Reflection: Function Notation - Section 4: Closure

The investigation for this lesson went very smoothly because it allowed students to refine their thinking from the previous lesson.  I was actually surprised how many students had made a table during their investigation of the tower task from the previous lesson.  Based on that work, the students were able to use their table to construct a graph of their function.

We had a very good dialogue around whether or not the points should be connected on the graph.  As I was monitoring student work, I noticed that most students had connected their points before reading the prompt regarding whether or not to connect them.  The next time I teach this lesson I will call attention to this prompt first so that it is in the back of students minds.  Once students reflected back on the inputs and outputs, they decided that the graph could be made up of a series of points that are not connected.  However, we also said that the function used to model this graph f(x) = 5x - 4, would be a line.  The students also made some interesting observations regarding the slope of the line and the rate of change in the problem.  Students noticed that since 5 blocks were being added each time the slope of the line would be 5.

The video portion of the lesson also went well.  I am currently in the process of "flipping" some of my lessons. So, I used this video as an opportunity to teach students how to watch a "math" video (since this is what they would be doing at home).  I explained to them that they would need to stop the video in order to process, or predict or write something down.  I had one of my students, Javonne, take control of the video and I asked her to pause whenever she felt there was something important to write down.  She stopped at nearly all of the prompts that I had planned which worked out very well.  It also showed me that students have some good insight into the important points in an instructional video.

From the video, students were able to work on the closing activity.  This gave me some very good insight into student's preliminary understanding of evaluating functions.  I was happy to see that most students used a calculator to help them with the evaluation so the emphasis was on the input/output and not the arithmetic.  Students did not get bogged down with the input/output notation (ex f(3)=8) they knew that they had to plug in 3 for x and that the answer would either be 8 or something else.  If the answer was something else then the original equation would be false.  As you can see from the student work (I chose three levels of students since all of the student work was basically correct) they seemed to have a good understanding of the content.

Closure Reflection

Function Notation

Unit 1: Functions
Lesson 4 of 18

Big Idea: Introducing function notation by using it to describe a familiar problem (Tower Task) enables students to grasp its usefulness and build on their understanding of the concept of a function.

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Standards:
Subject(s):
Math, Algebra, function, domain, range, evaluate expressions given variables, 9th grade
45 minutes

James Bialasik

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