Reintroducing Inequalities
5 min
Teacher Prep
Setup
Narrative
In this activity, students identify values that would satisfy the inequality x>1. Students recall the meaning of the > symbol and the fact that an inequality has many solutions. They also recall that 1 is not a solution to x>1.
Launch
Since it may have been a while since students encountered this notation, remind them that x>1 is read “x is greater than 1.”
Give students 2 minutes of quiet work time followed by a whole-class discussion.
Student Task
The number line shows values of x that make the inequality x>1 true.
Select all the values of x from this list that make the inequality x>1 true.
-
3
-
-3
-
700
-
1.05
-
1
Sample Response
3, 700, and 1.05
Activity Synthesis (Teacher Notes)
Ask students to share a few more solutions to x>1. After each student shares, ask the class whether they agree or disagree. Emphasize that this inequality has many solutions—in fact, any value greater than 1 is a solution.
To highlight the fact that “greater than 1” does not include 1, ask:
- “What does the open circle at 1 mean?” (It means 1 is not included.)
- “Why isn't 1 a solution to the inequality x>1?” (1>1 is not a true statement because 1 is equal to 1.)
Anticipated Misconceptions
Some students may think 700 is not a solution to x>1. Tell students that since there is an arrow at the end of the dark line, it includes all values that are greater than 1, even the ones not shown.
Standards
- 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.
- 7.EE.4.b·Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. <em>For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.</em>
- 7.EE.B.4.b·Solve word problems leading to inequalities of the form <span class="math">\(px + q > r\)</span> or <span class="math">\(px + q < r\)</span>, where <span class="math">\(p\)</span>, <span class="math">\(q\)</span>, and <span class="math">\(r\)</span> are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. \$
15 min
15 min
Knowledge Components
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Reintroducing Inequalities
5 min
Teacher Prep
Setup
Narrative
In this activity, students identify values that would satisfy the inequality x>1. Students recall the meaning of the > symbol and the fact that an inequality has many solutions. They also recall that 1 is not a solution to x>1.
Launch
Since it may have been a while since students encountered this notation, remind them that x>1 is read “x is greater than 1.”
Give students 2 minutes of quiet work time followed by a whole-class discussion.
Student Task
The number line shows values of x that make the inequality x>1 true.
Select all the values of x from this list that make the inequality x>1 true.
-
3
-
-3
-
700
-
1.05
-
1
Sample Response
3, 700, and 1.05
Activity Synthesis (Teacher Notes)
Ask students to share a few more solutions to x>1. After each student shares, ask the class whether they agree or disagree. Emphasize that this inequality has many solutions—in fact, any value greater than 1 is a solution.
To highlight the fact that “greater than 1” does not include 1, ask:
- “What does the open circle at 1 mean?” (It means 1 is not included.)
- “Why isn't 1 a solution to the inequality x>1?” (1>1 is not a true statement because 1 is equal to 1.)
Anticipated Misconceptions
Some students may think 700 is not a solution to x>1. Tell students that since there is an arrow at the end of the dark line, it includes all values that are greater than 1, even the ones not shown.
Standards
- 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.
- 7.EE.4.b·Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. <em>For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.</em>
- 7.EE.B.4.b·Solve word problems leading to inequalities of the form <span class="math">\(px + q > r\)</span> or <span class="math">\(px + q < r\)</span>, where <span class="math">\(p\)</span>, <span class="math">\(q\)</span>, and <span class="math">\(r\)</span> are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. \$