A B C D

Solutions for Session 10, Part C

See solutions for Problems: C1 | C2 | C3 | C4 | C5

Problem C1

 a. The teacher asks the students to consider reasons why some coins do not have mint marks. Then he pushes them to think about which mints can likely be eliminated based on the information they see across the four line plots. b. Some students think the coins with no mint marks were just mistakes. Others think that those coins are likely to be from Philadelphia, because so many nickels contain the Philadelphia mint mark. When thinking about which coins could be eliminated, the students eliminate Denver first and then San Francisco. c. At first, students are reasoning more from their own personal judgement, such as when one student says that the missing mint marks are a mistake because the machines were working too fast. Other students' comments were more grounded in the data.

 Problem C2 Two questions you might ask are, "Where do you think I got these coins?" and "How might that affect our results?"

Problem C3

 • How well do you think our sample of nickels represents the population of nickels in this country? • If we lived near San Francisco and collected nickels, how might our results be different? How about if we lived near Denver?

 Problem C4 The teacher might have the students make box plots for each category of coin mint mark.

 Problem C5 One example of a conjecture that students might make is "Philadelphia produces more nickels than the other mints." This could be formulated as a new question to be investigated: "Does Philadelphia produce more nickels than the other mints?" The students could investigate this question in several ways. They might want to just enlarge their own sample of nickels, with each student collecting nickels over the next week for further analysis. This could also evolve into an Internet project in which your students contact students in other parts of the country, especially those who live closer to the other mints. Each group of students could collect and analyze a sample of nickels. They could then compare across samples and finally combine them into one larger sample.

 Session 10, Grades 6-8: Index | Notes | Solutions | Video