# Solving and Proving Compound Inequalities

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## Objective

SWBAT...1. Solve and prove compound inequalities 2. Create a viable argument and critique the reasoning of others

#### Big Idea

Students actively engage in the note-taking process to master an important skill in Algebra!

## Entry Ticket: Compound Inequalities

15 minutes

To begin class I have students complete an Entry Ticket on solving simple inequalities (Entry Ticket Compound Inequalities). As an alternative, teachers can write the entry ticket on the whiteboard to save paper:

Entry Ticket

Directions: Solve and Graph

1. 3X + 14 < 26

2. -5X - 3X + 1 > 65

As we begin today's lesson I want to assess students' retention of this skill. If students are able to demonstrate a strong understanding of solving one variable inequalities at the onset, then it will make this lesson go that much smoother. One particular thing that I am looking for is whether the students are successful with the second problem. It has a negative coefficient on the variable. I want to make sure that the students recall how to handle an inequality when they might multiply or divide by a negative number.

## Active Note-taking: Solving Compound Inequalities

20 minutes

After the entry ticket, students engage in Two-Column Notes  as a way to interact with the material using a variety of language domains.

During this explicit instruction section, I review the powerpoint slides with students. The Turn and Talks  and check-ins embedded in the slide are suggestions for ways teachers can foster critical thinking and a more collaborative learning environment in their classroom.

I purposively leave out the steps for the last examples in the powerpoint so students can use their notes. The powerpoint slides can be used as Differentiated Instruction in a number of ways. Students who benefit from a note-taker can be given a copy of the notes, and the slides can be filled in at varying degrees to scaffold the learning process.

## Guided Practice: Solving and Proving Compound Inequalities

20 minutes

In this section, I have students continue solving problems using two-column notes. This encourages students to be more active participants in guided practice. I play a video from Khan Academy that has a number of compound inequalities for students to solve. This particular example is nice because it shows students the solution as an inequality, as a graph on a number line, and in interval notation. The use of multiple representations helps students to better integrate their understanding of the concept of compound inequalities.

As we view the video together, I have students take two column notes and complete the problem with a partner before showing them the solution. For example, I have students share the first step they did to solve the problem. Then, I play the video and we compare and contrast strategies.  I find that students engage with the video. I am also able to gradually pull back the supports and help students to become more independent in solving the problems.

## Independent Practice

20 minutes

For independent practice I assign a problem set that asks students to solve different types of compound inequalities.

I typically either assign a problem set from the textbook or I project problems on the white board. One good source for practice problems is Khan Academy. The problem set for compound inequalities can be found here: Khan Academy - Compound Inequalities Practice

An alternative for classes with access to the right technology is for students to complete the practice problems from Khan Academy online. This way students can interact and move more at their own pace through the problem set.

## Exit Ticket: Idea Organizer on Solving and Proving Compound Inequalities

15 minutes

To close class I have students complete an Idea Organizer after solving and proving a compound inequality (Exit Ticket: Solving Compound Inequalities Writing Idea Organizer).

My intent is to get students to write about their mathematical thinking. The power of writing as a tool for learning is amazing. Students really do jump on board in an environment that values writing. It is very difficult to find the time in the math classroom for writing, but the more I find a space for the activity, the more I find it to be valuable part of the lesson, rather than simply another layer added on.

The Idea Organizer can be assigned for homework. Teachers can also have students complete the organizer in class, and have students write up a written response for homework.