Three-tenths can be thought of as three out of every ten students. In this case, three out of every 10 students in the class can blow a bubble. There are two sets of 10 students in the class, each with three bubble blowers. So the total is six out of 20. The simplified fraction 3/10 could also be thought of as representing three pairs of students out of 10 pairs of students in Room A.

This task attempts to use communication to build on the earlier discussions to help make sense of a more abstract concept –– connecting simplified fractions with known ratios that come from real-world data. The purpose may be to prepare students for further problem-solving work or more experiences with equivalent fractions and real-world contexts.

Mr. Avilla's student, Carla, explains with confidence in her voice, "You can't just compare how many blew bubbles in each class. It matters what it's out of. I can put 8/40 on the other number line by writing it as 4/20, because eight divided by two is four, and 40 divided by two is 20. Of course, 4/20 is less than 6/20." Pointing to the three labeled points on her number line, she concludes, "Class G did better than Class B, but Class A is even better because it has 6/20, which is more than 4/20."

This problem provides another chance for students to reflect on what they understand, practice using a number line to compare fractions that come from real-life data, and communicate about how to compare ratios. Carla's answer demonstrates to the other students that a peer student can communicate with confidence and in detail. Her words may help others articulate some of their own observations. Additionally, writing symbols to support her words will be beneficial both to her and to her listeners.