Algebra 2 Online!
Henrico County Public Schools, Virginia
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AII.9
The student will collect and analyze data, determine the equation of the curve of best fit, make predictions, and solve real-world problems, using mathematical models. Mathematical models will include polynomial, exponential, and logarithmic functions.
 Essential Knowledge and Skills Collect and analyze data. Investigate scatterplots to determine if patterns exist and then identify the patterns. Find an equation for the curve of best fit for data, using a graphing calculator. Models will include polynomial, exponential, and logarithmic functions. Make predictions, using data, scatterplots, or the equation of the curve of best fit. Given a set of data, determine the model that would best describe the data. Essential Understandings Data and scatterplots may indicate patterns that can be modeled with an algebraic equation. Graphing calculators can be used to collect, organize, picture, and create an algebraic model of the data. Data that fit polynomial, exponential, and logarithmic models arise from real-world situations. See curriculum guide or framework for parent equations.
Vertical Articulation
1. SOL A.11 - collect/analyze data/determine equation of curve best fit to make predictions/solve real‐world problems, using models (linear/quadratic)
2. SOL AFDA.3 - collect data/generate equation for the curve (linear/quadratic/exponential/log) of best fit/use best fit equations to interpolate function values/make decisions/justify conclusions (algebraic/graph models)
Instructional Materials
1. VDOE ESS Lesson: Curve of Best Fit - Statistics (PDF) - Collecting and analyzing data, using curve of best fit (Word)
Real World Lessons
Practice
Self-Assessments
Skills
1. Mathematics Assessment Project:
• A07:Functions - Apprentice - You are given a set of points on a graph. Your task is to find one linear fuction and one quadratic function which, between them, pass through all the points.
• E11:Table Tiling - Expert - In this task, you must work out how many whole, half and quarter tiles tiles are needed to cover the tops of tables of different sizes.
2. JMU Pivotal Question: Curve of Best Fit (doc)
Videos
1. Video Tutor - Linear Models
Explore Learning
1. Determining a Spring Constant - Place a pan on the end of a hanging spring. Measure how much the spring stretches when various masses are added to the pan. Create a graph of displacement vs. mass to determine the spring constant of the spring.
2. Exponential Functions - Activity A - Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function.
3. Fourth-Degree Polynomials - Activity A - Compare the equation of a fourth‑degree polynomial to its graph. Vary the coefficients of the equation and investigate how the graph changes in response.
4. Logarithmic Functions - Activity A - Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function.
5. Logarithmic Functions: Translating and Scaling - Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph.
Websites
1. Notes: Scatterplots
Common Core Standards
 A-SSE.3c F-LE.1b F-LE.1c F-LE.2 F-LE.3 F-LE.5 S-ID.6a S-ID.6b S-ID.6c