26, 2016 TODAY'S AGENDA QUIZ
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- Irene Chapman
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1 TODAY'S AGENDA - Complete Bell Ringer (in Canvas) - Complete Investigation 1 QUIZ (40 minutes) - Be sure your assignments from the week are complete (bell ringers, hw, makeup work) - Investigation 2.1 Lesson Straight Diagonal Line Output increases by 2 each time - LINEAR Curved Line Output increases by a different # each time - NONLINEAR
2 Thinking with Mathematical Models Investigation 2.1: Modeling Linear Data Patterns Focus: How can you find a linear function that is a good model for a set of data and then measure the accuracy of that model with residuals? Vocabulary! Textbook pg. 134 FUNCTION: a relationship between 2 variables in which the value of 1 variable depends on the value of the other variable. examples: breaking weight of bridge depended on the # of pennies number of steel pieces depended on length of truss
3 Vocabulary! Textbook pg. 135 MATHEMATICAL MODEL: An equation or a graph that describes the relationship between 2 variables. process to create MM: 1. acquire data 2. create graph and plot data points 3. show a pattern 4. write an equation
4 GOALS for TODAY! We will be: 1. Fitting a line to data that show a linear trend and assessing a good fit of that model. 2. Using models to answer questions. Thickness vs. Strength What line would you draw as a model for the data pattern? Connect 1st and last point?
5 Part A (pg. 32) 1. Which of the two lines seems to fit the data better? Why do you think that? Vocabulary! Textbook pg. 136 RESIDUAL: The error calculated by finding the difference between an actual data point and the value that a model predicts. This helps us understand how accurate a model is.
6 Part B Complete the table for Figure 1 and Figure 2! (labsheet) (pg. 32) copy Part B Figure 2 (labsheet) (pg. 32) copy
7 Part B Cont. (pg ) 1. The first line goes through points (1, 12) and (6, 64). The equation for this line is y = 10.4x How would you describe the errors of prediction, or residuals, for this linear model? Part B Cont. (pg ) 2. Sally thinks the equation of the second modeling line is y = 10x. Do you agree with Sally? Explain. 3. How would you describe the errors of prediction, or residuals, for Sally's linear model?
8 Part B Cont. (pg ) Do the residuals suggest that one of the models is better than the other? Explain. Part C You can find linear models for many situations. The Student Paint Crew gives weekend and vacation jobs painting houses and apartments to high school and college students. The time a job takes depends on the area to be painted. (pg. 33)
9 Part C Cont. (pg. 33) Prior jobs give some data relating job area (in units of 1,000 square feet) and time to paint (in hours). The table below shows some of the data. 1. Plot the given data on the graph. 2. Draw a line to match the data pattern. Part C Cont. 3. Let's use this line: y = 2.4x (pg. 33) 4. Find the residuals for the model you developed. Explain what they tell you about the accuracy of the linear model. Area (1,000 sq. ft Actual Predicted by y = 2.4x Residual (Actual - predicted)
10 Label the y-intercept and slope in the formula below. y = m*x + b If points (2,3) and (-5, 7) are on a line, what is the slope of the line? m = y 2- y 1 x - x 2 1 Find the slope and y-intercept in the following equations and tables. Equation 1 y = 2-4x Equation 2 y = 3x + 13 Table 1 x y Table 2 x y
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