Pair up students before the beginning of the class and hand each pair an “Inequality Match” table. Pair students up with partners they don’t usually work with. The pair will be discussing the matching exercises together as well as reasoning together about the real world situations in the next section of the lesson. The match set is composed of three equations and 6 line graphs. Ask each pair of students to solve the inequality and match the solution set to its number line A through F in the right column. The first inequality involves dividing by a negative value, the second involves using the distributive property, and the third, solving with variables on both sides.
Students may match inequality #1 incorrectly failing to understand how the inequality symbol is affected when dividing by a negative number. They may need to be reminded that the symbol changes and why:
For the student:
First of all, the procedures for solving linear inequalities in one variable are much like those for solving linear equations. To isolate the variable, you can make use of the Properties of Inequalities. These properties are similar to the properties of equality, but there are two important exceptions. When each side of an inequality is multiplied or divided by a negative number, the direction of the inequality symbol must be reversed. Here is an example:
12 < 50
12/-2 < 50/-2 (divide each side by -2)
-6 < -25 NOTE THAT THIS IS FALSE SO WE MUST REVERSE SYMBOL
-6 > -25
Partner Activity 1:
Hand each pair of students a slip labeled Q1 Solution. (Resource NewInfo_Q1Solution) NOTE: The Q1A slip should be given as a Scaffold to ESL students or other students with language difficulties. All other students should work with the Q1B slip.
They will have to complete the blank segments on the slip. Project the real world problem titled Q1 Problem on the board. (Resource: NewInfo_Q1Problem) Tell the students that for the first problem, they will have the Q1 slip as a guide to solving the problem and graphing the solution on a number line. Have a volunteer read the problem out-loud to the class.
Once the problem is read, student pairs will work together to fill in the blanks on their slips with the correct expressions, in terms of x, that represent each part of the problem. Then they should solve the inequality. It is important to let the students struggle with this task. Walk around listening to the interchange and intervene only if necessary, without providing too much help. Ask students to substitute possible values of x into their expressions to see if it makes sense. Allow time for them to reason and discuss their work on their own and with other pairs if they want to.
Students may think that the cost price is 20. Indicate that this is merely the cost of making one calculator. Also, they may not include the 500,000 dollars in the cost price. Guide them to figure out for themselves that the investment is part of the cost. In this case I would ask, “ok, so if the company makes 1, 10, 100 calculators, how much money would the company have spent?” This may lead them to the correct expression. Their answers should include the money invested.
Once students are done, pick volunteers to answer each of the blanks in Q1 solution slip, on the board. Have students debate any incorrect answers. Most often than not, if students make don’t get an expression right the first time, they will come up with the correct expression after discussing and struggling with them. Use the “thumbs up, side, or down” to gauge student understanding during the process. The skill of writing the correct inequality that models the problem improves as they encounter more real world problems.
Partner Activity 2:
Hand each pair the “Q2_Application” resource and ask that they read and complete each problem. The first two have guidelines like the Q1 problem.
Once the students are finished with the Q2 Application, divide the board into four sections. Have volunteers go up and write the work for each of the problems. Have each of these volunteers orally explain their process. Incite seated students to ask questions if they have any. Volunteer students should try and answer them first; or any other student in the class.
To close the lesson, hand each student an “Here’s where I get stuck ” slip. Students
should write exactly where they get stuck or confused when solving any of the problems given. These slips should be used as formative assessment and in deciding what to re-enforce or reteach. Some students may not need to fill out a slip.
Lesson Extension: Compound Inequality word problem
The velocity of an object fired directly upward is given by V = 80 – 32t, where t is in seconds. When will the velocity be between 32 and 64 feet per second?
Homework: See resource; Homework_InequalityConnection