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2-1: Functions/ 2-2: Direct Variation Name: Jenifer Kennon Grade Level: High School (9-12) Subject: Algebra 2 1. WVCSOs:  M.O.A2.2.1- determine equations of lines including parallel, perpendicular, vertical and horizontal lines, and compare and contrast the properties of these equations  M.O.A2.2.7- define a function and find its zeros; express the domain and range using interval notation; find the inverse of a function; find the value of a function for a given element in its domain; and perform basic operations on functions including composition of functions  M.O.A2.2.8- analyze families of functions and their transformations; recognize linear, quadratic, radical, absolute value, step, piece-wise, and exponential functions; analyze connections among words, graphs, tables and equations when solving practical problems with and without technology  M.O.A2.2.11- solve practical problems involving direct, inverse and t variation 2. Objectives: Students will identify whether or not a relation is a function with eighty percent accuracy. Students will solve functions in word problems with 80% accuracy. Students will determine whether or not y varies directly with x, find the constant of variation, and find the function rule of given data with 85% accuracy. 3. 21st Century Themes: This lesson creates the basic ideas of thinking and reasoning. 4. 21st Century Skills: Students will demonstrate the ability to explore and develop new ideas, to intentionally apply sound reasoning processes and to frame analyze and solve complex problems using appropriate technology tools.

5. Materials:  Teacher i. Copies of all worksheets for students ii. Elmo iii. Projector iv. Pencil  Students i. Notebook or paper for notes ii. Pencil iii. Calculators (provided by teacher if necessary)

6. Technology components: Students will be allowed to use calculators if needed. The teacher will use the Elmo and projector as an instruction method. 7. Teaching Methods and Critical Thinking Components:  Full class instruction/lecture and individual work 8. Learning Activities:  Introduction i. Students will review from yesterday’s lesson by completing the 2.1Functions sheet. Once all students are finished, go over answers as a whole class.  Lesson: i. Introduce word problems. Be very specific with examples. Have the students identify what it is that represents x and what it is that they are solving for when they plug in x. ii. Begin Direct Variation. Direct variationor , where 1.

works for all coordinates except for (0, 0) this is the ratio of all outputs/input pairs; k is the constant of variation 2. The function rule is 3. Work through examples with students: Determine whether y varies directly with x. If so, what is the constant of variation and function rule? a. ; Yes, y varies directly with x; constant of variation is 2; function rule is x y 1 2 3 6 4 8 b. ; No, y does not vary directly with x x y 1 4 2 8 3 11 c. yes, c.v.= ; x -21 -14 -7 y 3 2 1 d. ; no x 2 3 6 y 5 7 13 e. Identifying Direct Variation from equations i. 3y=7x; can it be written as ? 1.

ii. 1.

cannot be written

iii. 1.

;

iv. 1. 4. Using proportions to solve direct variation a. Suppose y varies directly with x and y=9 when x=-15. What is y when x=21? i. Use two forms of in proportion 1.

solve for y.

;

b. Y varies directly with x, y=15 when x=3. What is y when x=12 i. ; ;  Conclusion: i. Answer any questions. Recap today’s lesson 9. Modifications: Becky (and all other students) will be allowed to use her calculator at all times. 10. Assessment: Lesson objective(s) Identify functions

Solve for functions in word problems

Direct Variation

Assessment method – Tier 1 Complete 2-1 Functions worksheet; to be turned in and graded for comprehension Complete word problem worksheet as a class and individually; to be graded for comprehension Students will complete the Constant Variation Puzzle sheet to be graded for comprehension.

11. Appendices:  Identifying Functions- 2.1-Functions  Word Problems  Puzzle: Direct Variation

Individual assessment needs Tiers 2, 3 Complete 2-1 Functions worksheet; to be turned in and graded for comprehension Complete word problem worksheet as a class and individually; to be graded for comprehension Students will complete the Constant Variation Puzzle sheet to be graded for comprehension.

12. Reflection: The Direct Variation Puzzle Sheet was changed to bookwork, page 71 numbers 7-24. The students showed a grasp on the material, but did not show a strong enough grasp to work on the puzzle yet. Students were successful with the word problems, but did not seem comfortable with them. I will be including more word problems in the next few lessons so they have more practice before the test. Caleb didn’t bring his book and was given a warning.