A B C D

Solutions for Session 10, Part D

See solutions for Problems: D1 | D2 | D3

Problem D1

 a. Janet is not willing to accept that there is variation in the raisin data. The teacher might point out to Janet that the raisins are packaged by weight, then have her examine the various sizes of the raisins more closely, and finally ask her to think about why the raisins are packaged by weight and not by number. b. Sahar is able to consider an interval of the data that is most representative of the data. The teacher could ask the class to speculate on the likelihood of her prediction. c. Jermaine reasons incorrectly that 40 is an outlier because it is the largest number separated from the others by a gap. The gap, however, is only one raisin, so based on this data, 40 is not unusual enough to be an outlier. The teacher might ask the rest of the class to discuss further the meaning of an outlier. d. Ramel is looking at the range of numbers written on the horizontal axis rather than at the span of the data points. The teacher could use the following questioning to get Ramel to focus on the data points: "What is the smallest number of raisins that we found in a box? Point to it with your left hand. What is the largest number of raisins that we found in the box? Point to it with your right hand. This distance from the lowest to the highest number is what we call the range." e. Ava reasons about an interval of the data that contains the most data points and provides an interpretation of raisin size based on this observation. This would be an opportunity to write out Ava's conjecture and ask the other children to evaluate it. Do they agree or disagree? Would they want to modify the conjecture in any way? f. Paul is reasoning with the mode as a summary statistic that describes a measure of center. The teacher might ask the rest of the class to react to Paul's prediction. How many of them agree, and why? How many disagree, and why? You could also ask Paul and the other children to comment on the likelihood that an unopened box contains 34 raisins.

Problem D2

 a. Bryce is noticing the mode of the data. The teacher could ask Bryce to think about the closeness of the numbers seven and eight and acknowledge that eight is more. b. Nicole is considering the variance of the data and the whole data set. The teacher might ask the rest of the class to react to the accuracy of Nicole's statement. c. Wallace is noticing that there is not much variation in the data. The teacher could ask Wallace to further explain what he means by "one more" and by a "tie." d. Maggie is formulating a conjecture or hypothesis about the data. This would be an opportunity for the class to plan a follow-up data investigation to test Maggie's conjecture. e. Zulay is thinking about the sample of students in attendance today and the population of the class. The teacher might ask the rest of the class to consider Zulay's comment and to then predict how they think the two children who are absent would respond to the question about dinosaurs.

Problem D3

 a. Ben is most likely reasoning by looking at the range of each data set. The teacher could ask the students to pretend that the data value at 0 is not there and to then think about Ben's statement. b. Damon is providing an interpretation of the data. The class could be asked to evaluate Damon's conjecture and to propose other reasons for the differences in the data. c. Emma is developing a hypothesis about the outlier 0. The teacher could ask the class to formulate other conjectures about the outlier 0. d. Tarra is reasoning about the data by looking at the modes of each data set. The teacher could introduce or reinforce the meaning of the term mode. e. Isaiah is interested in examining areas with no data as well as areas with data. He also notices that the green dots are more concentrated with little variation. The teacher might use this as an opportunity to focus further attention on the importance of examining gaps and considering how the data are spread out or bunched together.

 Session 10, Grades K-2: Index | Notes | Solutions | Video