Working out the Solutions

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SWBAT write and graph inequalities using real world examples.

Big Idea

Writing and graphing inequalities is a skill used in algebra


15 minutes

This is another great problem from illustrative math.  I chose this because it supports our learning about writing and graphing inequalities using a scenario that makes sense in their brains.  Also, students will be using a number line to show the solutions. 

As students are working out part a, watch to see that they do not represent any numbers on their number line that don’t make sense.  Students have been shown to draw an arrow to show solutions, but in this case, there is no such thing as a negative person and there is no such thing as ½ a person, therefore, the number line should be shown as points rather than a ray.

In part b, students will have more solutions because they are talking about weight. There is such a thing as ½ pounds etc. However, the students should represent this as a line segment because there is no such thing as negative weight.

Students should work independently and then allow time for them to discuss strategies and solutions.  If students represented the information differently, it would be a good idea to have a discussion about people and weight and how it can be represented.

For higher achieving students, ask them to write the inequality using one variable (compound inequality) to get a better representation of how the number line should work.

Tools:  Gone fishing question.


60 minutes

Students will be working through 3 rotations to get support and deeper their understanding of inequalities.  Students will rotate every 20 minutes.  Each station will focus on writing and graphing inqualities.

Students working in the computer station will be working with the IXL website.  They will be writing inequalities, from a number line, on the computer. I liked this activity because they have been working on graphing on the number line, but not much with writing from the number line.   

Students working in the independent station will be working on graphing inequalities on the number line and writing the inequality from a graph.  By getting the students to use a number line and determine what the graph or inequality should look like, you are having them engage in MP2.  They will be using a worksheet. I will have the solutions in a folder nearby for them to check their work.

Tools:  Graphing and writing inequalities worksheet from Kuta software.

Students may struggle with an inequality that looks like this 4 < x, where the variable is on the left.  Remind students that the variable represents our solution so we need to make sure we read that first.  So in this example, the inequality states “all of our solutions are greater than 4”.

Students working in the teacher station will be working with me on inequality word problems.  We will be finding key words and then writing and graphing the inequalities.  This station will require them to have a white board and a marker.  I’m going to be encouraging the students to write the inequality both ways ( x < 4 and 4 > x).  It’s important for them to get used to seeing them written both ways because when they start solving inequalities, the variable will be on both sides. I’m also going to be practicing reading the solution.  For example if x < 4, we would say “all of our solutions are less than 4”.  Hearing it will help make a connection to how and where the solutions are on the number line. By saying the inequality out loud and using the terminology, the students will be attending the MP 6. 


10 minutes

The students have been working hard on writing and graphing inequalities.  To bring this lesson to a close, I’m going to have students create their own inequality word problem.  They may make one up or think about an inequality they have encountered in their lives.  Then I’m going to have them write and graph the inequality and state the meaning of it.  For example…“all of our solutions…”  I will be collecting this on the way out so I can provide feedback to the students the next day.  By making the students write their own problem, represent it graphically and numerically, and explaining the solution, the students are attending to MP1,2,6.

Tools:  Writing your own inequality