Getting Started |
| Misconception/Error The student is unable to approximate the center of each distribution. |
| Examples of Student Work at this Level The student reports unreasonable values for the center of each distribution. Additionally, the student is unable to explain what measures of center indicate about a distribution either in general or in reference to the given distributions.
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| Questions Eliciting Thinking In general, what does a measure of center indicate about a distribution?
What measures of center do you know? How are they calculated? What do they tell you about a set of data?
What one test score might summarize or describe how students typically scored on the test in the morning class?
What one test score might summarize or describe how students typically scored on the test in the afternoon class? |
| Instructional Implications Review the concept of the center of a distribution. Describe measures of center in general terms (e.g., as a single value that gives an indication of a typical value in the distribution or where the values tend to cluster). Ask the student to inspect each distribution and describe a typical score for each. Guide the student to consider where the data clusters. If not done already, introduce the student to specific measures of center and how they are calculated. Provide the student with sets of data and ask the student to calculate measures of center and interpret their meanings in the context of the data. |
Making Progress |
| Misconception/Error The student is unable to explain the meaning of the center of each distribution in terms of the students' scores on the math test. |
| Examples of Student Work at this Level The student reports reasonable values for the center of each distribution but is unable to describe what these measures of center indicate about the distributions of test scores. The student:
- Offers no explanation for the meaning of the center of each math class.
- Makes an unclear statement about means, averages, or modes.
 
- Makes a comparative statement.
- Restates the measures of center previously identified.
- Describes the measure of center in terms of the mode rather than in terms of where the test scores cluster.
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| Questions Eliciting Thinking In general, what does a measure of center indicate about a distribution?
What do the measures of center that you described tell you about test scores for each class? |
| Instructional Implications Review the concept of the center of a distribution. Describe measures of center in general terms (e.g., as a single value that gives an indication of a typical value in the distribution or where the values tend to cluster). Model explaining that test scores for students in the morning class clustered around 80 while test scores for students in the afternoon class clustered around 50. Ask the student to explain why 60 is also a reasonable estimate of the center of the distribution of test scores for the afternoon class.
Explain that the mode is not always a good measure of center to use when describing a distribution. Show the student a distribution in which test scores do not cluster around the mode but another value (e.g., 50, 50, 50, 50, 85, 88, 88, 89, 90, 91, 93, 95, 97, 99, 100, 100). Ask the student if a value of 50 serves as an indication of a typical score for this set of data. |
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 reports reasonable values for the center of each distribution such as 80 for the morning class and 60 for the afternoon class. The student further explains that these measures of center give an indication of how a typical student scored on the test in each class by describing a value around which the test scores clustered.
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| Questions Eliciting Thinking Why did you choose these values as measures of center?
Did you calculate specific measures of center? If so, what measures did you calculate?
Based on the centers you reported, how did scores on the two tests compare? |
| Instructional Implications Provide the student with the actual test scores (on the Raw Data worksheet) for the two classes and ask the student to calculate both the mean and the median for each class. Then ask the student to compare these values and to consider why they are not the same.
Consider implementing the MFAS tasks Math Test Shape and Math Test Spread (6.SP.1.2). |
