2.+Overview

= Kaitlin Rohrbach = = TLT 438 = 
 * Topic **: Solving Quadratic Equations


 * Grade Level **: Grade Nine Algebra Students

This unit will provide students with the information they need to solve quadratic equations by four different methods: factoring, the square root property, completing the square and the quadratic equation. They will also learn how to decide on the correct method to use, graph quadratic equations by hand and graph using a graphing calculator. They will use the information they learn to develop an algorithm to solve quadratic equations. There will be many formal and informal assessments throughout the unit, the results of which I will use to improve the unit in the future. The students will become better at solving problems as a result of this unit.


 * Schedule:**



How did you execute factoring a quadratic equation on paper by finding the sum and product? Compare the steps you took when factoring using algebra tiles and on paper. || Factor quadratic equations using algebra tiles and on paper simultaneously, And find the zeros/solutions of a quadratic equation by factoring || Lesson on Factoring || Collecting some of the problems the students worked on in groups. This will be graded for completion. The teacher will check for correctness for her own reference to evaluate the effectiveness of the lesson and to see which students had difficulty. || Checking students understanding and asking essential questions while they are working on group work, and recording the information on a clip board. Asking essential questions during active teaching to determine where to spend more time and explain more thoroughly. Putting problems on the board that any students are having trouble with. This will determine where a majority of students are having trouble and it will clarify the problem. ||  || Asking essential questions during active teaching to determine where to spend more time and explain more thoroughly. Putting problems on the board that any students are having trouble with. This will determine where a majority of students are having trouble and it will clarify the problem. ||  || Students will be able to complete the square in order to solve quadratic equations of the form ax2 + bx + c = 0. || Lesson on Completing the Square || Students will be monitored through out the lesson by being called on to answer questions and provide the next step to solve the equation. When the students put their solutions on the board and explain them, I will be able to check for understanding. By practicing completing the square in class where they can ask for help, students will be more successful when they need to do their homework on their own || While the students are working on the seatwork problems, they will be monitored. I will check to make sure that each student understands the steps to take and why each step is necessary. I will record the information on a check sheet. ||  || Students will be able to complete the square in order to solve quadratic equations of the form ax2 + bx + c = 0. || Review for Quiz and go over any homework questions. || The quiz review worksheet will be collected the day of the quiz. || Board, seat and group work of all students will be recorded on a check sheet to be sure that everyone is prepared for the quiz. ||  || What do you notice about the equations that we can use the quadratic equation to solve? What form are they in? How does this form determine the values for a, b, and c? Can you carry out a problem using the quadratic formula to solve a quadratic equation for x? How do you check the answers you obtained by using the quadratic formula? || Derive the quadratic formula, and Solve quadratic equations using the quadratic formula. || Lesson on the Quadratic Formula || Checking the homework from the previous night. The students will get a grade based on the completion of the homework. The teacher will record the information in his or her grade book. || Walking around the room to see if students understood the concepts from the lesson. While they are working on seat work the teacher will see where students had trouble and if some students did not understand. During the homework check, the teacher can check for correctness but this will not be graded. When the students ask homework question and explain and put their solutions on the board, the teacher can make sure the students understand the solutions they obtained. If the students can explain what they did to the other students, then they have a firm grasp on the material. || The quiz is not the day after the review so that students have more time to study. This could be adjusted if students would prefer to have the quiz the day after the review. || Students will be able to complete the square in order to solve quadratic equations of the form ax2 + bx + c = 0. || Quiz on Completing the Square || The quiz results || The problems that many students got incorrect will help me adjust my lessons. ||  || Asking essential questions during active teaching to determine where to spend more time and explain more thoroughly. Putting problems on the board that any students are having trouble with. This will determine where a majority of students are having trouble and it will clarify the problem. ||  || Asking essential questions during active teaching to determine where to spend more time and explain more thoroughly. Putting problems on the board that any students are having trouble with. This will determine where a majority of students are having trouble and it will clarify the problem. ||  || Asking essential questions during active teaching to determine where to spend more time and explain more thoroughly. Putting problems on the board that any students are having trouble with. This will determine where a majority of students are having trouble and it will clarify the problem. ||  || Why is it important to know more than one way to solve a problem? || The students will be able to see how others completed the same performance task and see how to solve a problem in a new and different way. || Present Performance Tasks to the class || The evaluation of the Performance Task using the Rubric. || To see which students struggled an which excelled at the Performance Task activities. || Multiple days may be needed. ||
 * **Day** || **Essential Questions** || **Objectives** || **Task/Activities** || **Formal Assessments** || **Informal Assessments** || **Other** ||
 * **1** || Why is it important to know more than one way to solve a problem? || Introduce the lesson and the performance task || Introduction of Unit and Performance Task || None || Checking for student understanding of what is expected of them. || Remind students of when things are due everyday throughout the unit ||
 * **2** || How did you execute factoring a quadratic equation using algebra tiles?
 * **3** || Can you relate the Square Root Property to Completing the Square? What is a downfall of this method of solving a quadratic equation? || Students will be able to use the Square Root Property to solve quadratic equations of the form (ax + b)2 = c || Lesson on the Square Root Property || A worksheet on the Square Root Property that will be collected. || Checking students understanding and asking essential questions while they are working on group work, and recording the information on a clip board.
 * **4** || How can you use the square root property to solve for x? Check your solutions by working backwards. || Students will be able to find the necessary value to form a perfect square trinomial.
 * **5** || How can you use the square root property to solve for x? Check your solutions by working backwards. || Students will be able to find the necessary value to form a perfect square trinomial.
 * **6** || Compare the method used to complete the square to the method used to derive the quadratic formula. Do you notice any similarities or differences?
 * **7** || How can you use the square root property to solve for x? Check your solutions by working backwards. || Students will be able to find the necessary value to form a perfect square trinomial.
 * **8** || Which of the four methods can always be used? || Students will be able to decide which method is best to use to solve a quadratic equation based on the equation they are given. They will also realize that zeros, solutions, and x-intercepts are all the same thing. || Lesson on which method to choose || Worksheet on choosing the best method when solving quadratic equations. || Checking students understanding and asking essential questions while they are working on group work, and recording the information on a clip board.
 * **9** || Which of the four methods can always be used? || Students will be able to decide which method is best to use to solve a quadratic equation based on the equation they are given. || Performance Task: Group Algorithm Developed || Recording which students are giving their input into the group work to be used when determining their final grades on the Performance Task. || Checking students understanding and asking essential questions while they are working on group work, and recording the information on a clip board. ||  ||
 * **10** ||  ||   || Performance Task: Individual Algorithms Developed || Recording the students' progress to be used when determining their final grades on the Performance Task. || Checking students understanding and asking essential questions while they are working individually, and recording the information on a clip board. ||   ||
 * **11** || Which of the four methods is best to use if you are going to graph a quadratic equation by hand? || Students will be able to graph quadratic equations by completing the square and then find the zeros. || Lesson on Graphing by Completing the Square || Worksheet on graphing by completing the square that will be collected. || Checking students understanding and asking essential questions while they are working on group work, and recording the information on a clip board.
 * **12** || Why is it important to know more than one way to solve a problem? || The students will be able to think about what others will need to know to understand their algorithm. How can they explain their work to someone who knows little about solving quadratic equations. || Performance Task: Come together to make group sales pitch and discuss individual algorithms || Recording which students are giving their input into the group work to be used to determine their final grades on the Performance Task. || Checking students understanding and asking essential questions while they are working on group work, and recording the information on a clip board. ||  ||
 * **13** || How are the steps you took to graph a quadratic equation on a calculator related to the steps you took to graph a quadratic equation by hand? How are finding the zeros related? How might using a calculator be helpful on a test or quiz? || Students will be able to graph a quadratic equation using a graphing calculator and find the zeros. They will be able to make connections between using the calculator and doing the problem by hand. || Lesson on graphing using a graphing calculator and time in groups to make final adjustments on Performance Task || Worksheet on graphing using a graphing calculator that will be collected. || Checking students understanding and asking essential questions while they are working on group work, and recording the information on a clip board.
 * **14** || When can you use quadratic equations in other subjects or to model information in everyday life? Can you connect mathematics to real world situations?
 * **15** || Why is it important to know more than one way to solve a problem? || The students will prepare for the test. || Review for Test and go over any homework questions. || The review worksheet will be collected on the day of the test. || Board, seat and group work of all students will be recorded on a check sheet to be sure that everyone is prepared for the test. || Two days may be needed. ||
 * **16** || Why is it important to know more than one way to solve a problem? The test will include all essential questions. || To assess the students on the material they learned throughout the lesson. || Unit Test || The test results. || The problems that many students got incorrect will help me adjust my lessons in the future. ||  ||