1Task 4 Direct Instruction Lesson Plan Template - Mathematics PDF

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Lesson Plan Template. Math for Direct Instruction...

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Direct Instruction Lesson Plan Template

General Information Lesson Title: Pythagorean Theorem Subject(s): Algebra/Geometry Grade/Level/Setting: Middles School 8th Grade Classroom Whole class and groups Prerequisite Skills/Prior Knowledge: The student needs to be able to get onto their Chromebook and access Kahootz. The student needs to know the different triangles. (acute, obtuse, and right) The student will need to know how to use a calculator to access the square of a number and the square root of a number. The student will need to be able to recite some of the perfect squares. (3*3=9, 4*4=16, etc.) The student will need to be familiar with Desmos and GeoGebra graphing programs.

Standards and Objectives Common Core Standards CCSS.MATH.CONTENT.8.G.B.6 Explain a proof of the Pythagorean Theorem and its converse. CCSS.MATH.CONTENT.8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. CCSS.MATH.CONTENT.8.G.B.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Utah Standard 8.G.6 Explore and explain a proof of the Pythagorean Theorem and its converse. Standard 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Standard 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Learning Objective(s): Students will be able to solve the equations given of the triangles with an 80% or higher. Students will be able to write down the Pythagorean Theorem with 80% accuracy or higher. Students will be able to tell which 1 of the 4 facts are considered accurate about Pythagoras.

Materials

Technology

Rap Video. https://www.youtube.com/watch? v=nbopLhP4kpo Demo Video: https://www.youtube.com/watch? v=CAkMUdeB06o&t=19s Worksheet with problems Penny Pencil Ruler Scratch Paper Starbursts per group (3 colors) (9 of one, 16 of another, and 25 of another) Chromebook Kahoot/password

They are using Chromebooks to access a website called Kahoot for an exit ticket. They will also be using calculators to help figure out the problems that they will be given. For Students that want to try to create, They can go to Desmos or GeoGebra.

Language Demands

Language Function(s): Students will explain how to find the length of the hypotenuse of a right triangle. Students will be able explain how to find the missing leg length of a right triangle. Students will be able to explain the Pythagorean Theorem on their own without being told the exact formula. Students will explain who Pythagoras was and some highlights of his life. Vocabulary: Legs of a triangle The hypotenuse of a triangle Pythagorean Theorem Discourse and/or Syntax: Students will be working together to come up with solutions for the first problem, which is finding the length of the hypotenus equations using numbers and/or rulers. Students will then work as a class to keep coming up with ideas on how to solve the lengths of the triangle sides. Students will also be working independently to see if they can come up with the correct answers for their worksheets. Planned Language Supports: The teacher will introduce any new vocabulary for this lesson by saying the words but not giving the definitions, YET. The kids will be in mixed groups so that they are using their peer language. For ELL students, pictures of essential Geometry terms with their native language and the English words provided. Visuals/Videos given for use in this lesson. The teacher needs to walk around the room and make sure the kids understand the work that they are doing. Chromebooks are in their hands and are to be used. On the board will be posted examples of things the kids will need to help them discover the Pythagorean Theorem.

Instructional Strategies and Learning Tasks

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Anticipatory Set: Activity Description/Teacher Student Actions As the kids walk into the room, there  Each kid will flip the penny to see if they will be a picture of a triangle on the get heads or tails. whiteboard. It will be labeled with  If they got tails, they are to take their ruler numbers on the two legs. On their and paper and draw the triangle on the desk will be a ruler, paper, and a board. They are to find the hypotenuse penny. length by only using paper, a ruler, and a Also, on the other side of the board pencil. will be a picture of a cloud. There will  If they got heads, they will take the cloud be symbols and numbers to write an of information and come up with a equation that works in the large equation to the answer cloud. cloud. In a separate cloud is the  Students will then start explaining what answer to the equation that they are they have discovered with the either the

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to get. drawing or the number cloud. As the kids are working, walk around and make sure they all try to accomplish the equation. Presentation Procedures for New Information and/or Modeling: Activity Description/Teacher Student Actions Ask the students what they have  Have a student explain how they solved figured out by doing the activity that the cloud equation so that the other we just did? students might understand it. Ask if anyone was able to solve the  The student will repeat some of cloud equation. Pythagoras’ famous points of his life. Ask the kids if there is any unfamiliar vocabulary or phrases they are still confused about and need clarification. Read a few facts about the man Pythagoras. (paper at the end of the lesson)

Guided Practice: Activity Description/Teacher Student Actions Q Place more triangles(1 or 2) on the  After doing a few very similar problems, board and ask the kids which way they will feel confident with what they are would they instead solve it, the cloud doing. equations or drawing out the  With the four very similar triangles, see if calculator. they can figure out which one does not fit. Q Then place four triangles on the  Let one of the kids tell you why the last board, all with the exact triangle does not fit with the other three. measurements as their sides. On  Let the kids start telling what formula they three triangles, change the way it could write to explain how they are looks but put the numbers on the legs solving the equations. only. On one of them, write the measurement they are looking for on one of the legs and the hypotenuse. Independent Student Practice: Activity Description/Teacher Student Actions  Hand out the worksheet and ask them  Students should be able to work with a to work with a partner to get it partner or two to solve the equations and finished. Three questions are a bit "who done it." challenging, and when they solve the  They now have the formula for equations, they have to unscramble Pythagorean Theorem(with their own the letters to find out "who done variables). it."(worksheet at the end of this form) Culminating or Closing Procedure/Activity: Activity Description/Teacher Student Actions  The student will be able to watch the Q Show the Video about Pythagoras and video and answer a question about the Triangle. Pythagoras. Rap Video. https://www.youtube.com/watch?

v=nbopLhP4kpo Demo Video: https://www.youtube.com/watch? v=CAkMUdeB06o&t=19s Q Ask questions about the lesson and videos. Q Open the Kahoot program and click on the Pythagoras “Who Done it” quiz. (exit ticket)

Students will go to the Kahoot quiz and answer the available questions (the quiz is timed). Kahoots is their exit ticket.  After the video’s they will be able to write down the actual Pythagorean Theorem. 

Differentiated Instruction Gifted and Talented: Those who finish early have three challenge questions on a paper that is then posted on the board. Students will be able to solve the challenge questions. Students will open GeoGebra to try and make a triangle for a friend to solve. Give the students a chance to teach in small groups to help those who are still struggling. Students can create a project(poster, website, google draw) representing a connection between triangles and the Pythagorean Theorem.

EL: The teacher will support ELL students by giving them picture dictionaries, translations, or illustrations to help with the vocabulary words unfamiliar to them. The teacher will have a Word Wall that contains all of the vocabulary words. Give extra time to form answers and questions needed for solving the problem. Ask questions based on the individual level of learning.

Students with Other Special Needs: Provide extra time to accomplish the goals and assessments. The student will work with another adult, teacher, or gifted student to help lead and guide them a bit more. The teacher will provide the vocabulary a day or two earlier to get some extra tie with it. Students can use manipulations of any kind that will help them represent and connect to the task (geoboards) The teacher will provide them with part of the slope-intercept formula and definitions for the vocabulary. (some words missing that they have to fill in)

Assessment Formative The teacher will walk around the room and see what the student's math talks are. Hoping the math talk will lead them to the correct formula outcome for the slope-intercept form. The teacher will lead their discussion into the correct thought process if they have gone astray. The teacher will explain more if needed and use more examples if it is difficult for them to develop their ideas.

Summative The worksheet is put into Kahoot's by answering the questions. It lets the teacher know if they have responded to them correctly and who might need more help.

Draw 3-4 right triangles, using the following numbers for their legs: 1st Triangle: 12m and 16m 2nd Triangle: 12yd and 9 yd 3rd Triangle: 8in and 15 in 4th Triangle: 5cm and 12cm Then draw the last 4 triangles on the board:

Ask them which of the triangles does not fit what they have come up with and why. Then ask them what can you do to make it work? This will help them find the missing side when given the hypotenuse.

Three posters on the board:

“Who Done It?” Worksheet Solve each of the problems and submit your answer when we play kahoots.

For Problems 7-9, you need to solve the equation and unscramble the letters to find out "who done it? 7. Mr. Paco bought a movie screen. The screen is 48 inches wide and 27 inches high. What is the size of this movie screen? a. 55 in - Nets Click Ad b. 48 in - Rev Lover c. 27 in - Snoop I d. 75in – If Ken 8. A baseball diamond has four right angles and four equal sides. Each side is 90 feet. What is the shortest distance between home plate and second base? a. 90 ft – Hen Tick b. 127 ft – I Brr Lay c. 180 ft – No Mr Indigo d. 360 ft – Sty Over Acorn

9. Find the height, h, of the right triangle.

9cm

9 cm a. b. c. d.

4.5 cm – Muds Tar 7.8 cm – Coke Cap 9cm – Cheap 10 cm - Cartels

Pythagoras: Strange Facts about Pythagoras: "There was a whole cult behind the man who figured out how to measure the side of a triangle, and --- you might imagine---they had some pretty strange beliefs." (1)

1. He gave up his life to protect fava beans(broad beans). He felt that these beans gave you gas, and expelling gas took away the "breath of life." 2. He spoke behind a curtain because other than mathematicians, people were not to see his face. 3. He might have killed a man by drowning him because he discovered Irrational Numbers. (Hippasus) 4. New people to his cult had to be silent for five years. Pythagoras told them to learn self-control. 5. He had some stringent and specific rules for just about everything. He felt you had to put your right shoe on first. 6. He was one of the earliest Vegetarians that we know of in history. They did not believe in eating meat. He still ate Oxen whenever they solved a mathematical problem. 7. He believed in being reborn. He thought he was Hermes' son in his past life. 8. He was treated like a God. They even thought he had mystical superpowers. 9. He and his people prayed to the number "10." They felt that the number ten was of the highest order— the Big Daddy of his new faith. 10. He led a cult that worshipped numbers. He felt that numbers the elements behind the entire universe. He started a school with this belief. 11. There was also a legend that Pythagoras had a golden thigh that he would show to impress people to get them to join. No matter what you think of Pythagoras, his ideas were strange, but his work in math was incredible. There is a quote that I liked, "Anyone's life can seem strange you just need to take a look at it from the right angle."(1) Exit Ticket: Kahoot

I chose to do the Pythagorean Theorem for my lesson to engage students. I started with two problems on the board, and as they walked in, they flipped their penny. The penny chose the problem they had to discover an answer. The lesson is to allow students to appreciate how difficult it must have been for the ancient mathematicians to find this Theorem by doing this activity. I also then integrated the history of Pythagoras after they had a beginning start on how to solve the problem. I think the students will love the history behind the man who has been given credit for the Pythagorean Theorem.

I read three articles about the effectiveness of history used in math lessons. The history of math is full of emotion and can capture the students' interest and curiosity. It is said to enhance creativity and appeal to further their study of math. “Liu (2003) adds that using historical problems in class improves students' understanding of Mathematics as many concepts have undergone evolution and revisions over the centuries. History enables the students to understand Mathematical thinking and acknowledge its dynamic nature"(9). Sometimes, learning about history gives them a connection to the person in history or how it came about. It also helps to make connections with math that they have already had the pleasure of learning. “Tasks that require students to make multiple connections within and across topics help them appreciate the interconnectedness of different mathematical ideas and the relationships that exist between mathematics and real-life"(page 15) (10). Using historical problems in our lessons can help the students apply math in an everyday context. They learn of the value to society and how it has contributed to other subjects and then allow them to view math as part of their history and lives(4). In recent years pedagogy has pressed for changing and evolving our teaching to include the history for more understanding of the "why" in the Pythagorean Theorem. The article, Benefits from Integrating History of Mathematics into Teaching, explains why you should use history. One of them is it shows the development of math as a human activity. Another is it provides opportunities for cross-curricular work with math and other subjects. The last one was it gives a multicultural approach to your classroom(11). After watching the videos, discovering for themselves, and a list of things that Pythagoras was known for in history, it is easy to see that the students would better understand the foundation of the Theorem. History gives connection so they can see what it took someone to find a theorem, and it might also take the time to figure out how to do their work. It allows the student to have a complete picture of the topic, which provides a more in-depth education and understanding of the process.

Sources: https://listverse.com/2017/04/26/10-strange-facts-about-pythagoras-mathematician-and-cult-leader/ http://www.moomoomathblog.com/2015/03/10-fun-youtube-videos-covering.html https://www.maa.org/sites/default/files/HistoryMathCourses.pdf https://cs.appstate.edu/~sjg/class/5125-375/2whohowwhat.html

http://users.sch.gr/afylakis/ME2013/ME2013JShara.pdf https://www.uen.org/core/core.do?courseNum=5180 http://www.corestandards.org/Math/Content/8/introduction/ https://create.kahoot.it/details/1e311f6e-18e6-4855-8d70-0f9bb352bf97

https://www.researchgate.net/publication/324057547_Incorporating_History_in_a_Mathematics_Lesso n_on_Pythagorean_Theorem_A_Lesson_Study https://www.iaoed.org/downloads/EdPractices_19.pdf https://www.researchgate.net/publication/344840247_BENEFITS_FROM_INTEGRATING_HISTORY_OF_M ATHEMATICS_INTO_TEACHING...