##
* *Reflection: Developing a Conceptual Understanding
Domain and Range of Graphs Using Interval Notation - Section 4: Exit Slip

I purposely plan a problem in the Exit Slip for students to determine the domain and range of a function in which the arrow is slanted and not going in the left or right direction. In this lesson, some students have difficulty determining domain and range from arrows. Some students have difficulty understanding that negative infinity must be listed first in the interval, and then positive infinity. In my previous lesson, on stating domain and range using set notation, I emphasize what students need to focus on using colored pencils in the Guided Practice. For domain, students need to focus on how far left to how far right determines the graph, (the x's). For range, students need to focus on how low the graph goes to how high it goes (the y's).

*A Misconception*

*Developing a Conceptual Understanding: A Misconception*

# Domain and Range of Graphs Using Interval Notation

Lesson 5 of 13

## Objective: SWBAT write the domain and range of a graph using interval notation by comparing it to set builder notation.

#### Warm Up

*10 min*

I intend for this Warm Up to take about 10 minutes for the students to complete and for me to review with the students. I first ask students to write the domain and the range of each of the three graphs in set builder notation, and then I introduce the comparison of interval notation to the same graphs. Again, as I stated in the previous lesson, I want students to get a clear understanding of the meaning of linear inequalities before introducing interval notation in this lesson. I demonstrate introducing interval notation in the Warm Up below:

#### Resources

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#### Video and Notes

*15 min*

After the Warm Up, I play the video below in front of the whole class to reinforce how to write interval notation from inequalities. I have students take notes, pausing the video to ask questions when needed. It is a teaching strategy that I use often when I show videos in my classroom. It allows the students to see another teacher's perspective on the same content. I choose videos that are short enough to keep the students attention span. I set up questions to ask before the video provides the answers, and then show the video to reinforce what we discuss. In the video below, it shows several examples for students to try to write interval notation from an inequality.

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#### Independent Practice

*15 min*

Today's Independent Practice is meant to reinforce the Warm Up and the direct notes from the video. As students are completing the Independent Practice, I walk around the room to monitor progress. I do this with a spreadsheet to identify quickly which students are struggling. I have a pre-made spread sheet with all the students names listed in the first column, and I write in the title of the part of the lesson I am assessing for the day at the top of the column. I put a check mark for successful completion, or an x for remediation needed. As I observe the students working, students are stating that the interval notation is easier than the inequalities. However, as I am checking their work, several students still need one-on-one assistance from me or their table partners about when to use a bracket or a parentheses. I check the first two problems of the independent practice as I am walking around, and call the students identified on the spread sheet to a separate table to work with me for about five minutes. When they get to the table, I model Exercises 1 and 2 for them in the small group. Then I let students try Problems 3 and 4. Students will bring their work to me so that I can check their work closely. I have a provided an example of the spreadsheet in the resources.

I have been using a spreadsheet to provide immediate feedback (see the Spreadsheet Feedback reflection). In this lesson I was able to re-teach these students within the lesson. If time does not permit this in a lesson, I will follow up with the small group the following day. If a large group of students are struggling, I will step in front of the class to re-teach for a few minutes.

As students are completing their Independent Practice, I hand them an Exit Slip to complete as a formative assessment.

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#### Exit Slip

*10 min*

I will use today's Exit slip as a quick formative assessment to check student understanding of interval notation. The first two problems check for the student's ability to convert back-and-forth between inequality and interval notation. A student must understand the meaning of the square bracket and the parentheses related to the inequality symbols in order to be successful. This skill is important for students to understand what numbers to include or not to include in the solutions or domain and range.

Questions 2 and 3 also check for student understanding of the concept of infinity. Students need to correctly represent infinity using parentheses in interval notation. The final question on the Exit Slip is to check for student understanding that an odd function with arrows will have the same domain and range. The interval for both will be all real numbers, or negative infinity to positive infinity.

#### Resources

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: First Day of School
- LESSON 2: Introducing Functions
- LESSON 3: Identifying Functions and Providing Rationale
- LESSON 4: Domain and Range of Graphs Using Set Builder Notation
- LESSON 5: Domain and Range of Graphs Using Interval Notation
- LESSON 6: Evaluating Functions Using Function Notation
- LESSON 7: Evaluating Graphs and Equations Using Function Notation
- LESSON 8: Investigation of Distance and Time Graphs Using a CBR
- LESSON 9: Introduction of Parent Functions
- LESSON 10: Transformations of Parent Functions
- LESSON 11: Preparing for Partner Presentations on Transformation of a Parent Function(Day 1 of 2)
- LESSON 12: Partner Presentations on the Transformation of a Parent Function(Day 2 of 2)
- LESSON 13: Mastery of the Function Unit