# Lesson: Inequalities: Solving with 3 Variables

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### Lesson Objective

SWBAT assign numbers to the variables to solve an inequality with three variables

### Lesson Plan

Materials Needed: white board, dry erase markers
Vocabulary: multiplication, operations, equations, variables, division, addition, subtraction

……….

Do Now (3 -5 min): Each student is given a DN worksheet and asked to complete it independently. The worksheet reviews two-part inequalities with addition, subtraction, multiplication and division.

Opening (3 -5 min): Teacher quickly reviews answers to the Do Now and then says, “A couple of days ago, we learned how to solve inequalities with variables that had two-parts. However, when you all are given the DC-CAS, you will need to know how to solve an inequality that has three-parts! So, by the end of the lesson today, you will be able to independently use the strategy of assigning a number to a variable to solve a three-part inequality.”

Direct Instruction (15-20 min): Teacher then writes the following example on the board:

Example 1: On a test, Hannah scored 8 points higher than Todd. On the same test, Hannah scored 7 points lower than Juanita.

H represents Hannah's score on the test.
T represents Todd's score on the test.
J represents Juanita's score on the test.

Teacher says, “Who can identify how many variables we are working with in this problem” [3] Great! Now, who can tell me the names of the variables we are working with?” [H, T, J] Teacher writes the following on the board:
Step 1: Read the word problem
Step 2: Select/Identify variables H and T and J

Teacher says, “Ok, we have completed steps one and two for solving inequalities. Who can think back to a couple of days ago and tell me what step three is? [Set up the inequality] Great job, now since there are several inequalities given in this word problem, we want to set up all the inequalities so that we can compare them in just a second. Remember that the open side of the inequality sign always opens to the bigger number. The first part of the problem says, on a test, Hannah scored 8 points higher than Todd. So who scored a bigger number on the test? [Hannah] Awesome, so we write this inequality next to step 3 for this problem.

Teacher writes the following on the board:

Step 3: Set up inequality H > T

Teacher continues, ”Ok, the problem then says that on the same test, Hannah scored 7 points lower than Juanita. Now, who scored more points between Hannah and Juanita? [Juanita] Awesome! So we add this inequality to step 3 for this problem.

Teacher writes the following on the board:

Step 3: Set up inequality H > T
J > H
Teacher continues, “Now, in order to answer the type of questions you will be given on the DC-CAS, you all will have to do some trial and error in order to get the correct answer. On the test, you will be given a set of choices like this.”
Teacher writes the following on the board:

A. J < T
B. T < J
C. H > J
D. J < H

Teacher continues, “Now, don’t get frustrated! Remember, step four to solving inequalities from word problems is to check the answers. The only difference when you are solving three-part inequalities is that you will have to check ALL the answers to know which answer is correct. Lets walk through this one together. First, we need to assign numbers to our variables. In step 3, we wrote that H > T. Let’s say that T is going to equal 40, that would mean that H can be any number greater than 40, can someone give me a number? [Answers will vary, 60] Ok, so H is 60 and T is 40.” Teacher writes 60 > 40 on the board and says, “Now, we look at the next inequality in step 3. We already know that H is 60, and H is less than J, can someone tell me a number that the variable J could represent? [Answers will vary, 90] Awesome, so J is going to be 90.” Teacher writes 90 > 60 on the board and says, “Ok, so now we look at choices given to us substitute the correct number for each variable based on the work we just did.

Teacher writes the following on the board:

Step 4: Check

A. J < T Check: 90 < 40
B. T < J Check: 40 < 90
C. H > J Check: 60 > 90
D. J < H Check: 90 < 60

Teacher continues, “So, looking at these four inequalities, which answer is correct? [B] Awesome, how did you know that?” [Because that is the one that is true, etc.]

Guided Practice (8 -10 min): Teacher says, “You all did an awesome job, but I want to do one more together before I give you a chance to do one on your own.” Teacher writes the following example on the board and solves the problem with the students.

Example 2: Susan is ten years older than Jack. Jack is five years younger than Mark. Mark is twenty years older than Susan.
Let S represent Susan’s age
Let J represent Jack’s age
Let M represent Mark’s age

A. S< J
B. S < M
C. M > S
D. J< S

Independent Practice (10 min): Teacher gives each student their own copy of the Independent Practice (IND) worksheet. Teacher circulates the room to answer individual student’s questions.

Closing (2-3 min): Teacher calls the attention of the students back toward the front of the class to quickly review the answers to the Independent Practice worksheet/ ask what we learned about.

### Lesson Resources

 IND variables word problem   Classwork 2 DN greater less   Starter / Do Now 1
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