The sixth graders started the new school year working on challenging word problems, including one called Trail Mix:
Rowena and Polly are making trail mix. Rowena has 4 cups of raisins and Polly has 4 cups of peanuts. Polly pours exactly one cup of her peanuts into Rowena’s raisins and stirs them up. Then Rowena pours exactly one cup of her new peanut-and-raisin mixture back into Polly’s peanuts.
Mr. Zippin demonstrated this with red and white beans and then asked the 6th graders- “Did Rowena get more of Polly’s peanuts or did Polly get more of Rowena’s raisins?”
The students got a chance to share their ideas, first with their groups, and then with the entire class.
Next, the students had the opportunity to get hands-on with the beans themselves. They took ten white beans and ten red beans and put them in small containers. In teams, the students took turns taking 3 beans out of the white bean cup and putting them in with the red and mixing them up. Then, with their eyes closed, they took three beans out of the mixture and returned them to the white cup with only seven beans in it. They then recorded their results.
After doing the experiment a few times, the groups got another chance to discuss their ideas and possibly develop new conjectures.
What do you think? Did Rowena get more of Polly’s peanuts or did Polly get more of Rowena’s raisins?