# Creating Inequalities to Solve Problems

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## Objective

SWBAT use inequalities to describe and solve real world and mathematical problems.

#### Big Idea

This lesson allows students to cooperatively practice solving inequality word problems.

## Opening

8 minutes

For today's class students should be seated in groups of four.  Each student will be assigned a number 1-4 and the groups should be numbered.  I will explain the student numbers in the next section.  For the warm up, students will begin working independently and then can share with the person sitting next to them.

I plan to give students about five minutes to work independently on finding as many ways to write the inequalities as possible (Inequality Launch, Page 2).  Students can simply divide their notebooks or whiteboards into four quadrants.   After 5 minutes I will have them turn and talk with a partner and try to add to their list to make it as complete as possible.  If time permits, I will go around to each group to have the class come up with as many ideas as possible.  I have included a list (which is not exhaustive) to help offer ideas if students are stuck.

This opening activity will re-familiarize students with inequality vocabulary, and, how the variables are used with inequalities. At the end of this actvity we will construct a list of examples on the board (see Launch_Answers). I will leave the class list up for the entire period so that we can refer back to these ideas.

## Cooperative Practice

25 minutes

This activity is called Numbered Heads Together.  Each student is given their own dry erase board.  As stated in the opening, each student in each group is assigned a number 1-4.  The objective is to have all four students work together on each of the nine problems in this section.   The problems are given one at a time.  Give students approximately 2 minutes to work on each problem.  At the end of two minutes you can choose a number 1-4.  (For this I have used index cards numbered 1-4 or you can use an online random number spinner - students tend to like this better!).  Whichever number comes up is the student who needs to show their work for the group and the only work that counts for the group.  You can award points to groups with correct answers, or those who make the most progress, show the most perseverence, etc.

Advantages to the activity:

• The activity really forces students to work together due to the random accountability aspect.
• Students need to discuss their ideas (MP3) and be critical about which ideas they accept to put down as the group solution.  I always add the caveat that whichever number comes up that student must be able to explain the answer. This usually disuades students from simply copying one another.
• In this activity, students will need to look at each question as a "mini" problem that the group needs to understand and to make a plan to solve (MP1).

I make graphic organizers available to all students should they choose to use them.  The setup will be similar to equations. The difference will come in the work that students show when they determine how to apply the appropriate inequality.  I ask students to show the setup, work, and check on their whiteboards.

## Closure

7 minutes

Students will work individually on this Ticket out the Door.  Students will need to solve a real-life problem dealing with inequalities.  (This is a problem that students probably work out on a daily basis in some form or another!)  I will encourage my students to use algebraic expressions to represent the three classes.  However, if students are still having difficulty with the algebra, I will allow them to come up with a solution in the best way they can (MP1).  This ticket out will give you a good sense of where your students are both in terms of inequalities but also in terms of algebraic representations in general.