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Lesson Plan # 1 Problem-based lesson

Grade: 10-12 Objectives: Students will be able to: Learn uses of linear programming an optimization Apply linear programming to situations with two variables Optimize a function over a feasible region I. Students will be introduced to a problem-based lesson that resembles a real-world scenario. They will be asked to determine how much of a snack we would be able to provide while keeping cost at a minimum. The requirements are: no more than 700 calories, no more than 20 grams of fat, at least 17 grams of protein, and at lest 30 % of daily requirements of iron.  II. Students will be given two snacks, a graham cracker and a blueberry yogurt. Each serving cost of yogurt costs .30 and each graham cracker is .06.  III. Students will be provided class time to work in groups in order to determine how to solve this problem. Materials  I. Nutritional information for each snack.  II. Examples of information pertaining to similar situations.

Evaluation  I. Each member of the group will be asked to report in their math journal their understanding of the problem and misunderstandings. In this way I can obtain a private dialogue in which I may guide students to further understand how to proceed. Questions  I. How could you represent the given constraints mathematically?  II. What information do you know and what do you need to research?

III. How could you visualize the given scenario? Lesson plan # 2

Unit title: Linear Programming

Lesson title: Minimizing Cost Grade: 10-12 Subject: Algebra II ISTE NETS-S I. Communication and collaboration II. Research and Information fluency III. Technology operations and concepts IV. Critical thinking, problem solving, & decision making Objectives: Students will be able to: I. Discuss a strategy in which to obtain necessary information. II. Create a real-world scenario representing snacks obtained in our cafeteria by researching nutritional values. III. Analyze and correct each members work. IV. Give individual feedback through journal writing. Plan I. Students will be given examples in which real-world problems are solved using linear programming. <span style="margin: 0in 0in 0pt 0.5in; mso-list: l2 level1 lfo3; tab-stops: list .5in; text-indent: -0.5in;">II. Students will work in small groups in order to develop ways in which to solve the given problem. Understanding the problem and developing a strategy in which to proceed. <span style="margin: 0in 0in 0pt 0.5in; mso-list: l2 level1 lfo3; tab-stops: list .5in; text-indent: -0.5in;">III. Students will be given access to the internet in which to search the information needed to complete the assignment. <span style="margin: 0in 0in 0pt 0.5in; mso-list: l2 level1 lfo3; tab-stops: list .5in; text-indent: -0.5in;">IV. Students will share information in an attempt to help struggling groups find ways in which to proceed. Materials I. Computer lab <span style="margin: 0in 0in 0pt 0.5in; mso-list: l0 level1 lfo4; tab-stops: list .5in; text-indent: -0.5in;">II. List of constraints in which to follow <span style="margin: 0in 0in 0pt 0.5in; mso-list: l0 level1 lfo4; tab-stops: list .5in; text-indent: -0.5in;">III. Examples modeling similar scenarios Monitor <span style="margin: 0in 0in 0pt 0.5in; mso-list: l5 level1 lfo5; tab-stops: list .5in; text-indent: -0.5in;">I. I will monitor students individual progress through journal writing. Evaluate <span style="margin: 0in 0in 0pt 0.5in; mso-list: l1 level1 lfo6; tab-stops: list .5in; text-indent: -0.5in;">I. Students will be assessed through their progress in their journals.

<span style="margin: 0in 0in 0pt 0.5in; mso-list: l1 level1 lfo6; tab-stops: list .5in; text-indent: -0.5in;">II. <span style="margin: 0in 0in 0pt 0.5in; mso-list: l1 level1 lfo6; tab-stops: list .5in; text-indent: -0.5in;">Small equivalent problems will be given as small written assessments.

Lesson Plan # 3 Unit Title: Linear Programming Lesson Title: Presentation Grade: 10-12 Subject: Algebra II   ISTE NETS-S <span style="margin: 0in 0in 0pt 0.5in; mso-list: l1 level1 lfo1; tab-stops: list .5in; text-indent: -0.5in;"> I. Communication and Collaboration <span style="margin: 0in 0in 0pt 0.5in; mso-list: l1 level1 lfo1; tab-stops: list .5in; text-indent: -0.5in;"> II. Research and Information Literacy <span style="margin: 0in 0in 0pt 0.5in; mso-list: l1 level1 lfo1; tab-stops: list .5in; text-indent: -0.5in;"> III. Technology operations and concepts <span style="margin: 0in 0in 0pt 0.5in; mso-list: l1 level1 lfo1; tab-stops: list .5in; text-indent: -0.5in;"> IV. Critical thinking, problem solving, & decision making Objectives: Students will be able to: <span style="margin: 0in 0in 0pt 0.5in; mso-list: l0 level1 lfo2; tab-stops: list .5in; text-indent: -0.5in;"> I. Students will be able to work in groups in order to communicate their understanding of the given problem. <span style="margin: 0in 0in 0pt 0.5in; mso-list: l0 level1 lfo2; tab-stops: list .5in; text-indent: -0.5in;"> II. Students will demonstrate how they researched the necessary information. <span style="margin: 0in 0in 0pt 0.5in; mso-list: l0 level1 lfo2; tab-stops: list .5in; text-indent: -0.5in;"> III. Students will use technology to present to the class their presentation in order to obtain the customers business. <span style="margin: 0in 0in 0pt 0.5in; mso-list: l0 level1 lfo2; tab-stops: list .5in; text-indent: -0.5in;"> IV. Students will demonstrate critical thinking skills and creativity in order to show their understanding of the lesson’s objectives. Materials <span style="margin: 0in 0in 0pt 0.5in; mso-list: l3 level1 lfo3; tab-stops: list .5in; text-indent: -0.5in;"> I. Computer cart and projector <span style="margin: 0in 0in 0pt 0.5in; mso-list: l3 level1 lfo3; tab-stops: list .5in; text-indent: -0.5in;"> II. Graph paper, overhead transparencies, etc. <span style="margin: 0in 0in 0pt 0.5in; mso-list: l3 level1 lfo3; tab-stops: list .5in; text-indent: -0.5in;"> III. Speaking and communication rubrics Monitor <span style="margin: 0in 0in 0pt 0.5in; mso-list: l4 level1 lfo4; tab-stops: list .5in; text-indent: -0.5in;"> I. Students will be given time to present their work in progress to me in order for me to facilitate how to proceed. Back-up plan <span style="margin: 0in 0in 0pt 0.5in; mso-list: l2 level1 lfo5; tab-stops: list .5in; text-indent: -0.5in;"> I. Students who are having difficulty obtaining individualized information will be given a complete set of constraints in which they will optimize the maximum profit of a predetermined situation. Evaluation Students will be evaluated in how well they work in the collaborative setting. I will ask how they tried to solve the problems within their group settings before offering assistance. They will provide specific problems they faced before coming to me for further help.