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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
i. Distribute the worksheet and materials.
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
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.
viii. For homework, students are to complete exercise 6 as well as pick and
answer three additional exercises from exercises 8 - 12, remembering to
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
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
Extra time and assistance
on guided practice.
Provide a list of steps to
Reducing the number of
Having a worksheet to
write notes on.
Seeing sample problems
on the board.
Use individual dry-erase
Provide more challenging,
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
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
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.