Interpreting Inequalities
5 min
Narrative
The purpose of this Warm-up is to re-introduce tape diagrams for inequalities, which may be useful when students interpret related quantities in word problems in a later activity. While students may notice and wonder many things about these images, these are the important discussion points:
- The whole tape is shorter than the length labeled 40.
- We don’t know the length of 3x+16 but we do know it’s shorter than 40.
- We could represent the diagram with the inequality 3x+16<40 (or equivalent).
This prompt gives students opportunities to see and make use of structure (MP7). They might apply the structure that is familiar from representing equations and recognize how the same structure can be applied to inequalities.
Launch
Arrange students in groups of 2. Display the image for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss with their partner the things they notice and wonder.
Student Task
What do you notice? What do you wonder?
Sample Response
- It’s a tape diagram.
- It has three lengths each labeled x and one labeled 16.
- There’s a longer length labeled 40.
- Why is the 40 longer than the tape?
- How long is the tape?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the image. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If representing the tape diagram with an inequality does not come up during the conversation, ask students to discuss this idea.
Standards
- 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
All skills for this lesson
No KCs tagged for this lesson
Interpreting Inequalities
5 min
Narrative
The purpose of this Warm-up is to re-introduce tape diagrams for inequalities, which may be useful when students interpret related quantities in word problems in a later activity. While students may notice and wonder many things about these images, these are the important discussion points:
- The whole tape is shorter than the length labeled 40.
- We don’t know the length of 3x+16 but we do know it’s shorter than 40.
- We could represent the diagram with the inequality 3x+16<40 (or equivalent).
This prompt gives students opportunities to see and make use of structure (MP7). They might apply the structure that is familiar from representing equations and recognize how the same structure can be applied to inequalities.
Launch
Arrange students in groups of 2. Display the image for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss with their partner the things they notice and wonder.
Student Task
What do you notice? What do you wonder?
Sample Response
- It’s a tape diagram.
- It has three lengths each labeled x and one labeled 16.
- There’s a longer length labeled 40.
- Why is the 40 longer than the tape?
- How long is the tape?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the image. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If representing the tape diagram with an inequality does not come up during the conversation, ask students to discuss this idea.
Standards
- 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. \$