Reflection: Introduction to Functions - Section 4: Closing

 

Student responses to the exit ticket "What will you remember about how a function machine works?" were very interesting to me and followed a couple of themes.

First, two students remembered that the input is not necessarily limited to numbers.  In the opening of today's class, we used words and other examples to get students to understand the concept of a function, rather than the focus on a mathematical rule. I found it interesting that this was a big take away for students. I think it is sometimes helpful for students to step away from the more traditional idea of math in order to have deep understanding of a new concept.  One student commented that this was "great," which I thought was cute, but also reflected on how he was thinking positively about function machines.

Next, two students had somewhat different understandings about some work we did with the difference between a pattern and a function. In one of the In/Out tables we looked at, one student noticed a repeating pattern: take the third letter of the input for the first input, and then the fourth letter for the second input, then the third letter, then the fourth letter, etc.  Other students noticed (as the text wanted them to) that the Output was the second vowel of the input.  This led us to a nice discussion about how a function always has to give the same result for the same Input. That is, a pattern could take the third letter the first time and the fourth the second, but a function would always have to have the same Output for a given Input; it couldn't switch around.  In class, I was careful to compliment the student who had found a cool pattern that was not actually a function.  I think this lead to some confusion though, based on some of the Exit Tickets. One student wrote, "... patterns can't be a function."  In the next class, I will ask him to say more about this point to check for understanding.  Another student wrote, "...patterns can't always be function."  When I asked him to say more, he wrote, "A consistent output."  I would like to open class in our next lesson and have him explain his thinking. I like this phrase "a consistent output" and want students to revisit the idea that a function always has to give the same Output for the same Inputs. 

Lastly, another student wrote, "That the in & out have to be somewhat the same."  When I asked her more about this statement at the very end of class, I was trying to understand what she meant.  I said to her, but can't we put in a word and get out a number?  She said yes, but they have to be related.  I think this is a brilliant idea and a point that may be missing from this lesson. The relationship between the domain and the range.

I plan to open my next lesson with these exit tickets typed up and bring out these key points. 

  What Students Will Remember
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Introduction to Functions

Unit 1: Introduction to Algebra: Focus on Problem Solving
Lesson 6 of 14

Objective: SWBAT use tables as one representation of a function. SWBAT understand and use the terms input and output and correlate them to the domain and range of a function. SWBAT give verbal statements of rules.

Big Idea: What's happening inside that machine? Students are introduced to a "function machine" as a metaphor in order to begin to understand the concept of functions and how they work.

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Subject(s):
Math, tables of values, Algebra, domain, range, function, Algebra 1
  60 minutes
function machine
 
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