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How Many Jeans? Resource ID#: 70160 Primary Type: Formative Assessment This document was generated on CPALMS - www.cpalms.org Students are asked to select a measure of center to compare data displayed in dot plots and to justify their choice. Subject(s): Mathematics Grade Level(s): 9, 10, 11, 12 Intended Audience: Educators Freely Available: Yes Keywords: MFAS, dot plots, center, median, mean, mode, data distribution Instructional Component Type(s): Formative Assessment Resource Collection: MFAS Formative Assessments ATTACHMENTS MFAS_HowManyJeans_Worksheet.docx MFAS_HowManyJeans_Worksheet.pdf FORMATIVE ASSESSMENT TASK Instructions for Implementing the Task This task can be implemented individually, with small groups, or with the whole class. 1. The teacher asks the student to complete the problem on the How Many Jeans? worksheet. 2. The teacher asks follow-up questions, as needed. TASK RUBRIC Getting Started Misconception/Error The student does not select a measure of center based on the shapes of the distributions or the presence of outlie Examples of Student Work at this Level The student does not make any reference to the shapes of the distributions or the presence of outliers in the selec Choose measures of center to represent each distribution rather than one measure to compare. Suggest using the median because it will be the same for both classes. Compare the number of data points and notice the outlier but does not mention a measure of center. Suggest using the mean, "Because it will show the most difference between the two." Not choose a measure of center but instead describes the shapes of the dot plots. Select one of the dot plots as the best measure of center. Questions Eliciting Thinking Does it make sense to compare the mean of one distribution to the median of another? What are measures of center? Do you know any examples of measures of center? What did you mean by "it will show the most difference between the two"? Which class has a mean and a median that are different? Why do you think this happens? How does the distribution of the data affect the mean? The median? Instructional Implications If needed, review terminology associated with the shapes of distributions such as symmetric, normal, skewed, an Provide opportunities for the student to calculate both the mean and the median of a variety of distributions. Incl Next, replace one of the data points with an extreme outlier. Again, ask the student to identify the median and co may be a better choice of a measure of center. Make clear that the shape of a distribution and the presence of out Discuss how the calculation of the mean and the median is related to the influence of outliers. Explain that since unchanged if the final value, 5, is replaced by 100 since the median only takes into account the order of the data Provide additional opportunities to select measures of center to represent and compare distributions. Ask the stu Making Progress Misconception/Error The student selects a measure of center based on the shapes of the distributions but provides an incomplete justif Examples of Student Work at this Level The student: Provides an adequate justification for using the median for Class A but says it should also be used for Cl Correctly suggests using the median but does not clearly explain that the median is more resistant to outl Questions Eliciting Thinking What did you mean by "the plots are closer"? How did this affect your choice of measure of center? You said the distribution for Class A is skewed. Why is the median a better choice when the data is skewed? You said the distribution for Class A contains an outlier. Why is the median a better choice when the data contai Instructional Implications Discuss how the calculation of the mean and the median is related to the influence of outliers. Explain that since unchanged if the final value, 5, is replaced by 100 since the median only takes into account the order of the data Provide additional opportunities to select measures of center to represent and compare distributions. Ask the stud Got It Misconception/Error The student provides complete and correct responses to all components of the task. Examples of Student Work at this Level The student selects the median as a measure of center to compare the distributions and uses the shape of the dist outliers. Questions Eliciting Thinking Can you explain why the mean is more affected by outliers than the median? Instructional Implications Challenge the student to create three small sets of data: one in which the mean is less than the median, one in wh ACCOMMODATIONS & RECOMMENDATIONS Special Materials Needed: o How Many Jeans? worksheet SOURCE AND ACCESS INFORMATION Contributed by: MFAS FCRSTEM Name of Author/Source: MFAS FCRSTEM District/Organization of Contributor(s): Okaloosa Is this Resource freely Available? Yes License: CPALMS License - no distribution - non commercial Related Standards Name MAFS.912.S-ID.1.2: Description Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. ★ Remarks/Examples: In grades 6 – 8, students describe center and spread in a data distribution. Here they choose a summary statistic appropriate to the characteristics of the data distribution, such as the shape of the distribution or the existence of extreme data points.