Functions, Statistics and Trigonometry A
MA.11.FUNCTIONSSTATSTRIGATF.BNET4COPY
This course is intended for students who have completed Geometry and Algebra II. It is designed to empower students to further develop and extend those concepts of previous mathematics curricula through the integration and application of statistical, trigonometric, and algebraic concepts. Students will display, describe, transform, and interpret numerical information represented as data, graphs, or equations. Students will use a graphing calculator and statistical software packages to plot functions, explore relationships between equations and their graphs, create and simulate experiments, generate and analyze data, and develop limit concepts. The Texas Instruments TI-83/84 plus graphics calculator will be referenced throughout the course.
Enduring Understanding
The student will understand:
- Choose and create an appropriate visual representation of data concerning information about population to show evidence of conclusions drawn about the data.
- Calculate measures of central tendency, variance and standard deviation as a means of drawing or defending conclusions about the data.
- Identify the parent graphs for several functions and use the translation and scale change theorems to draw the images without using an x-y chart
- Find the composition of functions algebraically and graphically.
- Solve polynomial functions using a variety of algebraic techniques.
- Use complex numbers to represent and calculate the solutions to quadratic functions.
- Use exponential equations and logarithms to solve algebraic equations.
Essential Questions
- How do visual representations of data help defend or draw conclusions about the data?
- What information do the measures of central tendency, variance and standard deviation provide about a set of data?
- What effect do translations and scale changes have on the graphs of functions?
- What effect does composing functions have on the domain, range, and graph of the functions?
- What techniques can be used to solve polynomial functions?
- How can you use complex numbers to represent the solutions of quadratic functions?
- How can you use the exponential and logarithmic forms of numbers to solve an algebraic equation?
Content Topics
Unit 1
Data Investigation
Unit 2
Key Functions and Modeling
Unit 3
Polynomial and Rational
Unit 4
Exponential and Logarithmic Functions
Unit 5
Trigonometry
Key Skills
- Application/Synthesis
- Visual/Graphic Data Representation
- Statistical Analysis
- Create Mathematical Models of Real-World Situations
- Communicate Mathematical ideas written and orally
- Reading
- Note Taking
- Technology Use
Assessments
- Tests
- Quizzes
- Activities
- Asynchronous Thread Participation
- Teacher Observation/Interaction in Threads and Chats
- Electronic Portfolio
- Simulations
- Maps
- Student Pod cast
- Creative Writing
- Projects
- Research
- Graphing Calculator or Computer Application
Standards Alignment:
NCTM Standards:
Number & Operations, Algebra, Geometry, Measurement, Data Analysis & Probability, Problem Solving, Reasoning & Proof, Communication, Connections, and Representation. Pennsylvania
Academic Learning Standards:
Reading, Writing, Speaking and Listening
1.1.11 Learning to Read Independently
1.2.11 Reading Critically in All Content Areas
1.4.11 Types of Writing
1.5.11 Quality of Writing
1.6.11 Speaking and Listening
1.8.11 Research Mathematics
2.2.11 Computation and Estimation
2.3.11 Measurement and Estimation
2.4.11 Mathematical Reasoning and Connections
2.5.11 Mathematical Problem Solving and Connections
2.6.11 Statistics and Data Analysis
2.7.11 Probability and Predictions
2.8.11 Algebra and Functions Science and Technology
3.7.11 Technological Devices