Domain and Range of Graphs Using Set Builder Notation

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SWBAT identify the domain an range of graphs using set builder notation

Big Idea

Restrictions! Students gain a strong foundation for Inequalities, and use two different colors to organize the difference between domain and range.

Warm Up

10 minutes

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 use it to access their prior knowledge of inequalities or refresh their memory if necessary. Having a clear understanding of what the inequalities symbols mean, will help my students to achieve the goal of this lesson: to write the domain and range of a graph using set builder notation.

I review the Warm Up in the video below:

Guided Practice

15 minutes

Then I begin introducing the Guided Practice for this lesson.  I instruct the students that domain and range are based on  the end behavior of the graph.  I have students use two colored pencils for this activity.  One color for domain and one color for range.  Most of the students know that domain is what possible x's and the range is what possible y's.  When looking at a table, it is easy for students to identify the x's and the y's.  However, when looking at a graph, students have more difficulty.  I ask students how far left, and how far right does the graph go for domain.  For range, I ask how low does the graph go to how high does it go.  I emphasize equal to or includes, as well as not equal to , and does not include.  I call on students as we work through the Guided Practice.

I model an example below in the video:


I start off working and modeling a few problems, and then let them try one before we check it. Then after reviewing the one problem they work individually, I assign them two or three problems to work individually.  We check the problems again, and I call on students to come to the board to model the problems.  Then the students finish the Guided Practice, as I walk around to assist.  

After the Guided Practice, I assign the Independent Practice for students to complete.  


Independent Practice

15 minutes

As students are working on the Independent Practice using set builder notation, I walk around to monitor their progress.  I expect the Independent Practice to take about 15 minutes.  I also assist students that need more help with the inequality symbols when using set builder notation.  Some students I notice are writing the intervals for domain and range in interval notation instead of set builder notation.  I purposely planned for the students to use set builder notation first to develop a deeper understanding of inequalities before working with interval notation.  

I remind students to place their answers in set builder notation, which they have problems doing. That is why they are using interval notation.  It is a handful of students that are still struggling, but it relates back to not understanding the meaning of the inequality symbols.  More specifically, not understanding which one to use for open or closed circle.  A few students have problems with the direction of the arrow also.  Some of the students that are writing their answers in interval notation, are not using the parentheses or the square brackets correctly either.


Exit Slip

10 minutes

I plan for this Exit slip to take about 10 minutes.  I allow everyone time to finish the Independent Practice.  If the students need more time, I do this activity at the beginning of the next day's lesson. After students have completed the Practice, I show the students the first three answers to numbers 1, 2, and 3.  Then I ask the students who get all three questions correct to stand up.

I instruct each of them to find a table or an individual student that is not standing, and give them feedback on their paper.  I remind them to provide constructive feedback (MP3) in a positive manner.  I instruct them to start by trying to provide feedback to correct any of the first three answers that they missed, but then compare other answers on each others paper to look for differences.  

After the five minutes is up, I have students complete the Exit Slip.  The Exit Slip ask for students to provide feedback on anything they learned from this activity, or anything that they taught another student.

Most of the student responses on the Exit Slip indicated students still having problems with the meaning of the inequality symbols.  I did hear good feedback and conversations between students, explaining the inequality symbols.  I think that the one on one peer feedback was beneficial.  This is definitely a skill that I will keep checking.