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

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.

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

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

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.

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

Unit Overview Introducing the Big 6: Quadratic S ketching Techniques Cubic Generalizing power functions Absolute Value Square Root Exponential Linear

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

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

Practice makes pretty good! Evening Enrichment Opportunities

Assessment Teacher observations Assessment Tools

Teacher Observations AAAAccuracy of sketches VVVVerbal feedback SSSStudent interaction and peer instruction

Assessment Tools IIIIn-class demonstration and presentation of student work VVVVerbal CFUs QQQQ uuuu iiii zzzz zzzz eeee ssss and t t t t t eeee ssss tttt ssss AAAA llll tttt eeee rrrr nnnn aaaa tttt iiii vvvv eeee A A A A ssss ssss eeee ssss ssss mmmm eeee nnnn tttt ssss AAAA.... AAAA.... R R R R uuuu bbbb rrrr iiii cccc

FTU Quadratics and Polynomial Functions Exponential Functions Symbolic Language Fluency

Thanks! It was great!