Graph Inequalities on a Number Line

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SWBAT graph inequalities as open and closed point rays on a number line

Big Idea

Number lines represent solutions to inequalities (and equations).


10 minutes

This is a straight-to-the-point lesson to help students graph solutions to inequalities on a number line.  Some may argue that this is a 6th grade lesson, but I know that my students were not taught anything about inequalities during their 6th grade year.  Therefore, it is an important lesson.  Students are learning an important step in modeling solutions (MP4).

Every day, I post the names of students who were successful on the previous lesson's exit ticket.  My students get pretty excited seeing their names on the list.  I will let my students know that today's lesson is one where 100% of the class can have success - as long as they stay engaged.  I think it is a pretty easy lesson to master, but I will not say it in those terms. I don't want my struggling students to feel like they will only be successful on easy lessons.  

Though this is an easy lesson, students often make simple errors.

I will model each problem and then have students do a check for understanding problem.  For each model I will ask students to name values that are part of the solution.  I'll make sure students understand that the number line graph represents the variable.

I have noticed that students often do not draw open and closed circles well.  Their open circles sometimes look like they have a bit of shading and the closed circles do not look completely shaded.  I will exaggerate my drawings and encourage them to do so also.

I have also noticed that students do not always draw the arrow point on the ray.  They need to know that this is an important part of the graph as it represents values moving into positive or negative infinity.

Guided Problem Solving

15 minutes

These guided practice problems  can be solved in a few minutes.  Students may check in with their partners as needed.  I expect most students to have little problems with GP1 - GP5.  For problem GP6, I will probably need to call the class to order to discuss the inequality 5 > f.   What is the relationship between 5 and f?  How would we write this if we put the variable on the left side?  

Also, GP7 will not be graphed as a ray.  I will let my students know this.  I just like to see if they can figure this one out.  Perhaps you may want to change the numbers to put this in a more real-world context.  Perhaps 5 < p < 12.  p could represent the number of players required to be on a basketball team.

On GP8, students will probably want to know what variable to use.  Any variable is fine, but watch out for students that omit a variable all together.  Emphasize that the variable is important, as the number line represents its possible values.


Before moving on to the next section, I will ask students if they see any helpful shortcuts to graphing the inequalities.  If students need a hint I will suggest they look carefully at the graph and the inequality symbol itself.  After a bit of discussion they may notice that when the variable is to the left of the inequality symbol, the direction that the inequality symbol points to (the lesser side) is the direction the ray should be drawn.

Independent Problem Solving

15 minutes

There are only 8 problems for students to solve independently.  They are almost identical to the previous section, though I have two problems (versus 1) where the variable is to the right of the inequality symbol.  

While students are working, I will walk the room to check work.  I may ask questions as needed.

- What values make the equation true?

- Is the variable able to be equal to the value?  How do you know?

- On 5, is L greater than or less than 3?  Can it be equal?


Exit Ticket

5 minutes

Before beginning the exit ticket, I will ask students to discuss again how to graph solutions to inequalities.  What does an open point represent?  What does a closed point represent?  How do we know whether the ray should point to the right or left?  Under what situations might there not be a ray at all?

The exit ticket has 6 problems.  A student needs to answer at least 5 problems correctly to have a successful exit ticket.