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- 1. Candidate Name Matt Wilt Lesson Topic Solving Systems of Linear Inequalities Date of Lesson March 27th 2015 Grade Level High School Decision and Planning Sequence 1. Standards: Reasoning with equations and inequalities: Represent and solve equations and inequalities graphically: 12. Graph the solutions to a linear inequality in two variables as a half- plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 2. LessonObjective(s): Students will learn how to solve systems of linear inequalities in two variables by graphing the system and finding the intersection of the half planes. 3. Instructional Material/Resources: Worksheet (Kuta Software), Ohio’s New Mathematics Standards, Surface and Smart Board, Colored Pencils, Straight Edges 4. Prior Knowledge: The students have knowledge of graphing systems of linear equations as well as graphing an inequality as a half-plane to find the solutions. 5. Body of Lesson a. Anticipatory Set: “So now that we know how to graph linear inequalities and we understand how to find the solutions and what the graph looks like; what if we graph a system of linear inequalities? What will the graph and solutions look like then? That’s the goal of today’s lesson: to learn how to solve systems of linear inequalities by graphing and finding the intersection of the half planes. b. Teaching Strategies: Lecture c. Procedures: i. Distribute the worksheet and materials.
- 2. ii. Review – Briefly cover the previous day’s lesson on graphing an inequality in two variables as a half-plane to find the solutions. This will be done through the review exercises on the worksheet (Exercise 2). iii. Anticipatory Set iv. Introduce graphing systems of linear inequalities via the worksheet (Exercise 3). v. Work through exercise 4. vi. Work through exercise 7 as a class to check for understanding. The students should be guiding the teacher through the exercise. Note that this is a special case and there is no solution, as well as the linear inequalities need not intersect. vii. Closure viii. For homework, students are to complete exercise 6 as well as pick and answer three additional exercises from exercises 8 - 12, remembering to show work. d. Closure: 1. Rewrite the inequality in slope intercept form if not already in it. (y = mx + b) 2. Graph each inequality. (Graph) 3. Shade each half-plane for each inequality. (Shade) 4. Find the intersection (solution). 5. Special Cases (No Solution, Inequalities are parallel) e. Assessment: Formative assessment: While the students are working, following along and answering questions, I will be observing the students’ body language as
- 3. well as how they answer the questions to see if they understand the material. Understanding will also be based on participation when working through the exercises as a class. In addition, understanding will be based on correctness and completion of homework problems. Accommodations/Differentiation/Universal Design for Learning/Tiered LessonPlan Some (lower) Extra time and assistance on guided practice. Provide a list of steps to follow. Most (middle) Reducing the number of homework problems. Having a worksheet to write notes on. Seeing sample problems on the board. Use individual dry-erase boards. Few (higher) Pose open-ended questions. Provide more challenging, though provoking problems (e.g. three inequalities in the system). Teacher Reflective Evaluation Overall I am pleased with how the lesson went. There were many things I feel that I did well and also a few things that I can improve on. In regards to my strengths during the lesson, I feel that my communications skills were something that I did well. I moved about the front of the room often; straying from the location of my surface. I feel that my volume was at a good level. I made eye contact when I was able to. I also feel that my gestures were appropriate for different things I was saying such as when I discussed the intersection of the half planes and intersected my arms. In addition to communication skills, I feel that I was knowledgeable of the subject and clearly presented the main points of lesson. I also feel that my use of technology was appropriate because it allowed me to easily and clearly display the concept. Moreover, I feel that I made the
- 4. information comprehensible by reviewing the previous day’s lesson and then building on it with the new content. Additionally, I believe that I was encouraging and positive and gave ample time to think of a response when asking questions about and having the students guide me through exercise seven. I believe these questions were thought provoking such as when I asked why one of the linear inequalities would have a solid line. I also believe these questions checked for student understanding. In regards to my worksheet, I feel that it was helpful for the students; allowing them to follow along as well as provide them with extra practice in addition to the assigned homework. One last thing that I believe I did well, was following the basic steps of a teacher centered lesson: review (exercise 2), anticipatory set (my statement that included the goal of the lesson), presentation of new content (logical order), guided practice (working through exercise seven as a class), independent practice (homework), and the closure (five points to remember). In regards to some aspects that need improvement, I really feel that I need to improve my time management. The lesson went a few minutes over what I had planned. Despite having practiced the lesson and ensuring it would be in the allotted time frame, I lost time somewhere during the lesson. Moreover, I feel that I needed to pause more often during the lesson after going through steps to ensure that the students are caught up and in the same place on the exercise. In addition to time management, I feel that even though I had eye contact, I need to vary who I am looking at.

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