This Info Gap activity gives students an opportunity to determine and request the information needed to solve multi-step problems involving multiplication and division of unit fractions. In both cases, the student with the problem card needs to find out the side lengths of the area being covered and the size of the tiles. Then they can figure out how many tiles are needed. The numbers in the problems are chosen so that students can draw diagrams or perform arithmetic directly with the numbers.

This activity uses MLR4 Information Gap.

In this Info Gap activity, the first problem encourages students to think about multiplying the given fractions. The second problem involves a given area and a missing side length, which may encourage students to represent and solve the problem with a missing factor equation.

The Info 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).

• Invite students to share their responses to the problem about tiling the floor.
• “How did you know whether to use multiplication or division to solve the problem?” (I needed to use multiplication to find the area of the floor. I also used multiplication to figure out how many tiles I needed.)
• “How did you solve the problem?” (I found out how many tiles I needed for one square foot by drawing a picture and then multiplied that by the number of square feet in the floor.)
• Invite students to share their responses to the problem about the tiles for the wall.
• “How did you know whether to use multiplication or division?” (I used multiplication to figure out how many square feet of the wall I could cover with each box and how many square feet were in the wall.)
• “How did you solve the problem?” (I used division to estimate how many boxes of tiles I would need.)

The goal of this activity is to solve a variety of different problems, all of which can be solved by multiplying two fractions. However, the first problem may also be represented as division of a unit fraction by a whole number. The numbers are complex, making drawings an unlikely strategy to solve the problems. This encourages students to use their understanding of how to multiply fractions or divide with a whole number and a unit fraction. The Activity Synthesis focuses on why students chose multiplication or division to solve the problems.

• Ask previously selected students to share their solutions.
• Display:
  
• "How does the equation represent the first situation?" (The 11 grains of rice together weigh gram so I need to divide by 11 to find out how many grams each grain weighs.)
• Dislay:
• “How does the equation represent Mai's run?” (The is the full length of the road but she only ran of it so I multiply by .)