Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.
Learning Targets (I can)
Identify a statistical question.
Describe the difference between a statistical and non-statistical question.
About the Math
Developing understanding of statistical thinking: Building on and reinforcing their understanding of number, 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., 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
Identify a statistical question.
Describe the difference between a statistical and non-statistical question.
These tasks can be used with small group or whole group instruction.
Which of the following questions are statistical? What makes them statistical?
How heavy is Amira’s backpack?
How heavy are the backpacks of students in the class?
How much time did you spend doing homework yesterday?
How much time do students at this school spend doing homework?
Create a set of statistical and non-statistical questions in your journal.
What is the difference between a question that is statistical and one that is not statistical?
How many responses does a statistical question have?
Can a statistical question have a quantitative response? How about a qualitative response?
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.
These print resources can be used during independent or center time. These resources could also be used as lesson seeds.
INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT
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.