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Trapezoid Geometry Problem: Finding Maximum Areas

Solve a geometry problem involving a trapezoid, finding the areas of a triangle and rectangle, and determining their maximum values.

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Trapezoid Geometry Problem: Finding Maximum Areas

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  1. Week 2 Day 9 Thursday, July 8

  2. Write solution on paper & post up.Feel free to discuss with your table as you do. • Given trapezoid OABC where • OA = 4 cm • AB = 2 cm • OC = 6 cm • AO perpendicular to OC • M is a point moving on AO • Triangle MBC and rectangle MNPO are such that N is on segment BC and P is on segment OC. • Find the areaof the triangle MBC and the areaof the rectangle MNPO. • What is the maximum area for the triangle MBC and the rectangle MNPO? • When, if ever, will the area of the triangle be larger than the area of the rectangle?

  3. Gallery Walk

  4. After sharing solutions to geometry problem • Which solutions do you think are important to share with the class? Why? • What important mathematical points or points about mathematical reasoning would you like to make about this problem. • What student misconceptions or errors do you think students might have? (Do you think that these misconceptions would be taken care of by having kids share within their table and/or across tables?) • How can you make sure these are addressed?

  5. After sharing solutions to geometry problem • Which solutions do you think are important to share with the class? Why?

  6. After sharing solutions to geometry problem • What important mathematical points or points about mathematical reasoning would you like to make about this problem.

  7. After sharing solutions to geometry problem • What student misconceptions or errors do you think students might have?

  8. After sharing solutions to geometry problem • How can you make sure these are addressed?

  9. John’s 20 oz steak… An advertisement for Clyde’ states: John wants to have a 20 oz. filet mignon. How much should the restaurant charge him?

  10. After distributing possible answers to steak problem • What tool of public record would you use with this particular solution? • Why would you choose this method? • What benefits/challenges to productive discussion exist within this method?

  11. After distributing possible answers to steak problem • How would you organize a discussion around the solutions? Explain your reasoning using the mathematics you want students to think about. What questions would you ask to start the discussion?

  12. Refer to “Orchestrating Discussion” article • What information from the article did you use in thinking about your answers to the questions related to the steak problem?

  13. Homework Question: Why is it important to consider other ways of sequencing rather than always putting the weaker mathematical solutions first? …and Penny’s Marble Problem

  14. Summary optional discussion • Think over the other problems we have done during these two weeks: Salaries, Stairs, Maximize Area, Orange juice problem. Choose one of them and consider what in the article was relevant to a discussion of student solutions for the problem?

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