Getting Started 
Misconception/Error The student does not have a general understanding of the meaning of measures of center and measures of variability. 
Examples of Student Work at this Level The student may identify examples of measures of center and variability and describe how each is calculated but is unable to explain what each indicates about a set of data.

Questions Eliciting Thinking In general, what does a measure of center tell you about a set of data?
In general, what does a measure of variability tell you about a set of data?
I see you found several measures of center and variability; can you explain what each means about your data set? 
Instructional Implications Explain that measures of center provide an indication of a typical, representative, or summary value from a set of data. Review how each of the mean, median, and mode are calculated and explain how each describes or represents a typical value. Indicate that although data will vary around the measure of center, these kinds of measures are an integral part of a summary of a set of data.
Explain that measures of variability provide an indication of how much the data varies in a data set. Review how each of the range, interquartile range, and mean absolute deviation are calculated and explain how each describes or represents the spread in the data. Indicate that measures of spread are also part of a summary of a set of data.
Provide data sets with different centers and spreads (e.g., a set of math pretest scores that range from 0% to 73% and a set of math posttest scores that range from 78% to 100%). Have the student compare the data sets by calculating both a measure of center and a measure of spread. Assist the student in interpreting the measures and making comparisons in the context of the data. 
Making Progress 
Misconception/Error The student provides an unclear or incomplete explanation. 
Examples of Student Work at this Level The student’s explanation indicates some understanding of measures of center and/or measures of variability. However, the explanation is unclear or incomplete.

Questions Eliciting Thinking In general, what does a measure of center tell you about a set of data?
In general, what does a measure of variability tell you about a set of data? 
Instructional Implications Model explaining what measures of center and measures of variability indicate about a set of data. Assist the student in identifying and using appropriate vocabulary to describe each type of measure. Explain that each measure contributes information about two different aspects of data sets and both are used to summarize distributions of data along with descriptions of the distribution’s shape.
Provide numerous opportunities to describe and summarize distributions of data by calculating measures of center and spread and describing their shapes. 
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 is able to explain that measures of center provide an indication of a typical or representative value from a set of data while measures of variability provide an indication of how much the data varies in a data set. 
Questions Eliciting Thinking Which other feature of a distribution can be described when summarizing a set of data?
Is it possible for two data sets to have the same measure of center but different measures of variability?
Is it possible for two data sets to have different measures of center but the same measure of variability? 
Instructional Implications Challenge the student to create small data sets with the same mean but different mean absolute deviations or the same interquartile range but different medians.
Consider implementing MFAS tasks Explain Measures of Center and Explain Measures of Variability (6.SP.1.3). 