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Learning Target: Students will be able to solve quadratic inequalities graphically and apply these skills in real world applications. Formative Assessment: Students will follow along, answer questions during lesson, and discuss/compare ideas and solutions with peers. Students will successfully present in a group about a real world application of quadratic inequalities. Mathematical Practice: CCSS.MATH.PRACTICE.MPS Use appropriate too ls strategically. CCSS.MATH.PRACTICE.MP6 Attend to precision. Content Standard: CCSS.MATH.CONTENT.HSA.REI.D. I 0: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Activitiesffasks
What will the teacher be doing?
What will the students be doing?
Beginning of class routines: (5 min) Review of solving quadratic inequalities algebraically
Ask for the steps to solving a quadratic inequality. What is another way we can solve a quadratic ineq uality?
Students will go over the steps to solving a quadratic inequality algebraically and think of how else they could solve quadratic inequalities and discuss.
Activityff ask 1: (20min) Solving a quadratic inequality graphically
Another way we can solve these inequalities is to graph them. Like the other way, it usually takes 4 steps to solve a quadratic inequality graph ically. I. Get f(x) on one side and zero on the other Graph y = f(x) 2. 3. Find the zeros on the graph 4. Identify the interval(s) of the graph that satisfy the inequality Go over example I together then have students do example 2 on their own or in pairs before discussing as class. Split into groups to work examples 3 and 4. Have someone from each group sketch their graph and write their solution on the board. Discuss similarities/differences.
Students will follow along, take notes, answer questions, work examples, and d iscuss work and solutions.
Transition: (2 min) Questions
What questions do you have over solving quadratic inequalities graphically? Which method of solving do you prefer?
Students will ask questions if they have any and discuss which method they prefer and why.
here are several ways to apply what you have learned about solving inequalities in real life. We are going to divide into 5 groups, with each grou learning a real world application of quadratic inequalities. Once everyone has reviewed their assigned a lication, the groups will then " teach" it to the rest of the class.
Students will work in groups watching their assigned video on real world applications while taking notes and discussing within groups. Groups wi ll then lead a whole class discussion over each application video. Groups will point out and discuss the pros/cons of eac reso urce.
What questions do you have over solving quadratic inequalities? We saw five different real world applications, give some more examples of how you personally could apply this in your life.
Students will ask any remaining questions over the lesson. Wrap up discussion of possible personal use of solving quadratic inequalities.
Activityffask 2: (20 min) uadratic inequalities in real life.
Closure: (3 min)
Materials needed: White board, markers, and computers New Literary Resources (I resource f or each of the five groups): https://www.sophia.org/tutorials/linear-inegualities-in-the-real-world--2 https://www.sophia.org/tutorials/linear-inegualities-in-the-real-world--3 https://www.sophia.org/tutorials/linear-inegualities-in-the-real-world https://www.sophia.org/tutorials/linear-inegualities-in-the-real-world--4 https://www.sophia.org/tutorials/linear-inegualities-in-the-real-world--5
Our new literary resource allows students a glimpse at how others read and process new information in mathematics. Students often struggle when reading in mathematics for the simple reason that they approach the mathematics text the same as they would approach a new novel. It is essential for students to realize the difference. By examining these new literary resources alongside their textbooks, students will hopefully gain insight on how to successfully read mathematics content. The new literary resources we chose to include are five individual videos that walk students through different real world applications of quadratic inequalities. Each video is unique in its application, problem set-up, solution paths, and explanations, along with the formats of the videos themselves. Students sometimes have a difficult time paying their full attention while reading textbook material. With these videos, students can actively engage while watching and discussing. Furthermore, many students benefit from hearing the information as well as reading the information as it aids in the retention of new information. We will divide students into five groups, with each group having their own unique new literary resource. Students will engage in watching a video, actively taking notes, discussing the problem and solution path with their group, and planning a brief presentation for the rest of the class over their resource. Once presentations over each resource have been completed, students can compare the ideas and content of the new literary resources with that of their textbook. In addition, students can compare the new literary resources themselves and discuss the benefits and concerns of each resource.
Technology is a wonderful classroom resource, until it fails you in the middle of a lesson. We would plan ahead and have each of the resources saved to the desktop in case of an internet disruption. If for some reason every computer in the classroom fails to cooperate, we will instead have groups brainstorm ideas on real world applications of quadratic inequalities. Once each group comes up with an application, the groups will work to create a word problem to demonstrate the application. Students can then present in their group to the whole class over their findings. We would still deem this lesson a success, it would just be without the new literary resources. However, once this activity is complete we could use the next class period to compare our findings to those of the new literary resources.