimating the square root when it is not a perfect square without using a calculator. What teaching points do you want to remember to emphasize? I want to remember to emphasize the fact that the Pythagorean Theorem only applies to right triangles. I want students to have a deeper depth of understanding of the Pythagorean Theorem and not just memorization of the formula. Students should understand that the Pythagorean Theorem involves adding the areas of the squares made from the lengths of the legs of the right triangle to find the area of the square made from the length of the hypotenuse. I also want to remember to emphasize the fact that the inverse operation of squaring a number is finding its square root. Close: 10 minutes How will you summarize and pull together the content taught? I will remind students that the Pythagorean Theorem is not simply a formula to memorize. It is a method that involves using the information you have to solve for the unknown. Pythagoras found patterns and similarities between right triangles of different sizes, and after much observation he developed a simple formula that is very useful. It is not only useful but vital for architectural design and the engineering of buildings. How will you lead into the next lesson? I will tell students that while we have been using the Pythagorean Theorem to find the length of the hypotenuse, it can also be used to find the length of a leg of the right triangle which involves using the same formula, but solving for a different variable. We will learn more about this the upcoming week. Assessment: 5 minutes How will you evaluate this understanding of learned material? I will evaluate the understanding of the learned material by asking students open-ended and directed questions throughout class. Students will also complete worksheets for some stations that will be collected. These worksheets will provide me with insight into their current understanding and misconceptions. Students will also be assessed with a ticket out the door. Technology Connection/Integration (if applicable) How will technology be integrated into the instructional plan? The Smart Board and a tablet will be used at one station. At this station, students will navigate through the activities, using a different medium to compute the Pythagorean Theorem. The activities will have graphics and provide students with immediate feedback. What does the technology add to the lesson? Technology offers students an interesting and different medium to compute problems involving the Pythagorean Theorem. The websites also provide more real world applications for the Pythagorean theorem. The technology provides additional opportunities to practice using the formula, which is presented in slightly different ways to help students to recognize it in different contexts. Warm Up INTERACTIVE NUMBER LINE Three students at a time will be given a small dry erase board and will position themselves on the number line drawn on the floor. The class will then determine which number is the length of the hypotenuse. The following Pythagorean Triples will be used: 5, √144, 13 √9, 4, 5 8, 17, 15 1, √1, √2 9, 12, √225 Station 2 https://sn2prd0102.outlook.com/owa/attachment.ashx?attach=1&id=RgAAAACNmrV1XIbRT5y3 GHxzgKVnBwCNxsSnZ1TOT4HKooo1DMiWAAAAVwIWAACNxsSnZ1TOT4HKooo1DMiWAA Au0kaKAAAJ&attid0=EAB%2boaoYjsNPToIfAMYhtxjf&attcnt=1 THE PYTHAGOREAN THEOREM BOARD GAME Exact Value of The Hypotenuse The Approximate Value of the Hypotenuse (Rounded to the nearest whole number) = 36 =16 36+16= 52 7 Station 3 PROVE IT! 1. What is the formula for Pythagorean Theorem? ____________________________________ 2. can be said as A to the second power. How else can 3. be said?_____________________ can be said as a to the second power plus b to the second power equals c to the second power. How else can this formula be said?___________________________________ 4. Fill in the blank: All sides of a square are __________. 5. What is the formula for the area of a square, with side s? _______________________ s 6. If the area of a square is 25 square feet, what is the length of one side?______________________ 7. If = 25 what inverse operation must I use to find c? Fill in the blank: Take the __________________ of both sides. 8. Draw three squares that connect to TRIANGLE 1. Use side a of TRIANGLE 1 to draw SQUARE A. Use side b of TRIANGLE 1 to draw SQUARE B. Use side c of TRIANGLE 1 to draw SQUARE C. a c 1 b 1. Take only the amount of candy needed to fill in square a and square b on the triangle found below. 2. Use only the candy pieces from square a and square b to fill in square c. 3. You do not need any additional candy. DO NOT EAT THE CANDY UNTIL THE ACTIVITY IS COMPLETED. 4. Why does a triangle with these sides work so well with the candy activity? What do all the squares have in common? The table below includes triangles with sides that form perfect squares. Complete the Table: RIGHT TRIANGLE AREA OF SQUARE a AREA OF SQUARE b AREA OF SQUARE c LENGTH OF HYPOTENUS 12 5 9 12 8 15 EXTENSION: If , does ? Explain and provide an example for your reasoning. Does the candy activity work well with a triangle where a=1 and b=1? Draw a diagram to explain your reasoning. Formulate a real world situation that requires the use of the Pythagorean Theorem. Station 4 Which architectural structure did Pythagoras observe when formulating his theorem? Identify right triangles in the structures. The Great Pyramid of Giza in Egypt, Africa Chichen Itza Ball Court Watchtower Was Ancient Mayan Observatory, South America The Eiffel Tower TICKET OUT THE DOOR Kamaria went over Biko’s house to study for their math class. Kamaria lost track of time and realized that she had ten minutes to get home before the street lights came on or she would miss her curfew and be punished. Kamaria’s house is diagonally across from Biko’s house on Northfield Boulevard. How far is Kamaria’s house from Biko’s home, if Jolly Road is 8 feet long, and Old National is 15 feet long? Both Jolly Road and Old National Highway form a right angle connecting to Northfield Boulevard. Biko’s House Northfield Blvd Old National Jolly Road Kamaria’s House TICKET OUT THE DOOR Will a 36 inch tv (which is the measure of the diagonal of the tv screen) fit within a entertainment center that has a compartment for the tv that is 25 inches long and 25 inches in height? Show your work. 25 36 25 television entertainment center