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16.2

Activity

Standards Alignment

Building On

Addressing

Instructional Routines

MLR2: Collect and Display

Materials

None

Activity Narrative

In this activity, students analyze four situations and select the inequality that best represents each situation.

Students may notice and make use of structure (MP7) when reasoning about how the relationships in the situations can be represented by a specific inequality.

Launch

Tell students that their job in this activity is to read four situations carefully and decide which inequality best represents each situation. Give 5–10 minutes of quiet work time.

If needed, point out that none of the situations give the total. Students must infer what the total is based on the given inequality choices. For example, in the first situation every inequality has 3 numbers: , 5, and 25. The problem states that and 5 describe the parts, so we can infer that 25 is the total.

MLR2 Collect and Display. Collect the language that students use to explain why an inequality represents a situation. Display words and phrases, such as “most,” “least,” “lose,” “gain,” “bottom,” “top,” “above,” “below,” “under,” “over,” “maximum,” and “minimum.” During the Activity Synthesis, invite students to suggest ways to update the display: “What are some other words or phrases we should include?” Invite students to borrow language from the display as needed.
Advances: Conversing, Reading

Activity

None

Choose the inequality that best matches each given situation. Explain your reasoning.

The Garden Club is planting fruit trees in the school garden. There is one large tree that needs 5 pounds of fertilizer. The rest are newly planted trees that need pound of fertilizer each.
The Hiking Club is on a hike down a cliff. They begin at an elevation of 12 feet and descend at the rate of 3 feet per minute.
The Science Club is researching boiling points. They learn that at high altitudes, water boils at lower temperatures. At sea level, water boils at . With each increase of 500 feet in elevation, the boiling point of water is lowered by about .

Student Response

to access Student Response.

Building on Student Thinking

Activity Synthesis

If needed, discuss which inequalities are correct. Otherwise, proceed to the next activity where students will continue working with these situations. Consider not validating which inequalities are correct at this time. When students get into groups for the next activity, they can compare their responses with the members of their groups and resolve any discrepancies at that time.

Representation: Internalize Comprehension. Use color coding and annotations to highlight connections between representations in a problem. For example, use the same color to highlight key words or phrases in the situation with its corresponding number or symbol in the matching inequality.
Supports accessibility for: Visual-Spatial Processing

16.3

Activity

Standards Alignment

Building On

Addressing

Instructional Routines

None

Materials

To Gather

Tools for creating a visual display

Activity Narrative

In this activity, students interpret parts of an inequality in context, term by term; for example, what quantity must represent? Then they make sense of the entire inequality by thinking about what question would be answered by the solution to the inequality. Monitor for groups that create displays that communicate their mathematical thinking clearly, contain an error that would be instructive to discuss, or organize the information in a way that is useful for all to see. At this point, there is very little scaffolding for the solving of the inequality itself.

Launch

Arrange students in groups of 2–3 and provide tools for making a visual display. Assign one situation to each group. Note that the level of difficulty increases for the situations, so this is an opportunity to differentiate by assigning more or less challenging situations to different groups.

Engagement: Develop Effort and Persistence. Provide guides or checklists that focus on increasing the length of on-task orientation in the face of distractions. For example, create an exemplar display including all required components, highlighting different ways to communicate mathematical thinking clearly.
Supports accessibility for: Attention, Social-Emotional Functioning

Activity

None

Your teacher will assign your group one of the situations from the previous task. Create a visual display about your situation. In your display:

Explain what the variable and each part of the inequality represent.
Write a question that can be answered by the solution to the inequality.
Show how you solved the inequality.
Explain what the solution means in terms of the situation.

Student Response

to access Student Response.

Activity Synthesis

Select groups to share their visual displays. Encourage students to ask questions about the mathematical thinking or design approach that went into creating the display. Here are questions for discussion, if not already mentioned by students:

How did you figure out what each term in the inequality represents?
How did you decide on the direction of the inequality for the solutions?
Did anyone with the same problem do one of the steps differently? Share what you did differently so we can learn from what happened.
How do you know there are 25 pounds of fertilizer available?

Alternatively, have students do a Gallery Walk in which they leave written feedback on sticky notes for the other groups. Here is guidance for the kind of feedback students should aim to give each other:

What is one thing this group did that would have made your project better if you had done it?
What is one thing your group did that would have improved their project if they did it too?
How did this group decide the direction of inequality for the solutions?
Does their answer make sense in the situation?
Is their math work clear and correct?
If there was a mistake, what could they be more careful about in similar problems?

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Lesson 16

Interpreting Inequalities

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Activity

Standards Alignment

Building On

Addressing

7.EE.B.4.b

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Activity

Standards Alignment

Building On

Addressing

7.EE.B.4.b

Instructional Routines

Materials

To Gather

Activity Narrative

Launch

Activity

Student Response

Activity Synthesis

Lesson Synthesis

Student Lesson Summary

Standards Alignment

Building On

Addressing

Building Toward

7.EE.B.4.b

Building on Student Thinking

Building Toward

Building Toward