Expressions and Operations 

Equations and Inequalities 

Functions 

Statistics 

SOL Review Materials 




AII.9 
The student will collect and analyze data, determine the equation of the curve of best fit, make predictions, and solve realworld 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 realworld situations. See curriculum guide or framework for parent equations.


Vertical Articulation 
 SOL A.11  collect/analyze data/determine equation of curve best fit to make predictions/solve real‐world problems, using models (linear/quadratic)
 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 
 VDOE ESS Lesson: Curve of Best Fit  Statistics (PDF)  Collecting and analyzing data, using curve of best fit (Word)

Real World Lessons 

Practice 
 VDOE ESS: Curve of Best Fit Introductory Exercise (pdf)
 VDOE ESS: Curve of Best Fit Exploration (pdf)
 VDOE ESS: Curve of Best Fit Activities (pdf)
 VDOE ESS: The EwokJawa Problem (pdf)

SelfAssessments 
 SOL MiniQuiz: AII.9  Curve of Best Fit

Skills 
 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.
 JMU Pivotal Question: Curve of Best Fit (doc)

Videos 
 Video Tutor  Linear Models

Explore
Learning 
 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.
 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.
 FourthDegree 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.
 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.
 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 
 Notes: Scatterplots

Common Core
Standards 
ASSE.3c 
FLE.1b 
FLE.1c 
FLE.2 
FLE.3 
FLE.5 
SID.6a 
SID.6b 
SID.6c 

