Function Transformations UnitFor 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 akhfkhf )1(;)(

GoalsTeach the rules of FT as a single comprehensive set of principlesNot 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 OverviewIntroducing the Big 6:Quadratic Sketching Techniques

Cubic Generalizing power functionsAbsolute Value Square RootExponential Linear notationunctionf )(

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

AssessmentAssessment

•Teacher observationsTeacher observations

•Assessment ToolsAssessment Tools

Teacher ObservationsTeacher Observations

Accuracy of sketchesAccuracy of sketches Verbal feedbackVerbal feedback Student interaction and peer instructionStudent interaction and peer instruction

Assessment ToolsAssessment Tools

In-class demonstration and presentation In-class demonstration and presentation of student workof student work

Verbal CFUsVerbal CFUs QuizzesQuizzes and and teststests Alternative AssessmentsAlternative Assessments A.A. RubricA.A. Rubric

FTUQuadratics and Polynomial Functions

Exponential Functions

Symbolic Language Fluency

Thanks! It was great!