Reflection: High Quality Task Piecewise and Step Functions - Section 2: Launch


Students had an opportunity to work with their partners on this investigation.  I tried not to be too helpful as the students read and reasoned through the various portions of the investigation.  I used a document camera to show student work at various stages and to prompt discussion over various aspects of the investigation.

Some of my notes include the following:

1) Once students plotted the points at the bottom of page 1 many pairs had a tendency to immediately connect the dots.  This led to a good discussion with the whole class.  I showed one groups work (with connected dots) and asked other students how much the President made in 1990?  Students used the table to determine that the President made $200k.  Then I asked students to look at the graph that I had projected to see if they noticed a problem.  After students did a turn and talk they were able to come up with the fact that the graph showed that the President made approximately $350k.  This showed the students why they were not going to just "connect the points."

2) Students had some interesting discussions within their groups as far as what to do in between the points.  When I teach this lesson again in future years I will ask students to plot more years along the same step to see the pattern more easily.  For example, I would put questions on the investigation that would ask students to plot the salary for 1800, 1820, 1840, 1860, and 1870.  This would help students see that for all of these years (and the years in between) the President made the same salary.  Because of this, a horizontal line would represent all of the years in that interval.

3) Students really did not have much trouble with the x-value where the output jumps up to the next step.  I thought that this would be challenging for students.  However, because we have been spending time discussing the definition of functions (only one output for each input) they knew not to have to points for the same x-value.  Three of the groups struggled with how to handle this but the other 10 groups were able to determine how to represent the value at those x-values.

This ended up being a really valuable investigation.  Students were able to use step functions to model some real world data.  By looking at the context of the situation students were able to work through the nuances of graphing a step function.

  Launch Reflection
  High Quality Task: Launch Reflection
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Piecewise and Step Functions

Unit 1: Functions
Lesson 7 of 18

Objective: SWBAT construct piecewise and step functions and use them to model situations.

Big Idea: Students will construct a step function by analyzing salaries that increase at certain intervals. Students will transfer this understanding to constructing piecewise functions that are defined on specific domains.

  Print Lesson
Math, step functions, Algebra, piecewise-defined functions, domain, range, interval
  35 minutes
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