Lesson: Introduction to Inequalities

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Lesson Objective

SWBAT solve inequalities without variables

Lesson Plan

Materials Needed: white board, dry erase markers, IND worksheet
Vocabulary: operations, equations, variables, signal words, inequalities, expressions
Do Now (3 -5 min): Teacher writes x + 7 = 12 on the board and says, all of you saw this same problem in the beginning of the lesson yesterday and I told you that there are four vocabulary words that you need to know for this new unit: expressions, equations, inequalities, and variables. We learned about expressions, equations, and variables yesterday. I would like three volunteers to come to the front of the class and circle these three parts.” Teacher gives selected students three different colored markers and says, “____________, could you please circle the expression? [x + 7 should be circled] Very good, and _____________, could you please circle the variable? [x should be circled] Very good, and _____________, could you please circle the equation? [x + 7 = 12 should be circled] Great job, you all did awesome!”
Opening (3-5 min): Teacher says, “Today we are going to talk about a new vocabulary word, one that is very important in this new unit: the word is inequality. Teacher writes 102 + 3 < 99+ 80 on the board and says, does this problem have an expression in it? [Yes] Very good, actually this problem has two expressions in it. Does this problem have a variable? [No] Very good, it does not have a variable, but it does have a mathematical symbol called the less than sign. Is this problem an equation? [No] Why? [Because there is not an equals sign]. Ok everyone you are doing great so far. Today, we are talking about inequalities, and by the end of this lesson, you will all be able to set up and solve one-step inequalities. Are there any questions?”
Direct Instruction (10 – 12 min): Teacher returns to the inequality written on the board and says,  “This is an inequality. An inequality is a mathematical statement that includes two expressions and a less than or great than sign. The purpose of an inequality is to compare two numbers or sets of numbers to see which is less than and which is greater than the other number. Solving inequalities is as simple as solving both sides of a problem, in the end you just have to look at two numbers and see which one is bigger and which is smaller. 
Teacher points to the inequality on the board and continues, “Looking at this inequality, I simply solve both sides to make sure the inequality is true. Who can tell me the answer to 102 + 3? [105] Very good, and who can tell me the answer to 99 + 80? [179] Awesome!” Teacher writes 105 < 179 on the board and says, “OK, is this inequality true? Remember that the sign should point to the smaller number.” [Yes] 
Teacher continues, “You all are doing great, but now it is time to see whether you know how to choose whether an inequality needs the less than sign or the greater than sign to be true. Remember, the sign is like an alligator, it always opens to the bigger number and points to the smaller number, like an alligator that wants to eat the bigger meal.”
Teacher writes 123 + 4 ______ 187 – 5 on the board and says, “Can someone tell me the answer to 123 + 4? [127] Great, and can someone tell me the answer to 187 – 5? [182] Awesome!” Teacher writes 127 _____ 182 on the board and asks, “Do I need the less than or greater than sign to make this inequality true?” [Greater than] Teacher writes in the greater than sign and asks, “Is the alligator eating the bigger number? [Yes] Awesome, then we know that the problem is correct!”
Guided Practice (8 -10 min): Teacher says, “You all are doing great and I can tell that you understand how to solve inequalities, but I need to make sure that you know how to solve inequalities when you come across them in a word problem.” Teacher writes Example 1 on the board or on an overhead projector reads it to the students:
“Example 1: Mike earned 47 dollars on Friday and 34 dollars on Saturday. His friend Tyrone earned 100 dollars on Friday and 12 dollars on Saturday. Did Mike or Tyrone earn more money?”
Teacher says, “Ok, remember to refer back to the 4 steps that we learned yesterday. We must read the problem, we need to determine the question, set up the equation and then solve. Can someone tell me what the question is asking? [Who earned more money] Awesome! Who can tell me what type of equation we might use? [An inequality] You all are really paying attention, for this problem I will set up the equation.” Teacher writes 47 + 34 __________ 100 + 12 and says, “Ok, we can solve this together, 47 + 34 is 81 and 100 + 12 is 112.” Teacher writes 81 __________ 112 and says, who can come up to the board and write in the correct inequality sign? [<] Awesome, now I want to give everyone the chance to try some of these problems on your own. The worksheet your about to get has all the steps, please raise your hand if you have any questions.”
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 Inequality Word Problems   Classwork


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