MS After School Intervention
Theme: Summer Vacation
Unit: Solving Equations and Inequalities
Day 10 Lesson
Objective
Students will solve inequalities for the unknown.
Common Core Standards:
7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r , where p , q , 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.
8.EE.7 Solve linear equations in one variable.
8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a , a = a , or a = b results (where a and b are different numbers).
8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Materials

Chart paper

Markers
 “Solving Multi-Step Inequalities Practice Problems” resource sheet
 “Mix-N-Match Cards” resource sheets
 “Stoplights” resource sheet (one stoplight per student)
Choosing a Job (10 minutes)
Read the following problem to the students:

“You and a friend are looking through the newspaper for a summer job. There are two jobs that you are interested in. The first pays you $20 per hour, but you must pay $160 to buy a uniform. The second job requires no uniform but only earns $12 per hour. Your friend doesn’t want to pay for the uniform, but you would like to make more money per hour. How might you convince your friends to take the first job with you?”
Have students discuss the problem in groups. You may need to prompt them to consider convincing him by showing him how many hours you must work in order to earn more than the second job. Students may set up the inequality 20 x

160

12 x or an alternate representation of the same inequality.
Solving Multi-Step Inequalities (20 minutes)
Place various manipulatives and labels for various methods that students have used throughout the unit at different tables around the room (for example: tiles, algebra balance, rods and cubes, drawing pictures, using words to undo, solving algebraically, etc.). Allow students to choose which method they would like to use and move to the corresponding table. Once students have chosen the method with which they are most comfortable, have them complete the practice problems individually, checking their solutions with the group as they go.
Note: Students may find that they need to try a few different methods before they are comfortable.
At the end, have each group explain their solution to one of the problems to the class.
Practice Problem Solutions:
1. x ≥ –6 2. n > –3 3. b ≥ 0 4. x < 1
Group Gallery Walk (20 minutes)
Assign students to one of four small groups. Have the groups move to a new location in the room. Hand each group one of four problems, chart paper, and markers. Groups should set up, solve and graph their problem on the chart paper.
Once groups are finished, they are to post their problem and solution on a wall in the room. On the teacher’s signal, groups should pass from their problem to the next. Once there, students should work out the new problem on their own paper and write a comment on the chart paper such as “We agree with your solution,” “We think the answer should be ___,” or “We are not sure how you got this answer.” Groups should then return to their original problem to review other groups’ responses and possibly review their own work/solution.
Gallery Walk Problems:

1.

3 x

2 x

5
2.

( 2

2 m )

2

6
3.

9
 
8 ( 1

6 v )

1
4. 8 ( 1

4 x )

40
Solution: x > –1
Solution: m < –5
Solution: v

0
Solution: x < –1
Mix-N-Match (15 minutes)
Distribute one Mix-N-Match card to each student. Have students move around the room, switching off their cards so that they don’t have the same one for very long. Students should continue to trade cards until “freeze” is called.
Call “freeze” to have the students stop switching. Give the students a few minutes to evaluate their card. Call “match” to have the students walk around the room and find the student who has the graph card that corresponds to their problem. Have students hold up their cards to confirm that they have matched correctly.
After students have found their matches, call “mix” in order to repeat the process.
Debating your Job Choices (15 minutes)
Split the class into two groups. Re-read the problem scenario from the beginning of the lesson.
“You and a friend are looking through the newspaper for a summer job. There are two jobs that you are interested in. The first pays you $20 per hour, but you must pay $160 to buy a uniform. The second job requires no uniform but only earns $12 per hour. Your friend doesn’t want to pay for the uniform, but you would like to make more money per hour. How might you convince your friends to take the first job with you?”
Assign one half of the class to the first job, and the second half of the class to the second job. Each group must come up with a representation of an inequality and solution that would convince someone to take the job they have been given. Groups should be encouraged to use manipulatives or draw pictures if necessary, and to graph their solutions. Each group should have a spokesperson to present their representation and any other information they can think of to the rest of the class, to the teacher, or to an outside visitor (another teacher, an administrator, etc).
Closure (10 minutes)
Have students discuss the following questions. Have students pinch the stoplight sheet in

order to show how they feel about the content (green if they are comfortable moving on, yellow if they need to slow down, and red if they feel that they need to stop and revisit the concept).
1.
How do we feel about solving inequalities? Have a student explain, in their own words, how to solve.
2.
How do we feel about the rules for negatives for inequalities? Have a student explain the rules.
3.
How do we feel about graphing inequalities? Have a student explain how to graph.
4.
How do we feel about the difference between equations and inequalities? Have a student explain the differences.

1.

3 x

2 x

6
2. 3

6 n

4

17
3. 4 ( 8

2 b )

2 b

32
4. 5 x

7 ( x

1 )
 
9


3 ( 2 v

5 )
 
13
 v
5 ( x

1 )

2 x

20
 p

6 p

4

6 p
5

4 x
 x

8 r

7

9
 r

6

2 x

12

8 x

3 x
38

5 x

7 ( x

4 )
7

7 ( x

7 )
 
4

5 x