 Take out homework and a pencil to prepare for the homework quiz!  Check the file folder for your class to pick up graded work  Located by the bookshelf, blue crate.  Look behind the tab for your class period and take home anything with your name on it.

Chapter 1: Thinking with Mathematical Models

 Turn to page 31 in your textbook.  The points are not exactly in a straight line.  What line would you draw as a model for the data pattern?  How would you find an equation for this linear function?

 Which of the two lines seems to fit the data better?

 B) To find out how accurate each model is, you can calculate errors in the predictions made by the model. Those errors are the differences between the actual data and what each model predicts. Each such error is called a residual.  Your turn: Complete the handouts with tables for Figures 1 & 2  Do the residuals suggest that one model is better than the other?

 Any linear function can be expressed in the form y = mx + b  The coefficient m tells the rate at which the values of y increase (or decrease) as the values of x increase by 1. (aka Unit Rate)  It also tells steepness and direction (upward or downward) of the graph of a function  The value of b tells the point at which the graph of a function crosses the y-axis. That point has coordinates (0, b) and is called the y-intercept.

 In any problem that calls for a linear model, the goal is to find the values of m and b for an equation.  Turn to page 34 in your textbook

 What directions would you give someone to help him or her draw a mathematical model?  Once you have drawn the line, how do you find the slope and y ‑ intercept?  How can you compare the accuracy of two different possible modeling lines?

 If you have to make predictions from a linear model, which is more helpful, the equation or the line?  What are the advantages of having a linear model for your data set, rather than just a set of individual data points?

 Focus Question: What strategies do you use in writing equations for linear function?  Review Vocabulary: Residual  Treetop Fun! Treetop Fun!

 Tree Top Fun runs adventure sites with zip lines, swings, rope ladders, bridges, and trapezes.  The company uses mathematical models to relate the number of customers, prices, costs, income, and profit at its many locations.