**7.14 & 8.15a Solving Equations; 7.15 Solving & Graphing Inequalities**

__SOLs Covered__:**(14) Algebraic Concepts; (15) Inequalities**

__Math Dictionary Sections__:**Test 2.2 on Expressions, Equations, & Inequalities (Mon. 12/17)**

__Upcoming Assessments__:This week started and ended with quizzes. The students wrapped up the algebraic equations unit with a quiz on two-step equations on Monday before we got into solving and graphing algebraic inequalities. We started the inequalities unit off by reviewing more equations, merging into solving inequalities so students could see that the steps are essentially the same for both. The only difference (or complication as the kids may see it) is the rule on "flipping" the inequality symbol whenever division or multiplication with negative numbers is involved.

Students made their own sets of algebra tiles to help them model equations and inequalites outside of class, aiding in their comprehension of why we work the problems the way we do (i.e. the "backwards PEMDAS" with inverse/opposite operations). I am currently in making additional updates to the algebraic concepts (14) and inequalities (15) sections of the electronic math dictionary that will include examples of modeled equations and extra examples for showing work algebraicly. I hope to have the electronic copy finished and online in the near future, but I've already finished the slide show version of our Teddy Grahams and marshmallow activity from last week that I'll use to make the modeling notes. The algebra tiles version is next on my to-do list.

We also worked on how to graph the solutions to the inequalities. For this, students got to use Oreos© to represent the opened (for > or <) and closed (for ≥ or ≤) circles and pretzel sticks (or Twizzlers or Pixy sticks as each class donated different items for the activity) to represent the direction to draw the arrow. Another huge thanks to the students (and parents!) who brought in donations last week and those how brought in more this week: Jordan G., Emilio, Emma Jo, Jason, Mallory, Precious, Avia, Nick, Brent, Daniel, Megan, and Taylor. I worked on breaking students of the false assumption that the arrow is drawn in the direction the inequality symbol is pointing as that only works if the variable is on the left. Instead, they worked on checking numbers on either side of the solution. They were also taught to check the solutions by plugging the solution and the numbers on either side back into the original inequality to ensure everything works, including the proper "flips" for the inequality when dealing with negative multiplication/division.

Friday, as mentioned, had another quiz, this time on the inequalities. Students were allowed to use their Math Dictionaries for this quiz. This was in part due to the fact that they keep their algebra tiles stored there in an envelope and were encouraged to use those to help them work through the inequalities. I also allowed them to use the Math Dictionaries since some students have started to slack in the upkeep of their book, not adding all the examples they've been shown and many not bringing the book to class at all. Students were told that along with a few other things (their agendas and basic supplies), the Math Dictionaries were supposed to be brought to class everyday. Thus allowing its use was a reward for those students who are taking care of all of this as well as a reminder to those students who have started to slip in recent weeks.

Students were given a test review to work on after the quiz and to finish up over the weekend, so we can hopefully get started on the test (which will cover algebraic expressions, equations, and inequalities) by the end of class on Monday. It's important that we at least get started on the test Monday since many of the students will be on the Fort Lee field trip either Tuesday or Wednesday (depending on which block they have social studies). I've encouraged students to work on updating their Math Dictionaries as needed over the weekend, so they'll have it for the test as I will be allowing its use again.

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