Representing Situations with Inequalities

5 min

Narrative

In this activity, students recall the meaning of inequality symbols (<\lt, >\gt, ≤\leq, and ≥\geq) and the meaning of “solutions to an inequality." They are reminded that an inequality in one variable can have a range of values that make the statement true. Students also pay attention to the value that is at the boundary of an inequality and consider whether it is or isn't a solution to an inequality.

Launch

Give students 1–2 minutes of quiet work time. Follow with a whole-class discussion.

Student Task

  1. Match each inequality to the meaning of a symbol within it. Read the inequality from left to right.

    1. h>50h>50
    2. h≤20h \leq 20
    3. 30≥h30 \geq h
    • less than or equal to
    • greater than
    • greater than or equal to

  2. Is 25 a solution to any of the inequalities? Which one(s)?

  3. Is 40 a solution to any of the inequalities? Which one(s)?

  4. Is 30 a solution to any of the inequalities? Which one(s)?

Sample Response

    1. h>50h > 50: “greater than”
    2. h≤20h \le 20: “less than or equal to”
    3. 30≥h30 \ge h: “greater than or equal to”
  2. 25 is a solution to 30≥h30 \ge h because 30 is greater than or equal to 25.
  3. 40 is not a solution to any of the inequalities because 40 does not make any of the inequalities true when substituted in for hh.
  4. 30 is a solution to 30≥h30 \ge h because, while 30>3030>30 is not a true statement, 30=3030=30 is a true statement.
Activity Synthesis (Teacher Notes)

Draw students' attention to the last inequality (30≥h30 \geq h). Make sure students see that, even though the symbol is read "greater than or equal to," it doesn't mean that we're looking for values that are greater than or equal to 30.  The statement reads "30 is greater than or equal to hh," which means that hh must be less than or equal to 30.

Next, ask students how they know whether each of those numbers (the 50, 20, and 30, or the boundary values) is a solution to the inequality. Emphasize that we can test those boundary values the same way we test other values—by checking if they make the statement true.

Display these equations in one variable for all to see: h=50h = 50, h=20h =20, and 30=h30 = h. Discuss with students how these equations are different from the inequalities in one variable (aside from the fact that the symbols are different). Highlight the idea that there is only one value that could make each equation true, but there is a range of values that can make each inequality true.

Standards
Building On
  • 6.EE.5·Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
  • 6.EE.B.5·Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
Building Toward
  • A-CED.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <em>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</em>
  • A-CED.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <em>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</em>
  • A-CED.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <em>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</em>
  • A-CED.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <em>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</em>
  • A-CED.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <em>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</em>
  • HSA-CED.A.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <span>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</span>

15 min

15 min