I will begin with the essential question: How can we use multiplication and division to solve inequalities? I will state that all inequalities can be solved in the same manner as equations - using inverse operations. However, sometimes the solution to an inequality is not what we may think it to be - this is a hint towards having to flip the symbol when there is a negative coefficient.
Next I will model an example while students copy what I do. Examples 1 & 2 and 3 & 4 are paired. They appear to have the same solution but we will see this is not the case. To bring this idea out, I will ask my students to come up with values of x that would make each inequality true. So in example 1 students should suggest values greater than -2 yet they will notice that they must pick values less than -2 for example 2. This will help us make sense of why it is necessary to flip the inequality symbol when dividing both sides by a negative.
Next, I will ask students to write their answer to the discussion question at the bottom of the page. I will then ask a few students to share out.
Throughout the lesson students should be asked to justify their solutions. This will help them make sense to the meaning of their solutions and to exercise their abstract and quantitative reasoning (MP2).
There are 8 problems for students to solve. Generally, I willl allow them to work with their neighbors at this point. I have tried to pick fairly easy numbers so that students can easily solve the inequalities and then consider whether their solutions make sense.
See GP5 for a common error. Students might think they need to flip the inequality symbol because they multiplied 10 times -9. But the coefficient is not negative so this is not necessary. If students flip the sign to say p < -90, I will ask them to pick values less than -90 to divide by 10 to check for the truth of the solution.
Students now work independently. The first 8 problems are very similar to the previous 8 problems. Students should rely on those problems to help. I will ask students to make sure they write the first step (the inverse operation step) on their papers explaining that it helps me to better understand their work.
Problem 9 asks students to explain the meaning of a solution to an equation vs an inequality. I think it is important to repeatedly remind students that an equation has 1 solution and an inequality has many solutions.
The last 3 problems require students to write one-step inequalities from word problems. Students may need to pull out their notes from the lesson Translating Verbal Statements Into Inequalities. They will be able to use the graphic organizer to help choose the correct inequality symbol.
Before beginning the exit ticket, I will ask students to discuss how to solve multiplication and division inequalities? If it does not come up in the discussion, I will ask them to explain when must the inequality symbol be flipped?
There are 5 problems. Each problem is worth 1 point. Question 5 asks students to evaluate the work of a student. To earn 1 point for this problem the student should say that the solution is not correct because the student should have reversed the inequality symbol to say x > -6.