This activity gives students an opportunity to determine and request the information needed to set up and solve inequalities that represent real-life situations.  

The Information Gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).

Math Community
Display the Math Community Chart for all to see. Give students a brief quiet think time to read the norms, or invite a student to read them out loud. Tell students that during this activity, they are going to practice looking for their classmates putting the norms into action. At the end of the activity, students can share what norms they saw and how the norm supported the mathematical community during the activity.

After students have completed their work, share the correct answers and ask students to discuss the process of solving the problems. Here are some questions for discussion:

• “In Noah’s problem, is 1.5 loads of laundry a solution to the inequality?”
• “In Elena’s problem, can the width of the frame be -10 centimeters? Can the width of the frame be 0 centimeters? How about 0.1 centimeter?”
• “Which situations have only whole-number solutions?”
• “In Noah’s problem, should we round up or down?”

Highlight for students that both the solution to the inequality and the situation itself go into writing a reasonable answer to the question.

Math Community
Conclude the discussion by inviting 2–3 students to share a norm they identified in action. Provide this sentence frame to help students organize their thoughts in a clear, precise way:

• “I noticed our norm ‘’ in action today, and it really helped me/my group because .”

In this activity, students write and solve inequalities to answer the question. The context in this problem provides an opportunity for students to think about aspects of mathematical modeling like discrete versus continuous solutions and rounding (MP4).

The purpose of this discussion is to clarify how to write a reasonable answer to a question based on both the solution to the inequality and the meaning of the situation.

Consider discussing:

• “The number line shows that 5.5 is a solution to the inequality, but is it a solution to the problem in context?” (No, it is not a solution to the problem because the mover can’t load half of a box.)
• “Do we want to change the number line somehow to show this?” (We could plot discrete points, or we could simply leave it as is, but just know that for a problem with this context, we’re only going to use whole-number solutions.)
• “Which type of inequality would you use to describe answers using no more than or no less than?” ( and , respectively.)
• “How did you know which way to round?” (Round down, otherwise the values would go over the weight limit.)
• “What other limitations do the contexts place on the solutions?” (You can’t have a negative number of boxes.)