Function Transformations Unit

1. Function Transformations Unit For An Algebra 2 Course A Project Funded by the National Science Foundation, and written by Kirk Taylor

2. Why? • NCTM Standards and California Content Standards call for all students to have skill in function transformations. • Most Algebra 2 curriculums teach it, but not as a cohesive and comprehensive set of principles. • It gives students the power and knowledge to transform many types of functions.

3. Transform = Change Graphs are pictures of relationships Mathematics is a symbolic language of relationships

4. Goals • Teach the rules of FT as a single comprehensive set of principles • Not add time to the Algebra 2 calendar. • Use simple, low-technology and graphing calculators to give students confidence with functions

5. Learning Objectives • Students will learn to recognize by shape a group of six function families: Quadratic, Cubic, Absolute Value, Square Root, Exponential and Linear, and to learn the name of a ‘locator point’ for each family. • Students will learn the rules for function transformation, and be able to apply them to all six function families. They will be able to make accurate sketches of functions. • Students will be able to correctly identify to what degree functions have been translated, reflected, and/or stretched/compressed. • Students will increase their fluency with function notation.

6. Other Learning Objectives for the FTU • More math vocabulary: asymptote, increasing/decreasing function, odd/even function, inflection point, point symmetry, and more. • Better curve-sketching techniques • Establish foundations for further study

7. Unit Overview • Introducing the Big 6: • Quadratic Sketching Techniques • Cubic Generalizingpower functions • Absolute Value • Square Root • Exponential • Linear

8. Guided Inquiry Activities • Work collaboratively under well-defined guidelines • Make conclusions and conjectures based on experiences The Student’s Role

9. Guided Inquiry Activities The Teacher’s Role • Set clear rules for collaboration. • Set time limits. • Summarize points of the activity. • Assess students’ understanding and modify lessons as necessary.

10. Practice makes pretty good! • Evening Enrichment Opportunities

11. Assessment Teacher observations Assessment Tools

12. Teacher Observations • Accuracy of sketches • Verbal feedback • Student interaction and peer instruction

13. Assessment Tools • In-class demonstration and presentation of student work • Verbal CFUs • Quizzes and tests • Alternative Assessments • A.A. Rubric

14. Symbolic Language Fluency How Does an FTU Fit In? Quadratics and Polynomial Functions Exponential Functions FTU

15. Thanks! It was great!