Instructor: Ms. Marithza Rendon Grade and Subject: 9th and 10th Grade/ Accelerated Analytic Geometry (Math)
Lesson Title: Solving Quadratic Equations by Factoring Date: September 16,2014
1. LESSON CONTEXT AND RATIONALECulture and Context / · The target class population is approximately 65% White and 20% Black, and 15% other. This lesson is designed for an Accelerated Analytic Geometry class to help students master how to solve quadratic equations by factoring. Students will be working in groups to complete an engaging assignment that relates quadratic equations to real-life situations and challenges their problem solving skills. Students will be able to use their prior knowledge about finding greatest common factor and solving for a variable. The collaborative work students will be completing will allow students to question each other and develop learning communities within the classroom.
· In this lesson, students will be able to take responsibility in their learning. Students will be asked to choose one of the three assignments to complete. Allowing students to choose their assignment gives students the opportunity to take responsibility in their learning and help them develop confidence in math. This type of instruction allows students to achieve success within the zone of proximal development. The zone of proximal development gives students the opportunity to learn new information that is within their reach; thus giving them confidence in their work (Small & Lin, 2010, p. 2).
· The work that will be given to students will contain problems that students can complete on their own but also build students’ critical thinking skills. Such problems will involve students to understand and apply prior knowledge. Scaffolding questions will be given to help students uncover and apply main ideas, and students will be required to justify their answers (Tomlinson, 2001, p. 20).
· Based on formative and summative assessments, I will group students with other students within their own zone of proximal development in order for them to master solving quadratic equations at their own level and speed.
Identity and Intellectual Development / · Students will be asked to explain how to factor using completing the square. Each individual will write unique responses to the warm-up and classwork. Students will be able to build learning communities within the classroom and learn how to collaborate with others. Students are encouraged to express their responses in their own words. At the end of the lesson, students will be encouraged as a group to create a poster board of one of their solutions to present to the class. Each student will be asked to participate and contribute to the group presentation. Students’ ideas and individuality will be reflected in the presentation.
· Since students will be choosing their assignment, they are able to gain interest and confidence in their work. The assignments were created for students who are in different zones of proximal development. Allowing students to choose work that they can complete, but challenges them will allow students to gain confidence in themselves. If a group of students choose the higher-level assignment, they are able to challenge themselves while mastering the content. All assignments allow students to use prior knowledge and show students how quadratics are related to real-life situations. These questions also challenge students and will help students build problem-solving and critical thinking skills. These skills and knowledge will help students continue with the course.
Lesson Rationale / · The purpose of this assignment is to give students the opportunity to practice and master how to solve quadratic equations. Students will be able to work in groups, ask their peers questions, and understand how to apply this knowledge to real-life situations.
· As a result of formative and summative assessment, I have realized that all the students in the class were at different academic levels. Some students are able to master skills quickly, while others need extra time to practice and master the content. Often times, the students who complete assignments quickly are often bored or create a distraction in the learning environment. By creating alternative assignments, students who are gifted can be challenged in the classroom while those who need more time to practice can master the content at their own pace.
· Solving quadratic equations by factoring allows students to see how parabolic functions are used in everyday. Students are also able to use these skills to solve and graph quadratic equations at a later date. Methods that we will use in this lesson can also be applied to future lessons, such as conic sections.
· This lesson ties together many different strategies and topics that students previously learned. Previously learned topics that are included in this lesson include: solving for a variable, complex numbers, multiplying and diving fractions, the distribution property, finding the greatest common factor, and solving radical expressions. Students should understand and use these topics in this lesson.
· A homework assignment will be provided to students for them to complete at home. The assignment will provide students with more practice and apply the new knowledge learned.
Management / · I will strategically assign groups to prevent students from staying off task. During the group work, I will be walking around the room to observe team collaboration and to make sure groups are staying on task. Students will be reminded of the class rules if needed. If students are not working together as a team, groups may need to be changed or other actions may be necessary.
2. STANDARDS & REQUIREMENTS
2. CCGSP or GPS Standard(s) / MCC9-12.N.CN.7 Solve quadratic equations with real coefficients that have complex solutions.
MCC9-12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.
MCC9-12.A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.
MCC9-12.A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x-p)2=q that has the same solutions. Derive the quadratic formula from this form.
MCC9-12.A.REI.4b Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
Individual Education Plan Goal(s) and Benchmarks / · There are a few students that have ADHD. I will continue to make sure these specific students remain on task and provide them with feedback.
· Students who are above grade level will be given the opportunity to challenge themselves. They will be asked to derive the quadratic formula by completing the square. If students finish ahead of schedule, students will be asked to complete a poster board with their proof of the quadratic formula and present their findings to the class.
· Students who are below grade-level will be given the opportunity to work on a task that they are able to complete, but yet challenge them. They are able to complete the assignment at their own pace. If students finish ahead of schedule, students will be asked to present their findings to the class that will help them build confidence in their mathematical abilities.
· All students’ educational goal is to master how to solve quadratic equations using factoring with at least 80% accuracy. High expectations should be placed, so students can feel comfortable moving on in the unit.
Modification(s) /Accommodation (s) / I am using a differentiated lesson to help students master the content at their own pace. Each student learns differently, so I am hoping that this lesson will accommodate all the students’ needs. Accommodations include extra time needed to complete the assignment, time to ask their peers or instructor for questions, and time to receive immediate feedback from their peers or instructor.
Differentiation / The lesson will involve students choosing their assignment for this particular day. All assignments will encourage students to practice how to solve quadratic equations using factoring and provide students will real-life and challenging problems. There are three different levels of readiness of this assignment. Students who need extra practice will be able to complete the activity and master the content, while students who are preforming above grade level will be given the opportunity to challenge themselves. If students who are preforming above grade level choose an assignment that is below their zone of proximal development, they will be encouraged to help their peers or work on a more challenging assignment after they completed their original task. If students who are preforming below grade level choose an assignment that is above their zone of proximal development, they will be given the opportunity to challenge themselves: encouragement may be necessary.
3. RESOURCES
Academic Language / · Oral and written language will be used in this lesson. Students will be asked to write and explain how to solve quadratic equations using completing the square as a warm-up. A few students will also be asked to describe the mathematical procedure on how to solve quadratic equations to the class. In the assignment, students will then be asked to justify their answers and evaluate quadratic expressions. Students will also be asked to compare two mathematical procedures. Students will then verbally describe their thinking process and reasoning to the class and groups.
· Students will be asked to use vocabulary words learned in this unit. Vocabulary words include factor, greatest common factor, and coefficient.
· Scaffolding questions may need to be asked, if students are having trouble completing the assignments. Questions may include: What is the greatest common factor? Think about our end goal, what do you think we need to do next in order to get there?
· Students will also need to know and understand how to use the mathematical symbol ± (plus or minus).
Language Functions / · The purpose for which the language is being used in this lesson is to solve. Students will learn how to solve quadratic equations using factoring and students will be asked to describe the process and justify their responses.
Language Vocabulary / · Vocabulary words for this lesson include: coefficient, quadratic, equation, square root, greatest common factor, factor, distributive property, and variable.
Materials / · The materials needed for this lesson include: three-assignment worksheets, paper and pencil, art supplies, presentation boards, and rulers.
Technology / · For this particular lesson, students will be encouraged to use calculators to help them solve the equations.
4. LESSON PROCEDURE
Enduring Understanding / · How can we use completing the square method to derive the quadratic formula? Can we use this formula for every quadratic equation?
· When do we know the solutions to a quadratic equation are real or complex?
· How can we use quadratic equations to solve real life problems?
· What kind of examples can you provide that describe why quadratic equations are useful in our everyday lives?
Essential Question(s) / · How many solutions are we solving for?
· How do we choose which method to use when solving quadratic equations?
· What are our solutions telling us?
Lesson Objective(s) / · Students will be able to solve for zeros in quadratic equations and interpret the results.
Assessment Link / · Students will be able to learn different methods of solving quadratic equations in real-life situations and interpret the results.
Introduction to Lesson / · Students will be asked to write a brief paragraph that describes how to solve quadratic equations using completing the square as their warm up. Students will be using their prior knowledge and use academic language to complete this task. A brief overview of the agenda will be given to the students verbally (and it will be written on the board). Then, students will be asked to verbally share their paragraphs to their group members, and then a few students will share their ideas to the class. This introduction will take approximately 10 minutes to complete.
· I will then explain to the students that we will be working in groups to complete the assignment they choose. I will show and briefly explain each assignment and students will then be asked to choose an assignment as a group. This should take approximately 5 minutes.
Body of Lesson / · I will then allow students to complete the differentiated assignment as a group. A brief example on the white board may need to be provided to remind students how to complete the square prior to the group assignment. I will be visiting each group and provide each student immediate feedback of their work during the group activity. If students finish early, then they will be asked to create a mini-presentation of their work on a poster board. This part of the lesson will take approximately 30 minutes.
Closure / · Students who completed the mini-presentation will then be asked to present their findings. I will then close the lesson by explaining to the students that I am providing them tools and different methods to solve quadratic equations, and the following day we will learn how to use the quadratic formula.
· Students will be asked to use the completing the square method to derive and apply the quadratic formula (one of the mini-presentations)
· This closure should take approximately 5 minutes. Homework will also be given to the students on their way out to practice and apply their new knowledge.
5. ASSESSMENT
Evaluation (Assessment Plan for IEP Goals and/or 504 Plans) / · I will use formative and summative assessment to assess my students’ understanding of the content. Formative assessment will be assessed based on the accuracy of their group work, homework, and quiz/tests. Summative assessments will take place informally. Questions will be asked to students and responses will demonstrate the students’ knowledge. Also, depending on how students perform in their groups, this will demonstrate students’ knowledge of the content. Questions, activities, and assessments will address all standards listed above.
· Students will be able to complete assigned tasks and verbally (or by writing) how they are able to justify and explain their responses.
· I will provide students with correct answers and during the group activity, I will be visiting each group and I will provide each student feedback based on their responses.
· Based on their verbal and written responses, I will be able to measure a student’s mastery of the content and if students comprehend major vocabulary words in this unit.
· I will assess students on other skills as well. These skills include problem solving skills and critical thinking skills.
6. REFLECTION
Analyzing Teaching Effectiveness / · This lesson will provide students the opportunity to master the content at their own pace while receiving immediate feedback from the instructor and their peers. Students will be able to collaboratively work on the activity and verbally explain and justify the procedures they used while answering the problem. Students will be able to build learning communities within the classroom and develop problem-solving skills.
· Demonstrating students how to use the quadratic formula to solve quadratic equations can extend this lesson. Graphs can also be used to support student responses as well. Excel and graphing calculators can be used to demonstrate to students the reasoning behind quadratic formulas and provide students a visual representation of the solutions.
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