# Inequalities

Sample student work using inequalities to create boolean expressions for button-clicking fun!

It’s been a great start to second semester, and I am continuing to add coding lessons to my Common Core 7th grade math classroom! For the first week back, the topic was inequalities.  Inequalities have applications in computer programming that can allow your programs to branch and make decisions – making coding more interactive and fun!

Common Core / Coding lesson relating to:

• CCSS.Math.Content.6.EE.B.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
• CCSS.Math.Content.7.EE.B.4b Solve word problems leading to inequalities of the form px +q > r or px + q < r, where pq, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid \$50 per week plus \$3 per sale. This week you want your pay to be at least \$100. Write an inequality for the number of sales you need to make, and describe the solutions.

Background: It’s a new semester and we’re starting a new unit on Equations, Expressions, and Inequalities.  I made a quick decision to start the unit with inequalities.  Last year, inequalities were taught last in the unit, and it felt disconnected from the rest of the learning. I didn’t feel I taught it well.  My thinking is that this year, if I start with the symbols and vocabulary of inequalities and weave them in throughout the entire unit, they can be given equal treatment with equations and equivalent expressions.  As far as I know, the kids really did not get much exposure to inequalities last year, so I need to work with them on the 6th grade and 7th grade expectations, which is fine. They’re really similar.

Lesson:

1) I started with some notes to have the students capture vocabulary, symbols, and graphing.  We do the exercises on page 1 and 2 as group activities or pair/shares with whole-class discussion afterward.
On pages 3-4, I bring in boolean expressions, which are an application of inequalities.  In computer programming, inequalities have the potential to introduce something really fun for the kids, because they can turn a bounded region on the canvas into a BUTTON!  The notes demonstrate using boolean expressions to define (x,y) coordinates on a plane that would satisfy all of the inequalities in them.  On the last page, there is an example JavaScript program (I introduced it as a “skeleton” program and filled in the blanks as a whole-class activity) that kids can type in, and they’ll get a rectangle on the screen that becomes a button you can press.

NOTES: inequality_notes

NOTES FILLED IN: inequality_notes_completed

2) On day 2, We started with inequality warm-ups.  We then went to Khan Academy and clicked on Create a New Program. I tasked the kids with entering the sample program, and then problem-solving to add a second button that they create – or other interesting features that involve a mouse click and inequalities.  I graded them on effort only, as I don’t believe in assessing practice.

WARM-UP: inequality_warmups

EXAMPLE JAVASCRIPT PROGRAM: HERE

3) On day 3, I assigned a set of exercises on Khan Academy, and then had them continue work on their “button” programs. Some of the kids produced amazing work.  Some produced adequate work.  Almost everyone produced something, and in conferring with kids, I think they are getting the hang of inequalities nicely.

EXERCISES: INEQUALITIES ON A NUMBER LINE

4) On day 4, I assigned one more set of exercises on Khan Academy and gave a homework assignment on inequalities on a number line.  I can’t post the assignment due to copyright issues.  While we’re ramping down the writing and graphing of simple inequalities, we are concurrently ramping up writing expressions, combining like terms, and studying the distributive property. We will continue to weave inequalities into our work as we work with equations!

EXERCISES: INEQUALITIES IN ONE VARIABLE 1

5) On Day 5, we moved full-steam into other activities having to do with writing equivalent expressions, a different standard (which, perhaps, will contain more coding activities!).  I did do a 15-minutes warm-up: A wreck-it Ralph activity in which students had to debug a program and get it working.  I used this one.  We did this whole-class, but I wondered if it would make sense in groups.  I believe it would have taken more time, but would have been more engaging this way.

Troubleshooting: Broken Button-Click Program

Reflection: On the positive side, engagement – engagement – engagement!  Kids get so excited by making their computer programs interactive. They were even bought in to the inequality activities involving graphing and note-taking because they felt it had a purpose for learning more about computing.  For the first time, I had a number of kids that stayed up late working on programs because they had a great idea they couldn’t let go.  They e-mailed me for help over the weekend.  Another positive is that kids have settled into work groups that help each other with the programming.  Some work groups are more high-functioning than others, but since I have some that are very high-functioning, I can focus on the ever-shrinking number of kids who are pretty lost.
On the negative side, the math of boolean expressions is really slow in coming. My classes are so big – if I had time to confer for ten minutes with every student, one-on-one, my job would be much easier. JavaScript is a difficult language to learn for newcomers, and they are not used to thinking about matching the curly braces {}, where to add the semicolons, and making sure every open parenthesis ( is matched by a closed parenthesis ).  These troubles are growing with the addition of functions and “if” statements.

I think I can work through some of these negatives by doing a couple of “wreck-it Ralph” troubleshooting activities to help students with the syntax of JavaScript.  Debugging someone else’s program is a powerful tool.

Ongoing: I am looking for a way to tie in a unit project in which students can create their own innovation using inequalities and equivalent expressions! I have not yet worked out the details, and I am open to suggestions!