Sample Constructed-Response Item Grade 8 Math Old Faithful Eruptions Grade 8 CCSS 8.SP.01 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Practice 2. Reason abstractly and quantitatively. Standards 6. Attend to precision. Source: http://wps.aw.com/wps/media/objects/15/15719/projects/ch3_faithful/time.html Shown below is a sample constructed-response item. This item involves a number of separate steps and the application of one or more practice standards. The constructed-response items are designed to assess one or more of the CCSS. The items are scored using an item-specific rubric on a scale of 0 to 4 points. The Old Faithful geyser in Yellowstone National Park erupts regularly but with some variation in the duration of the eruptions and in the time between eruptions. The graph below shows the data for all the eruptions over a span of three days in April. Part A Plot the eruption data for a fourth day, shown in the table below, on the grid. Duration of the Eruption (minutes) 1.92 Time Until the Next Eruption (minutes) 57 4.00 87 1.85 73 4.55 94 Part B A visitor to Yellowstone sees an eruption that lasts 2 minutes. Estimate how long it will be before the next eruption. Part C Describe the patterns shown in the data on the graph. Use numbers from the graph and statistical terms such as clusters, outliers, and positive or negative correlation in your description. Scoring Rubric 4 3 2 1 0 The student earns 4 points. The student earns 3 points. The student earns 2 points. The student earns 1 point OR demonstrates minimal understanding of the standard being measured. The student’s response is incorrect, irrelevant to the skill or concept being measured, or blank. Sample Answer Part A. Correct graphing is shown in red on the grid below. Part B. 60 minutes Part C. The duration of eruptions falls into two clusters, 1.5 to 2.5 minutes and 4 to 5 minutes. For eruptions that are 1.5 to 2.5 minutes long, the time until the next eruption is 45 to 70 minutes. For eruptions that are 4 to 5 minutes long, the time until the next eruption is much longer—90 to 100 minutes. This shows a positive correlation overall between duration and the time until the next eruption. Points Assigned Part A. • 2 point for correctly graphing all four coordinate points (very close approximations are acceptable). OR • 1 point for correctly graphing 2 or 3 of the coordinate points (very close approximations are acceptable). Part B. • 1 point for any value between 50 and 75 minutes Part C. • 1 point for correctly describing a pattern shown in the data using numbers and at least one statistical term.

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