Standard #: MA.6.DP.1.2

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.6.NSO.2.3
• MA.6.NSO.3.5
• MA.6.AR.2.2
• MA.6.AR.2.3

 

Terms from the K-12 Glossary

• Data
• Mean
• Median
• Mode
• Range

 

Vertical Alignment

Previous Benchmarks

• MA.5.DP.1.2

Next Benchmarks

• MA.7.DP.1.1
• MA.7.DP.1.2

 

Purpose and Instructional Strategies

In grade 5, students interpreted numerical data, with whole-number values, represented with tables or line plots by determining the mean, median, mode and range. In grade 6, students find and interpret mean, median, mode and range given numerical data set with positive rational numbers. In grade 7, students continue building their knowledge while using measures of center and measures of variability to compare two populations. 

• Instruction includes developing statistical questions that generate numerical data.
• Instruction includes the understanding that data sets can contain many numerical values that can be summarized by one number such as mean, median, mode or range.
• Instruction includes data sets that have more than one mode. Students should understand that a mode may not be descriptive of the data set.
• Instruction includes not only how to calculate the mean, but also what the mean represents (MTR.4.1).
• Instruction focuses on statistical thinking that allows for meaningful discussion of interpreting data (MTR.4.1). Students should be asked:
  • What do the numbers tell us about the data set?
  • What kinds of variability might need to be considered in interpreting this data?
  • What happens when you do not know all the measures in your data set?
  • Can you find missing data elements?
• Instruction includes student understanding of the difference between measures of center and measures of variability.
• Instruction includes students knowing when a number represents the spread, or variability, of the data, or when the number describes the center of the data.
• The data set can be represented in tables, lists, sets and graphical representations. Graphical representations can be represented both horizontally and vertically, and focus on box plots, histograms, stem-and-leaf plots and line plots.

 

Common Misconceptions or Errors

• Students may incorrectly believe that “average” only represents the mean of a data set. Average may be any of the following: average as mode, average as something reasonable, average as the mean and average as the median.
• Students may confuse mean and median.
• Students may neglect to order the numbers in the data set from least to greatest when finding the median or range.

 

Strategies to Support Tiered Instruction

• Teacher discusses with students how the use of the word average in daily life may show a different meaning of the word each time, just as other mathematical words have different meanings in everyday life. This will help students to understand that “average” does not only represent the mean of a data set.
• Teacher provides instruction focused on measures of center, co-creating anchor chart or graphic organizer.
• Teacher provides examples visually that show the clear middle of a data set, but where the average is not the same. This visual will help students understand that the middle of a data set does not mean that amount is the average.
  • For example, the figure below shows a data set with mean of 7 and median of 4.
    
    
    

 

Instructional Tasks

Instructional Task 1 (MTR.4.1, MTR.5.1)
Salena has 15 students in her class. The mean shoe size is 8.5. She records the shoe sizes below, with one missing: What shoe size is missing? Explain how she can find the missing shoe size.