Today we finally got to Functions!

In the morning we discussed two items.  First, how do the ideas about processes and proportions discussed track back to the elementary levels?  Second each participant started with a problem from their curriculum and tried to make it open-ended.  These will be collected and distributed to the rest of the group.

We then moved into the formal idea of a function, connecting it back to the processes we discussed on the first day.  We introduced a lot of new terminology: function, domain, range, well-defined, one-to-one, and onto.  We talked about everyday correspondences and whether they might be functions, and we discussed what it means for a function to be the inverse of another.

Handouts

• Unit 3: Functions
• Module 4: Functions (actually, these are labeled as pages 3.2 – 3.7 for the Unit 3 packet)
• (We will not be discussing Unit 2, but those handouts are available if you want them for completeness’ sake.  Likewise for Modules 2 and 3.)

Homework

• Principles to Action, Section entitled “Elicit and use evidence of student thinking” (pages 53-57)
• Take a look at the previous blog post’s article “Why do Americans stink at math?”
• Consider the following “magic trick.”  (1) Start with your age.  (2) Multiply your age by 10. (3) Subtract your age from the previous result.  (4) Add up the digits of the previous result.  (5) Repeat step 4 with the new result until you get down to a single digit.  (6) Subtract 1.  (7) Convert your result to a letter, where A=1, B=2, C=3, etc.  (8) Think of a US State starting with that letter.  Why should I know you are thinking of this state?
  • Convert the trick into a chain of 7 functions.  Which are one-to-one?  Which are onto?
  • Does it matter what age you start with?  Why or why not?