This is from Pearson's Algebra 1 textbook for iPad.
What I Did
- Establish a need for the graph, in general. Why are we drawing a graph? What's the point? Does my ability to draw a graph serve any larger purpose than getting me points on an assignment? This task doesn't have an answer to that question.
- Establish a need for the step graph, in particular. Why are we drawing a step graph? What's the point. Does the step graph have any advantage over other graphs? This task doesn't have an answer to that question.
Tom Ward has me covered on the first point. Nothing's topping this aspirational save-the-date for his 2019 marriage to Ms. Stone. What will postage cost then?
Graphs and equations of data are useful when they let us predict something external to the data we know. We don't know the price of postage stamps in 2019 so we can extend a linear model beyond the data and find out what it might be.
Mr. Ward will need to scrounge up 54 cents per invitation.
But he still hasn't given us a reason to care about the step graph. For that we look at internal data. We tell the kid, "Hey, your graph is messed up. If you hand that graph to someone, it says the cost of postage in 2003 was 39 cents and the cost in 2005 was 41 cents. But the cost in both those years was only 37 cents."
If you're going to make a graph that tells the story of the data accurately you're going to need a different model than a straight line. Enter the step.
What You Did
Aside from Tom Ward's superb work, over on the blogs:
- Scott Hills seizes the opportunity to show students the benefits of a well-scaled axis.
- Beth Ferguson removes step graphs from the task, which is one way to handle the problem.
- Evan Weinberg goes digital, though I'm not sure what the digital medium adds here. He also just asserts that the student's graph "should be a step function," which highlights the difficulty again of motivating a need for this function family.
Over on the Twitter:
@ddmeyer Get rid of text. Change table to pics of stamps with the years labeled. Ask to predict $ a letter costs this year and in 2020
— Mr Leibold (@leiboldmath) July 26, 2013
@ddmeyer investigate a longer time line and a line of best fit to determine future increases. Discuss "vertical distances" to each point.
— Jacob O'Brien (@jacobobrien82) July 25, 2013
@ddmeyer Ask students to guess the postage rate in 1995. Eliminate the table; look up data online. Compare with general price levels (CPI).
— Dave Radcliffe (@daveinstpaul) July 25, 2013
@ddmeyer switch to email? (Just kidding) :-)
— Jeff Cohen (@jeffcohen) July 25, 2013
Instead of a wedding invitation, change it to a graduation invitation. Have the kids estimate how many invitations they would have to mail out. They could then calculate the cost of their invitations. You could also have them calculate the cost that their parents/grandparents paid for their graduation invitations.