Reflection: Developing a Conceptual Understanding How Will Your Salary Grow? - Section 3: Group Activity: "How Will Your Salary Grow?"


When students work to fill in their tables of values, I hope that they will notice patterns and try to generalize what's happening in each column.  To notice patterns is naturally engaging.  For example, many students note that the sums of all the powers of 2 up to any given row will be one less than the next power of 2, which is fundamental to understanding binary numbers and the nature of any base-n number system.  We also talk about where each value comes from, by pointing to cells in our table.  Any given "Plan B Total" is the sum of the previous total and the new daily pay next to it.  Tomorrow, students will use this idea to write formulas in Excel, which will then extend to writing recursive rules for sequences the next day. 

Upon teaching this lesson again, I'm happy with the balance that this activity strikes between being a rote task and chance to investigate bigger ideas.  Its nature as a fairly simple, repetitive task gives all students the chance to access it and to feel successful as they re-establish their best habits for the new semester.  Then, as a rich trove of patterns and the behavior of numbers, this task sets the stage for plenty of great mathematics to come!


  Previewing Recursive Definitions
  Developing a Conceptual Understanding: Previewing Recursive Definitions
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How Will Your Salary Grow?

Unit 8: Linear and Exponential Functions
Lesson 1 of 19

Objective: SWBAT observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.

Big Idea: One key word in standard F-LE.3 is "eventually"! Students explore a situation that reveals how exponential growth might take a little while to catch up with linear growth, but that when it does...

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