A.11 
The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve realworld problems, using mathematical models. Mathematical models will include linear and quadratic functions. 

Essential Knowledge and Skills 
 Write an equation for a curve of best fit, given a set of no more than twenty data points in a table, a graph, or realworld situation.
 Make predictions about unknown outcomes, using the equation of the curve of best fit.
 Design experiments and collect data to address specific, realworld questions.
 Evaluate the reasonableness of a mathematical model of a realworld situation.

Essential Understandings 
 The graphing calculator can be used to determine the equation of a curve of best fit for a set of data.
 The curve of best fit for the relationship among a set of data points can be used to make predictions where appropriate.
 Many problems can be solved by using a mathematical model as an interpretation of a realworld situation. The solution must then refer to the original realworld situation.
 Considerations such as sample size, randomness, and bias should affect experimental design.


Vertical Articulation 
 SOL 8.13  a) make comparisons/predictions/ inferences, using information displayed in graphs; b) construct/analyze scatterplots
 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)
 SOL AII.9  collect/analyze data/determine equations of the curve of best fit/make predictions/solve real world problems, using models (polynomial/exponential /log)

Instructional Materials 
 VDOE ESS Lesson: Quadratic Curve of Best Fit  Statistics (PDF)  Determining a quadratic curve of best fit (Word)
 VDOE ESS Lesson: Line of Best Fit  Statistics (PDF)  Developing a curve of best fit for data (Word)
 VDOE ESS Lesson: How Much Is That Tune?  Statistics (PDF)  Solving systems of two linear equations in two variables (Word)
 VDOE ESS Lesson: Linear Curve of Best Fit  Statistics (PDF)  Determining a linear curve of best fit (Word)
 Notes: TI83 Best Fit Models (pdf)
 Notes: TI83 Curve Fitting with Residuals (pdf)

Real World Lessons 
 Dan Meyer: Will It Hit The Hoop: Will the ball go in the hoop?

Practice 
 ExamView Quiz: Line of Best Fit
 Prentice Hall Quiz: Data Analysis
 Prentice Hall Quiz: Line of Best Fit

SelfAssessments 

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.
 A23:Scatter Diagram  Apprentice  In this task, you will use a scatter diagram to compare the results of two school tests.
 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.
 Six Tasks for Quadratics (pdf)

Videos 
 Video: PH Making a Scatter Plot
 Video: PH Using Scatter Plots and Trend Lines to Make Predictions
 Video: PH Modeling Data Using a Linear, Quadratic, or Cubic Model *New 2009 SOL Content*
 Video: PH Writing an Equation for a Trend Line
 Video: PH Writing an Equation for a Line of Best Fit
 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.
 Estimating Population Size  Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake.
 Function Machines 2 (Functions, Tables, and Graphs)  Drop a number into a function machine, and see what number comes out! You can use one of the six preset function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph.
 Quadratics in Factored Form  Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response.
 RealTime Histogram  Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected.
 Roots of a Quadratic  Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
 SlopeIntercept Form of a Line  Activity B  Compare the slopeintercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response.

Websites 
 Interactive: Linear Regression Applet  plot up to 50 points and predict the line of best fit
 Interactive Notes: Line of Best Fit  lessons and practice problems at Regentsprep.org
 Notes: Using the TI Calculator to Find the Quadratic Function *New 2009 SOL Content*

Old Website Links 

Common Core
Standards 
8.SP.3 
FLE.1a 
FLE.2 
SID.6a 
SID.6b 
SID.6c 
SID.7 
SID.8 
