Target Audience: 7 th grade Algebra class. Lesson Topic: The Quadratic Formula

Transcription

1 Target Audience: 7 th grade Algebra class Lesson Topic: The Quadratic Formula Purpose and relevance: Throughout a student s mathematic career they will realize that knowing how to factoacr is very beneficial. Factoring is used when solving polynomial equations, simplifying things, constructing a graph, and many other problems. In the next chapter of the student s Algebra I book they will be asked to graph functions without using a graphing calculator. Students need to know how to factor a quadratic equation so they can identify key features of a graph of a quadratic equation. This is the third lesson of factoring polynomials students have received for their 7 th grade Algebra I class. The students have learned, practiced, and have been assessed on factoring simple polynomials. An example of a simple polynomial is 3x 12 = 0 and the student has to solve for x Maryland State Voluntary Curriculum- the student will demonstrate the ability to investigate, interpret, and communicate solutions to mathematical and real-world problems using patterns, functions, and algebra. Technology Standards Select and use technology tools to enhance learning Select and use technology for communication INTASC Standards The teacher understands and uses a variety of instructional strategies to encourage students development of critical thinking, problem solving, and performance skills. The teacher uses knowledge of effective verbal, nonverbal and media communication techniques to foster active inquiry, collaboration, and supportive interaction in the classroom. The teacher understands and uses formal and informal assessment strategies to evaluate and ensure the continuous intellectual, social, and physical development of the learner. Objectives: SWBAT recite the quadratic formula factor equations using the quadratic formula Materials: Quadratic Formula Flipchart Promethean Board pen and clickers Classwork Ditto Exit Ticket Procedures: Drill/Pre-assessment: For this section the teachers will use the Promethean Board Clickers. A question will be up on the Promethean Board and the students will have to select the correct answer using their Clicker. The teachers will compile results to see student responses. Once seeing the results the teachers

2 should ask the students what type of method they used to factor the equation. This is here we will introduce the use for the quadratic formula and begin our lesson. Questions that will be on the Promethean Board: 1. Factor the following, a. ( )( ) b. ( )( ) c. ( )( ) d. ( )( ) Answer: b 2. Factor the following, ( ) a. ( )( ) b. ( ) c. ( )( ) d. ( 1) Answer: b 1. Introduce the objective for today s lesson Have students read the objectives 2. Introduce the term quadratic equation Instruct students to take out the Math Notebooks and being taking notes. Define quadratic equation as: a polynomial equation of the second degree. It is in the form where are coefficient integers. Put the following example on the Promethean Board: Select a student to label the in the example. Students will use the Pen to label them on the Promethean Board. Answers: Put another example on the Promethean Board. Select a student to label the in the example. Students will use the Pen to label them on the Promethean Board. Answers: 3. When to use the quadratic formula Teacher: Every felt like not factoring? Or come across a problem where you can t factor? Sometimes the quadratic is too messy, it doesn t factor at all, or you just don t feel like factoring Quadratic formula can always find the solution Must have your equation in the form (quadratic) = 0 Post examples of when to use the quadratic formula. 1. Mention that you just don t feel like factoring this. 2. Mention that it is very difficult to factor this equation and it would require knowledge of how to complete the square. Post examples of when to not use the quadratic formula

3 1. Cannot use for the quadratic formula for a cubic. 2. How can we change this quadratic so we can use the quadratic formula? 4. Give students the quadratic formula Give two examples. The first example will be solved by the teacher, the next a student. The quadratic formula will be posted on the flipchart for students to refer to. Have student come up and show their work on the Promethean Board. Allow student to use the calculator tool. If the student needs help allow them to call on other students. 1. Answer: 2. Answer: See if the students have the quadratic formula memorized already. Would they have been able to solve the previous examples without having the formula right in front of them? It is important to have this formula memorized. It is used in a lot of further math courses, and you may not have time to go look it up in a book. It really is something all math students should know. 5. Show clips of Quadratic Formula Show Glee clip that will interest the students 28:30 time To help student s remember the formula the teachers will play a Youtube video of the Quadratic Formula song that is sung to the tune of Pop Goes the Weasel The students should sing the song in the You Do section of the video. Sing the quadratic formula as a class, pointing at each letter as the song is sung. 6. Now the class is ready to do some practice problems using the quadratic formula. The formula will not be on the board. The teacher should instruct the students to raise their hands if they need help remembering the formula. The teachers will have the students answer the following questions using the Promethean Clickers. 1. True or False Is this the quadratic equation? Answer: False. Ask the class what we need to do to change this to make it correct. Answer: make it

4 2. Solve, Round your answer to two decimal places, if necessary. Answer: 3. Solve, Round your answer to two decimal places, if necessary. Answer: 7. The teachers should review the answers with the class and go over any questions students may have. The students will now complete a worksheet that will focus on all the factoring techniques they have learned. The worksheet Factoring Fun is attached. Some of the problems are color coded for our Learning Disabled students. For our ESL we have the instructions in Spanish. 8. The teachers should ask the students what they did today in class and if it met their objective. 9. Hand out the exit ticket. The Exit Ticket is attached, again we have a version for our LD and ESL students.

5 Factoring Fun! After learning about the quadratic equation, you now know every method of factoring that any other mathematician knows! Grouping, completing the square, and now the Quadratic Formula. In the following problems, please use whichever method you feel is appropriate to solve for the x-intercepts. Beware not all of them are solvable by all 3 methods! 1) 7x² + 2x 8 2) x² 2x 2 3) 3x² + x 2 4) x² 5x 5) x² + 6x + 2 6) x² 5x + 5 7) 5x² 2x + 2 8) 2x² 8x + 5

6 Factoring Fun! (LD Student) After learning about the quadratic equation, you now know every method of factoring that any other mathematician knows! Grouping, completing the square, and now the Quadratic Formula. In the following problems, please use whichever method you feel is appropriate to solve for the x-intercepts. Beware not all of them are solvable by all 3 methods! 1) 7x² + 2x 8 2) x² 2x 2 3) 3x² + x 2 4) x² 5x 5) x² + 6x + 2 6) x² 5x + 5 7) 5x² 2x + 2 8) 2x² 8x + 5

7 Diversión de Factorización! Después de aprender sobre la ecuación cuadrática, usted ahora sabe cada método de la factorización que cualquier otro matemático sabe! La agrupación, completar el cuadrado, y ahora la Fórmula Cuadrática. En los problemas siguientes, por favor use cualquier método que usted siente es apropiado para solucionar para el x-intercepts. Precávase no todos ellos son solubles por 3 métodos! 1) 7x² + 2x 8 2) x² 2x 2 3) 3x² + x 2 4) x² 5x 5) x² + 6x + 2 6) x² 5x + 5 7) 5x² 2x + 2 8) 2x² 8x + 5

8 Exit Ticket State the quadratic formula: Solve the equation using the Quadratic Formula. Show ALL work t 4.9t 2 = 0 Exit Ticket (LD Student) The quadratic formula: Solve the equation using the Quadratic Formula. Show ALL work t 4.9t 2 = 0

9 Boleto de Salida Declare la fórmula cuadrática: Solucione la ecuación usando la Fórmula Cuadrática. Muestre TODO el trabajo t 4.9t 2 = 0