Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
Learner Express: Modules for Teaching and Learning
Students use abstract and quantitative reasoning to estimate how many beans are in a bag, and then share and justify their results. Run Time: 00:05:15
At the 38th Street School in Milwaukee, Wisconsin, Ms. Ernestine Mosley's five- and six-year-olds are developing number sense by practicing their estimation skills. After looking at three plastic bags"one with 11 beans, one with 25 beans, and one with 50 beans"students are told to refer to these quantities as they estimate the number of uncounted beans in their own bags. First, students make individual estimates. Next, in small groups, they share the reasoning used to formulate their estimates, and discuss their results. Then, groups are asked to come to consensus on an estimate. This number is recorded on a class chart, and eventually compared with actual bean counts. The class concludes with children again discussing how estimates are made and how estimates compare with actual counts.
(Practice Standard)—Common Core Practice Standard #2—Reasoning abstractly and quantitatively—is the prevailing standard in this clip. As students move from individual estimates to group estimates, they use abstract and quantitative reasoning to make sense of the number of beans in their bags. In one group, the students contribute in different ways to this estimation. One student serves as a "peer" group facilitator. She never offers a personal prediction; rather, she facilitates the sharing of predictions and justifications. The boy in the group seems to rely heavily on his observational skills and offers justification based on relative size and quantity arguments. Another girl parrots her classmates' responses and offers a justification similar to the student who preceded her in the discussion. Two other girls, however, use mental benchmarks or reference points to help them with their quantitative reasoning. Both girls compare the beans in their bag to the reference bags and determine that their bag's content is greater than 11, greater than 25, and greater than 50. Also, that it seems to be some multiple of ten. Student comments suggest that abstract and quantitative reasoning played a part in the mental calculations that produced their estimates.
(Content Standard)—The content standard most prevalent in this "bean counters" lesson is—Measurement and Data 3.MD—Students demonstrate that they can solve problems involving estimates and measurements of quantities.
What do you think the purpose was for using referent bags with quantities of 11, 25, and 50 beans? What are the pros and cons of requiring members of a group to come to consensus on an estimate for the quantity of beans in its bag? Would you have required it? Why or why not?
2. Reason abstractly and quantitatively
3.MD Measurement and Data