Translate and Solve Inequalities

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SWBAT translate and solve two step inequalities.

Big Idea

Students work independently and in pairs to translate and solve word problems involving inequalities

Do Now

10 minutes

Students enter silently according to the Daily Entrance Routine. Their Do Nows are already at their desks and consist of true/false questions and fill in the blank questions to assess their mastery/understating of questions involving absolute values and the inequality symbols which compare them. Students are instructed out loud and on their papers to enter their answers into clickers, with the 4 fastest earning booth seats. I make sure to check in with students who did not finish the classwork, making sure to give a follow up time to check and make sure it is completed.

Clicker assessment is stopped 5 minutes before the end of this section. I take the last five minutes to review the lowest question. We also review #6 and I ask for different variations of the question. The following video depicts how that discussion might be led.

Pushing students through this line of questioning exercises MP8, expressing the regularity in repeated reasoning. We are also directly addressing 7.NS.A1.D, applying operations as strategies to multiply the integers. As students move through more examples of the products of signed numbers they begin to form their own rules through the patterns (i.e. a product is negative if there are an odd number of values multiplied). Common core asks students to create and make sense of rules in order to apply them to different situations. The better way to do this is by having students push themselves to understand why the rules work, rather than having them memorize the rules and run the risk of misinterpreting or misremembering.  

Lastly, we are working toward mastery of 7.NS.A.2A (relating multiplication to rational numbers) and 7.NS.A.1D (addition/subtraction of rational numbers) with the last 5 questions. Today we will be concentrating on problem solving, thus it was best to start off with skill work around rational numbers to prepare and practice. 

Class Notes

15 minutes

Do now sheets are put away and class notes are distributed. We begin by translating two step inequalities and solving. I still have not introduced the product/quotient of a negative in an inequality since students are still in need of practice with solving.

Then we read, translate and solve the word problem included. I ask students to again take 3 minutes and turn to their neighbor to write a story/problem which uses one of the phrases included in the table. We share out 2 – 3 problems and show the solution on the back of the class notes sheet.

Students are then asked to take out their blue “Ready” books. These workbooks include test prep questions as well as modeled/self-guided question meant to scaffold student through the concept. They are published by "Curriculum Associates". The question we review in class is included in the pdf document for our SMARTBoard notes (pg 13). I model reading the problem, annotating important information and then answering each of the questions with with help from students. I've also created a separate sample question in this document that follows a scaffold format. Notice how each question guides students to make connections between the inequality symbols and the words at least, greatest, no more than, etc. MP1 is a very important practice to emphasize during this lesson as some students may struggle to identify the correct inequality symbols to use. It is equally important to flag those students who struggle to translate word problems into algebraic expressions/phrases for each inequality sentence. 

Class Work

20 minutes

After answering the first three questions on this page (pg 156) I ask students to complete the rest silently for the first ten minutes of class work time.  Then I stop students to review the rest of the answers on page 156 and then I review the next problem which shows the translation and a different way to graph only whole numbers (those appropriate to the context of the situation) on the number line. I ask students to turn to their neighbor and ask/answer the following questions:

  • What is step 1 at the top of this page?
  • How do you know which symbol you should use in this problem?
  • How do you know if it should be inclusive or not?
  • What does being inclusive vs. not being inclusive mean?
  • Why don’t fractions satisfy the solution of this problem?


After reviewing their answers out loud students must again work silently to complete the next and final page. These questions include more comprehension of the context of the situation. My goal is to get students used to thinking through an entire problem persevering to make sense of the relationships and operations between numbers. (MP1)

Sample questions have been created in this document to give some examples of the types of problems students encountered. 


10 minutes

During the last ten minutes of class students will receive an exit ticket where they need to translate and solve an inequality. The homework is to complete anything that was left incomplete curing class. Answers will be posted on our class website.  Exit tickets are to be returned upon leaving the class. I will be using these to pull a lunch time study group the next day.