Through the Grapevine
In the problem Through the Grapevine, students use mathematical concepts of statistics including measures of center and representations. In addition, students use proportional reasoning, analyze trends in data sets, and design their own survey. The mathematical topics that underlie this problem are measures of center, samples, proportional reasoning, scatterplots, the interpretation of data sets, and designing and carrying out a survey and data analysis. In each level, students must make sense of the problem and persevere in solving it (MP.1). Each problem is divided into five levels of difficulty, Level A through Level E, to allow access and scaffolding for students into different aspects of the problem and to stretch students to go deeper into mathematical complexity.
PRE-K
In this task, students make predictions about how many raisins might be in a box of raisins. The students then count the raisins in their box and the teacher charts the results. The teacher poses questions about which box had the most raisins and which had the least.
LEVEL A
In this level, students collect data from raisin boxes, examine data sets to find the most and the least, generate graphs, and make predictions.
This level addresses Common Core standard 2.MD.D.10 by having students draw a graph to represent a data set. Students are also asked to solve compare problems using the information presented in the graph. This level could also address standard 2.MD.D.9 if the students are directed to organize their data into a line plot.
LEVEL B
In this level, students find the mean number of raisins in a box based on a sample of many boxes of raisins. They then use that mean to make predictions in related situations.
This level address Common Core standard 7.SP.A.2 by asking students to use the mean of a sample to make inferences.
LEVEL C
In this level, students analyze the median, mode, and range for a sample from many boxes of raisins. They then consider which measure of central tendency is a more appropriate descriptor of the “average” number of raisins in a box. Finally, they reason proportionally with this “average” to estimate how many raisins would be in different sizes of raisin boxes.
This level address Common Core standard 7.SP.A.2 by asking students to use measures of center and spread to make inferences.
LEVEL D
In this level, a scatterplot is presented. Students are asked to draw conclusions from the data shown in the scatterplot. They then draw a line that best fits the data and use that line to make predictions and to describe a trend.
This level addresses Common Core standards 8.SP.A.1 and 8.SP.A.2 by asking students to fit a line to the scatterplot and then describe and interpret the pattern of association they see in the data.
LEVEL E
In this level, students design their own survey, collect data, analyze the results, and draw conclusions.
This level is connected to Common Core standards S-IC.B.4 as students are asked to design and conduct a survey. Depending on how students decide to treat their data and report their findings, this level could address S-ID.A.1, S-ID.A.2, and S-ID.A.3 or S-ID.B.5 and S-ID.B.6c.
PROBLEM OF THE MONTH
Download the complete packet of Through the Grapevine Levels A-E here.
You can learn more about how to implement these problems in a school-wide Problem of the Month initiative in “Jumpstarting a Schoolwide Culture of Mathematical Thinking: Problems of the Month,” a practitioner’s guide. Download the guide as iBook with embedded videos or Download as PDF without embedded videos.
SOLUTIONS
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