Unit+2+-+Modeling+with+Linear+and+Exponential+Functions


 * ======**DPS Unit 2 Guide** ======

**Functions: Linear, Quadratic, and Exponential Models:** //Construct and compare linear and exponential models and solve problems//

 * ======F-LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions ======
 * Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals.
 * Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
 * Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
 * F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

**Algebra: Creating Equations**: //Create equations that describe numbers or relationships//

 * ======A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Instructional focus should include equations arising from linear functions ======
 * ======A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. ======
 * ======A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. ======

**Algebra: Reasoning with Equations and Inequalities**: //Understand solving equations as a process of reasoning and explain the reasoning//

 * ======A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. ======

**Algebra: Reasoning with Equations and Inequalities:** //Solve equations and inequalities in one variable//

 * ======A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. ======

<span style="font-family: Arial,Helvetica,sans-serif;">**Functions: Building Functions:** //Build a function that models a relationship between two quantities//

 * ======<span style="font-family: Arial,Helvetica,sans-serif;">F-BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Formal recursive notation is not used. ====== ||

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> a) Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models. > b) Informally assess the fit of a function by plotting and analyzing residuals. > c) Fit a linear function for scatter plots that suggest a linear association.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Statistics and Probability: Interpreting Categorical and Quantitative Data - **//Interpreting Categorical and Quantitative Data - Interpret linear models//======
 * __S-ID.6__ Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
 * __S-ID.7__ Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
 * __S-ID.8__ Compute (using technology) and interpret the correlation coefficient of a linear fit.
 * __S-ID.9__ Distinguish between correlation and causation.


 * Standards S-ID.6a, S-ID.6c, and S-ID.7 are addressed substantially in Unit 3 of the Core Plus Course 1 text.**
 * Standards S-ID.6b (residuals), S-ID.8 (correlation coefficient), and S-ID. 9 (correlation vs. causation) will need to be supplemented. If you have access to Course 2 materials, these standards are addressed in Unit 4 of Course 2.**

Other activities that may be useful:
 * [[file:dpscommoncoremath1/correlation.doc|correlation.doc]]
 * [[file:dpscommoncoremath1/least_squares_regression line-How do children grow.doc|least_squares_regression line-How do children grow.doc]]
 * [[file:dpscommoncoremath1/r_squared.doc|r_squared.doc]]
 * [[file:dpscommoncoremath1/Height vs Shoe.doc|Height vs Shoe.doc]]
 * [[file:dpscommoncoremath1/book page thickness.doc|book page thickness.doc]]
 * [[file:dpscommoncoremath1/boxplotsANDscatterplots.doc|boxplotsANDscatterplots.doc]]
 * [[file:dpscommoncoremath1/The Game of Greed.doc|The Game of Greed.doc]]
 * [[file:dpscommoncoremath1/gabalot_phone_calls.doc|gabalot_phone_calls.doc]]


 * Technology Activities:**
 * My Graph Is...
 * How Tall

**Web Resources:**

**NCTM** Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body

Exploring Linear Functions: Representational Relationships

** Applet showing effect of outliers on regression lines: **
 * [[image:http://www.nctm.org/uploadedImages/Math_Standards/Principles_and_Standards_for_School_Mathematics/E-Examples/Grades_9%E2%80%9312/7-5-50x50.jpg caption="7-5-50x50.jpg"]] ||  ||

<span class="wiki_link_ext">http://www.stat.sc.edu/~west/javahtml/Regression.html

Applet exploring linear functions, slope, and y-intercept: @http://www.nctm.org/standards/content.aspx?id=26790

**Applet for understanding the least-squares regression line:** @http://www.nctm.org/standards/content.aspx?id=26787