Statistics

Students get their first experience of statistics in this unit, defining a statistical question and investigating the key concepts of measures of center and measures of variability.

Unit Summary

In Unit 8, sixth graders get their first experience of statistics. Students come into sixth grade with some prior knowledge around data representations, such as bar graphs and line plots; however, this is the first time that students ask the question “what is statistics” and “what can it help me solve?” Students begin the unit by first determining what a statistical question is. Then they ask how they can interpret the data that comes from these questions (MP.2). Students learn various ways to represent the data, including frequency tables, histograms, dot plots, box plots, and circle graphs, and they analyze each representation to determine what information and conclusions they can glean from each one (MP.4). 

Students will investigate two key concepts that will be important for future studies: measures of center and measures of variability. They’ll look at measures of center to investigate what a “typical” or average response to a question might be; they’ll look at measures of variation to understand how similar or different the data in the set may be or how reliable a measure of center might be. Students investigate all of this within context in order to better understand how statistics can be used to investigate questions and understand more about our world.

In seventh grade, students will continue their study of statistics and investigate multiple data distributions simultaneously. They will also deepen their understanding of sampling and how to use random sampling to draw inferences about populations. 

Note: This course follows the 2017 Massachusetts Curriculum Frameworks, which include the Common Core Standards for Mathematics (CCSSM). In the CCSSM, the concept of Mean Absolute Deviation (MAD) is first introduced in sixth grade; however, in the Massachusetts Frameworks, MAD is first introduced in seventh grade. As a result, the concept of mean absolute deviation is not included in our sixth grade curriculum. Please see this note on the standards for suggestions on how to incorporate MAD into our sixth grade curriculum if you are following the CCSSM.

Pacing: 15 instructional days (13 lessons, 1 flex day, 1 assessment day)

For guidance on adjusting the pacing for the 2020-2021 school year due to school closures, see our 6th Grade Scope and Sequence Recommended Adjustments.

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Assessment

This assessment accompanies Unit 8 and should be given on the suggested assessment day or after completing the unit.

Unit Prep

Intellectual Prep

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Internalization of Standards via the Post-Unit Assessment

  • Take the Post-Unit Assessment. Annotate for: 
    • Standards that each question aligns to
    • Strategies and representations used in daily lessons
    • Relationship to Essential Understandings of unit 
    • Lesson(s) that Assessment points to

Internalization of Trajectory of Unit

  • Read and annotate the Unit Summary.
  • Notice the progression of concepts through the unit using the Lesson Map.
  • Do all Target Tasks. Annotate the Target Tasks for: 
    • Essential Understandings
    • Connection to Post-Unit Assessment questions
  • Identify key opportunities to engage students in academic discourse. Read through our Teacher Tool on Academic Discourse and refer back to it throughout the unit.

Unit-Specific Intellectual Prep

Model Example
Tally chart
Frequency table

 

Dot plot
Histogram
Box plot
Circle graph

Essential Understandings

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  • Statistics is a powerful tool to seek answers to statistical questions and to understand data distributions and what inferences can be drawn about the data.
  • Graphical representations of data, including dot plots, histograms, box plots, and circle graphs, are useful to organize data and highlight information about the overall shape of the data set. 
  • Measures of center, including the mean, median, and mode, provide information about the center of data sets. Depending on the shape and distribution of a data set, one measure may better represent a data set than others; however, with explanation, there may be a valid reason to choose any of the measures of center.
  • Measures of variation or spread, including the range and interquartile range, provide information about the spread, variation, or consistency of a data set.
  • When making decisions about data, it is valuable to consider both measures of center and measures of variation.

Materials

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  • Calculators (1 per student)
  • Optional: Play money (1 set per small group)
  • Number strips (1 per student) — These require some cutting, which can either be done prior to the lesson or during the lesson if scissors are provided to the students. Note, the same strips are used for both Lesson 6 and Lesson 9.

To see more information about the materials in this unit, view the Unit Materials Overview.

Vocabulary

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five-number summary

cluster

outlier

distribution

box plot

median

categorical data

interquartile range

circle graph

statistical question

numerical data

frequency table

symmetrical

dot plot

skewed left/right

histogram

measure of center

mean (average)

lower quartile

upper quartile

mode

range

To see all the vocabulary for this course, view our 6th Grade Vocabulary Glossary.

Lesson Map

Topic A: Understanding Statistics & Distributions

1

    6.SP.A.1

    6.SP.B.5.A

Define and identify statistical questions.

3

    6.SP.B.4

Represent data using histograms.

Topic B: Measurements of Center & Variability

5

    6.SP.A.2

    6.SP.B.5.C

Define and determine the mean of a data set.

6

    6.SP.A.2

    6.SP.B.5.C

Define and determine the median of a data set.

7

    6.SP.A.2

Define and determine the mode of a data set.

10

    6.SP.A.3

Compare measures of center and measures of spread to describe data sets.

Topic C: Box Plots & Circle Graphs

11

    6.SP.B.4

    6.SP.B.5

Represent data using box plots.

12

    6.SP.B.4

    6.SP.B.5

Analyze box plots and other representations, and summarize numerical data in context.

13

    6.SP.B.4

Analyze circle graphs in context.

Common Core Standards

Key: Major Cluster Supporting Cluster Additional Cluster

Core Standards

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Statistics and Probability
  • 6.SP.A.1 — 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.

  • 6.SP.A.2 — 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.

  • 6.SP.A.3 — Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

  • 6.SP.B.4 — Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

  • 6.SP.B.5 — Summarize numerical data sets in relation to their context, such as by:

  • 6.SP.B.5.A — Reporting the number of observations.

  • 6.SP.B.5.B — Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

  • 6.SP.B.5.C — Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

  • 6.SP.B.5.D — Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

Foundational Standards

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Measurement and Data
  • 4.MD.B.4

  • 4.MD.C.5

  • 5.MD.B.2

Ratios and Proportional Relationships
  • 6.RP.A.3

  • 6.RP.A.3.C

The Number System
  • 6.NS.B.2

  • 6.NS.B.3

Future Standards

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Interpreting Categorical and Quantitative Data
  • HSS-ID.A.1

  • HSS-ID.A.2

  • HSS-ID.A.3

  • HSS-ID.A.4

Statistics and Probability
  • 7.SP.A.1

  • 7.SP.A.2

  • 7.SP.B.3

  • 7.SP.B.4

Standards for Mathematical Practice

  • CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

  • CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

  • CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

  • CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

  • CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

  • CCSS.MATH.PRACTICE.MP6 — Attend to precision.

  • CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

  • CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.