AndreaAustinMath


 * Lesson Topic and Description:** Graphing Systems of Inequalities

- graphing systems of inequalities
- linear programming - linear programming applications

**__Provision for Acceleration and Compression of Content__**
-only brief review of graphing a linear equation/inequality

**__Enrichment__**
-students will write a system of linear inequalities and objective function based on a linear programming application from a real world situation -students then solve the system of linear inequalities and use the vertices of the feasible region to find the maximum/minimum value for the objective function in order to answer the question
 * -have students solve a larger system of inequalities (6 equations or more?)...compare written solution with graphing calculator solutions**

**__More Advanced Reading and Vocabulary__**

 * vocabulary---what is feasible region? What are constraints, etc....

**__Use of Primary Sources, Artifacts, and Real World Objects__**

 * An actual business model to show how this has been used to maximize profit

**__Interdisciplinary Connections__**
-power of economics

**__Includes In-Depth and Critical Analysis__**
- examine results of linear programming application problem to determine if answer is realistic/appropriate

**__Fosters Creative Expression__**
- students can work as a group to create their own original linear programming problem. This activity can include a challenge to see which group can create the most challenging problem. -have students create a more efficient profitable business

‍ **__Exploration of Areas of Choice__**
- students can choose to work on a linear application problem over a topic that is of interest to ‍‍‍‍‍‍‍‍‍them

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Level of Thinking Questions 1. Define constraint, feasible region, minimum and maximum. 2. Explain the steps for solving a linear programming problem. 3. Solve the system of inequalities by graphing and write the vertices of the feasible region. 4. Examine the outcomes after substituting the vertices of the feasible region into the objective function to determine the minimum and maximum values. 5. Judge the outcome of your linear programming application. Is it reasonable? Why or why not? 6. Develop your own linear programming application problem over a given topic.


 * Unit Name and Lesson Plan Title: Graphing a System of Inequalities**


 * Author: A. Austin Grade and Subject:** Algebra 2H

Upon completion of this lesson, students will be able to solve a system of inequalities by graphing and successfully solve an application of linear programming problem.
 * Annotation:**

**‍Student Learning Outcomes or Objectives:** ‍Students will be able to define the terms feasible region, constraints, objective function, and minimum/maximum. Students will be able to solve a system of linear inequalities by graphing. Students will be able to solve a linear programming application problem. Students will be able to examine the results of a linear programming problem to determine the answer to a real-world problem.

(likely some or all will be above grade, may be from more than one subject, includes skills)
 * Standards:**

1 70 minute class period (include numbers of items needed, all technology needed, titles and authors of any materials needed)
 * Total Duration:**
 * Materials and Equipment Needed:**

**Lesson and Learning Activities:**
 * **Steps including time for each:** (logical progression, clear teaching instructions with good detail; how students are working; type of learning)
 * **Lesson attachments or weblinks:** (for particular steps with guidance for what, who and how to use it)
 * **Differentiation within High Ability Group:** (for students who have already mastered material or who can work at a higher level than other high ability students )

**Assessment:** (measures identified Student Learning Outcomes; clear directions for students; evidence of higher level thinking is included; written materials attached; scoring system attached including any rubric, checklist, etc. )