Student Actions

Teacher Actions

• Develop a deep and flexible conceptual understanding by using manipulatives to find the mean of a data set by "leveling” the data.

• Develop the ability to communicate mathematically by using precise language and describing data sets in terms of mean, median, and mode.

• Develop strategies for problem-solving by using multiple strategies to create these data summaries.

• Develop a deep and flexible conceptual understanding of the procedures and algorithms used to find the mean, mode, range, and median of odd-numbered data sets.

• Establish mathematics goals to focus learning that require manipulatives that allow the students to explore thevisualization of how "leveling or evening" out the data could occur.

• Implement tasks that promote reasoning and problem-solving where students explore data-collection methods and how they affect the nature of the data set.

• Pose purposeful questions that assess student reasoning of mean, median, and mode as different ways to find the center.

• Support productive struggle in learning mathematics by having students explain their strategies for creating a data set when given a range, median or mean.

• Elicit and use evidence of student understanding of the range and central tendency and when to use it by providing multiple real-world situations that require data collection and analysis.

Key Understandings

Misconceptions 

• Find central tendency and range with any given set of data. 

• Understand that range is the distance between the maximum and minimal data points, not a measure of finding the center. 

• Understand that mean is determining the "average" of all data points in a set.

• Understand that median is the middle value with 50% of the data points on either side. 

• Understand that mode is the representative value that describes the typical, or most often occuring, response.  

• Interpret bi-modal data sets, where there is more than one mode (bi-modal is not student language for 5th).

• Determine the mean by dividing and interpreting the remainder correctly.

• Subtract the minimum from the maximum in order to find the range of the data.

• Use the terms mean, median, mode, and range interchangeably.

• There can only be one mode of a data set.

• A number that is repeated in a data set only has to be used once when determining the mean or the median.

• Range and central tendency are the same.

• The median is the middle number listed in the data set where the order of values do not matter.  

  Knowledge Connections

Prior Knowledge

Leads to 

• Organize data on a frequency table or line plot. (4.D.1.1)

• Organize data on a pictograph or bar graph. (3.D.1.1) 

• Interpret the mean, median, and mode for a data set. (6.D.1.1)

• Explain and justify which measure of center should be used in a given situation with a given set of data. (6.D.1.2)

• Design experiments, collect data, and calculate measures of center. (7.D.1.1)

Sample Assessment Items

The Oklahoma State Department of Education is releasing sample assessment items to illustrate how state assessments might be designed to measure specific learning standards/objectives. These examples are intended to provide teachers and students with a clearer understanding of how the state assesses Oklahoma's academic standards and their objectives. It is important to note that these sample items are not intended to be used for diagnostic or predictive purposes. Ways to incorporate the items.

• 5.D.1.1 Range
• 5.D.1.1 Median