Zachary Okolowitcz Theory/Technology Integration Fall 2014 Lesson Plan 3: Web Resources Lesson 3: Solving Quadratics Using the Quadratic Formula Standards: HSA-CED.A.1: Create equations in one variable and use them to solve problems. HSA-REI.B.4a: Use the method of completing the square to derive the quadratic formula. HSA-REI.B.4b: Solve quadratic equations…by the quadratic formula. Objectives: Students will be able to: A: Solve quadratic equations using the quadratic formula. B: Describe the process to derive the quadratic formula. C: Interpret the discriminant of a quadratic equation. Materials: Classroom Materials: Chromebooks Challenge Activity Handout Exit Slip Handout Homework Worksheet Starter/Motivational Activity: Students will have Chromebooks that are available within our math department throughout this lesson. Try to complete the challenge problem independently. If you are unable to do so, use the internet to find out how the quadratic formula is derived. If you are using the internet, please explain what you have found and the process to taking a quadratic in standard form and manipulating it to become the quadratic formula! CHALLENGE!! CHALLENGE!! CHALLENGE!! Can YOU solve the arbitrary formula for a quadratic ax2+bx+c=0, by first completing the square, and then solving for x!! Lesson Procedure: Students will be working with 12 Short videos that walk through different types of problems that can be solved using the quadratic formula. These include basic computation problems, more challenging computation problems, discussion of the discriminant, and word problem applications. After completing the Challenge problem and discussing the derivation of the quadratic formula, students will watch and take notes on the following problems within the given links. They are to pause and make comments within their notes and also get the problems into their notes. I will be circulating the room as this is being completed so students can ask me further questions if need be. Student Links will be available on my classroom website under the Lesson Plan 3 link within the quadratics unit. Go over Challenge Problem: Discussion of the importance of properly putting a quadratic in standard form and identifying a, b, and c. Practice of this and plugging into the quadratic formula and simplifying to reveal roots/solutions. Students will have a hard copy of the following guided notes and practice examples done which will also include the links to the practice problems they are to complete on their own and take notes on. Students will go to my website to be able to click on and go to the links of each individual video. Name:________________________________ Date:__________ Solving Quadratics Using the Quadratic Formula Example 1: Student Links to completing practice problems 1-4: 1: http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05 _mp1/HSCC_Alg%201_09_05_mp1.html 2: http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05 _mp2/HSCC_Alg%201_09_05_mp2.html 3: http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05 _mp3/HSCC_Alg%201_09_05_mp3.html 4: http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05 _mp4/HSCC_Alg%201_09_05_mp4.html Example 2: Modeling Students will now complete practice problems 5 & 6: 5: http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05 _mp5/HSCC_Alg%201_09_05_mp5.html 6: http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05 _mp6/HSCC_Alg%201_09_05_mp6.html Example 3: Student Links to 7-9: 7: http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05 _mp7/HSCC_Alg%201_09_05_mp7.html 8: http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05 _mp8/HSCC_Alg%201_09_05_mp8.html 9: http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05 _mp9/HSCC_Alg%201_09_05_mp9.html Example 4: Student Links to practice problems 10-12: 10: http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05 _mp10/HSCC_Alg%201_09_05_mp10.html 11: http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05 _mp11/HSCC_Alg%201_09_05_mp11.html 12: http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05 _mp12/HSCC_Alg%201_09_05_mp12.html Closure/Lesson Assessment: Closure/Exit Slip: Students will be asked to complete the following: Explain the process to use the discriminant along with the quadratic formula to find the solutions to a quadratic equation: _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ Rubric to Grade Exit Slip: Rating: 1 2 3 Description: Minimal effort in Student identifies the Student correctly describing the use of importance of identifies the use and the quadratic formula determining what a, b, application of the and the discriminant to and c equal and quadratic formula and solve a quadratic discusses the use of the the discriminant. equation discriminant with flaws in explanation HW: Select Problems from the following Assignment: In Exercises 1–3, write the equation in standard form. Then identify the values of a, b, and c that you would use to solve the equation using the Quadratic Formula. 1. x2 5x 2. x2 3x 10 3. 5x2 2 7x In Exercises 4–11, solve the equation using the Quadratic Formula. Round your solutions to the nearest tenth, if necessary. 4. x2 6 x 9 0 5. x 2 5 x 14 0 6. x 2 9 x 10 0 7. 3 x 2 2 x 1 0 8. 3 x 2 5 x 4 0 9. 4 x 2 4 x 1 0 10. 6x2 5x 6 11. 5x2 9x 3 12. Your friend competes in a high-jump competition at a track meet. The 2 function h 16t 18t models the height h (in feet) of your friend after t seconds. a. After how many seconds is your friend at a height of 4 feet? b. After how many seconds does your friend land on the ground? In Exercises 13–15, determine the number of real solutions of the equation. 13. x2 2x 1 0 14. x2 4 x 7 0 15. 3x2 2x 6 In Exercises 16–18, find the number of x-intercepts of the graph of the function. 16. y x2 3x 5 17. y 3x2 7x 8 18. y 5x2 10x 1 Select at least one web-based application or tool that will add value to your unit of study (or a specific lesson). Incorporate one or more Web resources (tools or applications) into Lesson Plan 3. This resource and a sample of how it is incorporated into the unit will be linked to your ePortfolio (website). Examples include: blog, wiki, interactive, new media tool application. Deliverables: 1. Lesson Plan 2. Sample Product (as if a student created or completed it)' 3. Assessment (how student work will be assessed; i.e. rubric, checklist, peer feedback) 4. Incorporated into ePortfolio / website