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Investigating the Pythagorean Theorem Mathematics, level: Senior Posted Tue May 10 Discovering the Pythagorean Theorem I. Overview of the lesson- Students will do an activity to help them discover the Pythagorean theorem and then they will write journal entries on their thought process as they came up with the solution.
Mandated Material Standards - Using Geometry standard Students prove the Pythagorean theorem. Time Allotted for the Lesson- 50 minutes V. Goals of the Lesson- For students to discover the Pythagorean theorem from a real-world situation and to see how they can use it in geometry.
Objectives- For students to discover the Pythagorean theorem, to work on problem-solving skills, to learn reading comprehension in real-world math problems, to learn through class discussion, and to improve expressing their thoughts, feelings, and strategies through journal writing.
Skills Provided- Teacher needs to help students with the Tri-Square Rug Game if they get stuck, but let them try to do it all on their own. Also, the teacher needs to facilitate a class discussion on the game and how it relates to geometry and the real world, to hand out a worksheet with problems related to the Pythagorean theorem, and to read the journal entries to assess students' understanding of the day's activities and homework.
Suggested Procedures- Teachers can begin the lesson by presenting the Tri-Square Rug Game [from Interactive Mathematics Program, Year Two] and letting the students know that they have to solve the problem find out when the game will be fair for both players.
Students are then given time to make their posters and have group discussion on what the solution is. After groups are finished with these steps, the teacher should lead a whole-class discussion about the solution what it means and other related issues.
Teachers should then give the closing time to explain the homework and then let students write in their journals giving them suggested questions to answer to help guide their writing if they get stuck to show how they solved the problem and what they think about the solution, etc.
When students turn in their homework the next day, teachers can check homework to see if they understand how the Pythagorean theorem relates to solving equations and they can check the students' journals to understand their thinking process about their homework and the topic in general.
If students are having trouble, as indicated from observation or their journal writing, teachers can then seek out these students to help them one-on-one. Opening of the Lesson- At the beginning of class, I will introduce the Tri-Square Rug Game and tell the students that they need to discover when Bob and Judy will have a fair game.
Students will then be able to start their discovery of the solution. They will form triangles by putting the edges of three rugs, or squares, corner to corner. They must then find the area of the squares to see if Al or Betty has a better chance of winning where Al wins if he hits the biggest rug with a dart and Betty wins if she hits either of the two smaller rugs.
They will cut and paste their examples of various situations Al is favored to win, Judy is favored, or it is a fair game onto the poster board. After students have discussed the problem in their groups, we will have a class discussion about the work they just did and decide on a formal solution as a class.
Students will then do the closing activity. Closing- Students will then draw conclusions about when there will be a fair game which is when the rugs form a right triangle and be able to see where the Pythagorean theorem comes from.
Students will then write in their journals about what they discovered through this project: They will also include excerpts from the class discussion and their opinions about it and also the thinking process they used to come to these conclusions and their personal opinions about the results.
Student Assessment- By reading the students' journal entries, I will be able to see who understood the lesson and who did not, so that I may spend time with certain students who were struggling to make sure that they grasp this important concept. Extension of the Lesson- For homework, students will have a worksheet that includes problems dealing with the Pythagorean theorem.
Resources Necessary- Journals for the class, worksheet for homework and a worksheet explaining the Tri-Square Rug Game resource: Interactive Mathematics Program, Year Two. Key Curriculum Press, Berkeley.Toys & Games. Personal Care.
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Shop with confidence. plombier-nemours.comted Procedures- Teachers can begin the lesson by presenting the Tri-Square Rug Game [from Interactive Mathematics Program, Year Two] and letting the students know that they have to solve the problem (find out when the game will be fair for both players).
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I love the look of Trolley Hand Tufted Rug 5 X 8 but I didn't want to spend a lot of money on one (or buy a cheap one that would fall apart after one season). A square ruler with a line along its diagonal makes it easy to complete the trim-back steps. Add an extra 1/8" to 1/4" (depending on your comfort level) to the square size required for your units.
Sew two squares together as explained on the previous pages.