Lesson 3
Standards
MM3A3a Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.
MM3A3d Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.
Essential Question
How do you find all real zeros of a polynomial function?
Learning Objectives
· Students will learn how to use the rational root theorem.
· Students will learn how to use the factor theorem.
· Students will learn how to find all real zeros of a polynomial function.
· Students will learn how to find zeros of a polynomial function on a graphing calculator.
Learning Activity
Students will watch the video on how to find rational zeros of a function.
Video: http://www.youtube.com/watch?v=Sbpo2phnKxo&feature=relmfu
Then students will complete the worksheet (attached at the bottom) working in groups of three. When they are finished they will watch the video on how to find the real zeros of a polynomial function using a graphing calculator.
Video: http://www.youtube.com/watch?v=fafRUO2SUVQ&feature=related
Students will then continue working with their group to check their solutions for the four polynomial functions using a graphing calculator.
6E's
Engage: Students are engaged during the activity because they are watching a video and using a graphing calculator.
Explore: The students are exploring by using the graphing calculator to find the zeros of a polynomial function.
Explain: Students are required to explain what they see when they graph the polynomial function and what their thoughts are with their group.
Elaborate: At the end students will write a journal entry explaining what they learned today. They will need to answer the following questions.
· What is the rational root theorem?
· What does it mean to find the real zeros? What are the real zeros?
Evaluate: A rubric is provided that will check for student understanding of the activity.
Extend: Students will create their own polynomial function and are required to list the possible rational roots, test the zeros using synthetic division, and use the factor theorem to find the real zeros. Students will then be required to sketch a graph of their function labeling the zeros. This will be done on poster board and turned in the following day.
lesson3worksheet.docx | |
File Size: | 45 kb |
File Type: | docx |
Rational Root Theorem Synthetic Division Factor Theorem Graphing |
Unacceptable
0 pts. Listed very few or none of the possibilities using the rational root theorem. Did not use synthetic division. Did not list any factors. Did not graph the function using a calculator. |
Good
1 pt. Listed most of the possibilities using the rational root theorem. Used synthetic division, but made a few errors. Used the factor theorem, but did not include all the factors or made a mistake. Graphed the function, but did not find the zeros correctly. Used the trace button to guess zeros. |
Excellent
2 pts. Listed ALL of the possibilities using the rational root theorem. Used synthetic division with no errors. Used the factor theorem correctly, listed all the factors, and made no mistakes. Graphed the function and found the zeros using the zeros button on the calculator correctly. |