This Info Gap activity gives students an opportunity to determine and request the information needed to solve multi-step problems involving multiplication of a whole number by a fraction. In each case, there are multiple ways to solve the problem but the information card does not have the one piece of information—the missing side length—that the student with the problem card could use to find the area. The cards are designed this way to encourage the students to discuss and communicate further.

This activity uses MLR4 Information Gap.

The Info Gap structure requires students to make sense of problems by determining what information is necessary, and then ask for the 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). Moreover, they are prompted by their partner to explain why they need each piece of information so they need to articulate their strategy and reasoning. The Info Gap structure also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).

• Select 2–3 students to share the correct answers and discuss the process of solving the problems.
• “What questions did you ask to get the information you needed to solve the problems?” (I was missing just one piece of information—the width of the paper towel or the length of the corn field. I asked for this information but my partner did not have it. I was stuck and then my partner said they had information comparing the length and width. I was able to use that to find the width or length and then the area.)

The purpose of this activity is for students to find the missing value in equations involving a whole number and a fraction. They find missing factors or products to make equations true. Many of the problems encourage students to think in steps, interpreting a fraction in terms of division by the denominator and multiplication by the numerator.

• Ask previously selected students to share their responses.
• “What was different about you and your partner's strategies?”
• “Which problem did you find most challenging and why?”
• “Which problem made the most sense to you and why?”