Objectives: To develop the symbolic formula for a linear function from the characterization of constant rate of change (slope) and to interpret the meaning input, output, slope, intercept and intersection of two lines in some real world situations.
Preliminaries/Lead-In:
Suggested Procedures: I will let them work on 1a -d and then discuss those as a class - possibly having someone show what they did on the doc camera. Then I will take over and probably do 1e and f as a class together - I expect many students to be a little unsure through question 1 why they are doing things in this way - some will want to jump straight to the equation of a line which is fine but I will want them to understand why that will get them the same thing as proceeding through the other parts. On 1f I will ask how the y-intercept corresponds to the data set (ie we can work back from 1 and see what the value of y is at x=0). I will then let them do 2 and then check to see how they decided to do it - I will expect that some will use the process from 1e and others will use 1f. I think this is likely all we will get done in class so before sending them home to try the rest of it I will talk to them about 3 and what I mean by explain in practical terms.
I will expect to talk to them when they come back having finished the activity and talk about each of the last questions. Q4 addresses a number of ideas. The first is a more subtle use of input and output in a and b to see if the students are really understanding that. Also in b they need to factor the quadratic - here I will point out that we will every now and then expect them to be able to do this so if they are not comfortable with it then they should review it. Then in c they should be able to recognize that this is not a linear function as the rate of change is not constant. They also have to figure out how to calculate an average rate of change given a symbolic function which is not linear - some students have trouble with this (not sure what "points" they are using). They should recognize that this is a concave up function given their work in CA 1.3. Q5 causes a lot of confusion as they are given two rates (birth and death) that are modeled by linear functions. They have to figure out what the line is representing and not get confused with the rate of change of the line. The main idea in this question is that they will need to find the intersection of these two lines in order to answer b. I like this question because it brings up a lot of good confusion which we then need to talk through as a class.
Wrap-Up/Take-Away:
Possible Homework: Probably Q3 on will be homework as I don't expect to get through much more than that in class.
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