Linear models and equations Investigation 2

What you need: paper calculator 2 What you need: paper calculator 2.1 How can you find a linear function that is a good model for a set of data?

Kids will have copies of these two graphs Kids will have copies of these two graphs. We hope that as kids discuss #1 they realize that figure 2 is a better model for the data since most of the points are really close to the line. Ask students what each line suggests about the constant rate of change of each graph (figure 1 is about 10, figure 2 is 10) Ask students where each graph starts

Figure 1 Have students plug the layer numbers in for x in the equations to get the breaking weight predicted by the line Then find the residual.

Figure 2 Have students plug the layer numbers in for x in the equations to get the breaking weight predicted by the line Then find the residual.

How would you describe the errors of Prediction, or residuals, for each model? Do the residuals suggest that one of the models Is better than the other? Explain.

Homework 1-3, 35

What you need: paper hw hw log sheet calculator 2 What you need: paper hw hw log sheet calculator 2.2 How do you write an equation for a linear function given a graph, table, or two points?

Any linear function can be written as an equation in the form y= mx + b

Slope - 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 y-intercept – tell you where the line crosses the y axis the ordered pair is (0,b)

Students will have a copy of A 1-4 Students will have a copy of A 1-4. Our goal is that they are to describe the slope by counting the distance up and over for any two points on the line.

Students should be able to find the rate of change in the tables pretty easily…remind them it is always the coefficient of x In a. Students should be able to find the y intercept since it is in the table, b. May present more of a challenge since x=0 isn’t in the table

Homework 6-8, 57

What you need: paper hw hw log sheet calculator How can I write an equation for a linear function when given a table?

57. Story one – graph A story two – graph D Story three – graph B

What you need: paper hw hw log sheet calculator How can I write an equation for a linear function when given ordered pairs or a graph?

What you need: labsheet 2 What you need: labsheet 2.3 from yesterday hw hw log sheet calculator 2.3  What Strategies can you use to write         equations for linear functions?

Paper (from yesterday) You need: Calculator Labsheet 2.3 Paper (from yesterday)

Homework 5, 9-19, 37-42, 58,62

What you need: paper hw hw log sheet calculator 2 What you need: paper hw hw log sheet calculator 2.4 What strategies do you find useful to find solutions for linear equations?

62. H

Homework 20-25, 65-68

What you need: paper hw hw log sheet calculator 2 What you need: paper hw hw log sheet calculator 2.5 when the graphs of 2 linear functions intersect, what do the coordinates of that point tell you?

Ask students how attendance changes for each activity as the probability of rain increases

Homework 26-34, 43-44

Any number 3 or bigger Any number less than 6 Any number 2 or bigger Any number 9 or less