Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
Learning Targets (I can)
Describe a set of data using median.
Describe a set of data using mean.
Describe a set using data using range.
Determine when median, mean, or range is a good choice for describing a data set or situation.
Describe the impact of an outlier on a median, mean, or range.
Analyze the overall shape of data collected.
About the Math
Developing understanding of statistical thinking: Building on and reinforcing their understanding of numbers, students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected. (CCSC Grade 6 p.38)
In learning Grade 6 mathematics, students build on the knowledge and experiences in data analysis developed in earlier grades. (See K-3 Categorical Data Progression and Grades 2-5 Measurement Progression.) They develop a deeper understanding of variability and more precise descriptions of data distributions, using numerical measures of center and spread, and terms such as cluster, peak, gap, symmetry, skew, and outlier. They begin to use histograms and box plots to represent and analyze data distributions. As in earlier grades, students view statistical reasoning as a four-step investigative process:
Formulate questions that can be answered with data
Design and use a plan to collect relevant data
Analyze the data with appropriate methods
Interpret results and draw valid conclusions from the data that relate to the questions posed.
Such investigations involve making sense of practical problems by turning them into statistical investigations (MP1); moving from context to abstraction and back to context (MP2); repeating the process of statistical reasoning in a variety of contexts (MP8). (CCSC writing team p. 2 (December 2011) www.commoncoretools.wordpress.comLinks to an external site.) Essential vocabulary for this standard includes: data, probability, statistical question, statistical variation, statistics, and variability. Visit the online dictionaryLinks to an external site. or visual math dictionaryLinks to an external site. for vocabulary support.
Progression of Standard within Grade 6 (5 AGL)
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
Progression Throughout Year
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Describe a set of data using median.
Describe a set of data using mean.
Describe a set using data using range.
Determine when median, mean, or range is a good choice for describing a data set or situation.
Describe the impact of an outlier on a median, mean, or range.
These tasks can be used with small group or whole group instruction.
A set of nine pieces of data, all of which are different, has a mean of 30 and a median of 10. What could the data values be? Find a set of data values with a large spread.
What is the difference between a set of data's center and a data's spread?
Using the example of test scores (out of 100), create a set of ten pieces of data that would skew to the left. Then, create ten different values that would skew to the right. What does it mean when the data is skewed?
A set of nine pieces of data, all of which are different, has a median of 10. What could the data values be?
How do you know your median is 10?
What is the smallest value you had? Did it have to be less than 10? Why?
What was the greatest value you had? Did it have to be greater than 10?
How did you determine your set of data values?
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides.These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first(often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
Print Resources
Book Thumbnail
Book Title
Grade
Pages
Teaching Student-Centered Mathematics
6-8
The Mean Foot, Activity 15.7, Page 344 Finding the Balance Point, Activity 15.8, Page 345 You Be the Judge, Activity 15.10, Page 347
Teaching Student-Centered Mathematics
5-8
The Mean of Means, Activity11.4, Page 314 Equal Means, Activity 11.6, Page 317 Toying with the Measures, Activity 11.7, Page 317 Bus Time, Activity 11.8, Page 317
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.