## Reflection: Developing a Conceptual Understanding Understanding Domain and Range - Section 2: Investigation

In the opening activity for this lesson, the students had some interesting conversations.  I was able to monitor the student discussions as they discussed the problem.  Some students had misconceptions about what the graph represented.  I tried not to "fix" any of the student thoughts at this point in time hoping that the scaffolded investigation would guide students to clearing up misconceptions.

Before giving students the investigation, I asked students to use the graph to picture what happened in this race.  I had students turn and talk with their neighbor to share their ideas and create a verbal story about the race and how it unfolded.  While students were constructing their story with their neighbor I listened and found two groups who could share their ideas with the whole class.  The above activities helped students to process the question and understand it more deeply.  This understanding helped them to create meaning around the abstract concepts such as f(5) and g(15) in the context of the question.

When students were investigating the domain and range of this scenario they made fewer mistakes on finding the range.  This was a surprise to me as I anticipated more issues with students finding the range.  Students did very well with question number 8.  Even if they did not use the function notation of f(13)=g(13) they were able to say something about the race being tied at that point in time.  You can see in the attached work that I commented on the student's answer for number 5.  Many students said that you "cannot have negative time" which shows that they have a misunderstanding about the meaning of each variable (x and y).  I will address this misunderstanding in the lesson on multiple representations of functions.  In the opening students can explore what will happen if Adam spends more money than he has (the graph goes below the x-axis).  They can make sense of this as being debt in the context of that particular question.

Developing a Conceptual Understanding: Investigation Reflection

# Understanding Domain and Range

Unit 1: Functions
Lesson 5 of 18

## Big Idea: Real life examples make it easier to understand the application of the concept of function. This lesson allows students to determine domain and range based on feasible inputs and outputs for a function.

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Standards:
Subject(s):
Math, Algebra, domain, range, function
40 minutes

### James Bialasik

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