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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
Unit Description
Unit: 7
Title: Statistics
Suggested Length: 4 Weeks
Big Idea(s)
Enduring Understandings
Develop an understanding of statistical thinking.
What enduring
understandings are
essential for application to
new situations within or
beyond this content?
Enduring Skills Rubric measures competency of the following skills:
Relations & Functions
 Mathematical relationships can be represented and analyzed using
words, tables, graphs, and equations.
Data Collections
 An appropriately selected sample can be used to describe and make
predictions about a population.
 The size of a sample determines how close data from the sample
mirrors the population.
Data Representation
 Each type of graph is most appropriate for certain types of data.
Data Distribution
 The best descriptor of the center of a numerical data set (i.e., mean,
median, mode) is determined by the nature of the data and the
question to be answered.
 Outliers affect the mean, median, and mode in different ways.
 Data interpretation is enhanced by numerical measures telling how
data are distributed.
Essential Question(s)
What questions will
provoke and sustain
student engagement
while focusing learning?
Curriculum and Instruction
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What is the best way to organize a set of data?
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What kinds of graphs will best represent a given set of data?
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How can I describe the center of a set of data?
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How can I describe the spread of a set of data?
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How can I use data to compare different groups?
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How do I choose and create appropriate graphs to represent
data?
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What conclusions can be drawn from data?
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
Standards
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How can I recognize when a question is statistical and when it is
not?
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What is the difference in a measure of center and a measure of
variation?
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them. Students will
make sense of the data distributions by interpreting the measures of center
and variability in the context of the situations they represent.
2. Reason abstractly and quantitatively. Students reason about the
appropriate measures of center or variability to represent a data distribution.
3. Construct viable arguments and critique the reasoning of others. Students
construct arguments regarding which measures of center or variability they
would use to represent a particular data distribution. They may critique other
students’ choices when considering how outliers are handled in each
situation.
4. Model with mathematics. They use measures of center and variability and
data displays (i.e. box plots and histograms) to draw inferences about and
make comparisons between data sets. Students need many opportunities to
connect and explain the connections between the different representations.
Students collect data regarding real-world contexts and create models to
display and interpret the data.
5. Use appropriate tools strategically. Students consider available tools
(including estimation and technology) when answering questions about data
or representing data distributions. They decide when certain tools might be
helpful. For instance, students in grade 6 may decide to represent similar
data sets using dot plots with the same scale to visually compare the center
and variability of the data.
6. Attend to precision. Students use appropriate terminology when referring
data displays and statistical measures.
7. Look for and make use of structure. Students examine the structure of data
representations by examining intervals, units, and scale in box plots, line plots,
histograms and dot plots.
8. Look for and express regularity in repeated reasoning. Students recognize
typical situations in which outliers skew data. They can explain patterns in the
way data is interpreted in the various representations they study throughout
this unit.
Standards for Mathematical Content
6.SP.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
Curriculum and Instruction
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
old are the students in my school?” is a statistical question because
one anticipates variability in students’ ages.
6.SP.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.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.4
Display numerical data in plots on a number line, including dot
plots, histograms, and box plots.
6.SP.5
Summarize numerical data sets in relation to their context, such as
by:
a. Reporting the number of observations.
b. Describing the nature of the attribute under investigation,
including how it was measured and its units of measurement.
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.
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.
Supporting
Standard(s)
6.NS.1
Which related standards
will be incorporated to
support and enhance the
enduring standards?
6.NS.2
Curriculum and Instruction
Interpret and compute quotients of fractions, and solve word
problems involving division of fractions by fractions, e.g., by using
visual fraction models and equations to represent the problem. For
example, create a story context for (2/3) ÷ (3/4) and use a visual
fraction model to show the quotient; use the relationship between
multiplication and division to explain that (2/3) ÷ (3/4) = 8/9
because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How
much chocolate will each person get if 3 people share 1/2 lb of
chocolate equally? How many 3/4-cup servings are in 2/3 of a cup
of yogurt? How wide is a rectangular strip of land with length 3/4 mi
and area 1/2 square mi?
Fluently divide multi-digit numbers using the standard algorithm.
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
Instructional
Outcomes
What must students learn
and be able to do by the
end of the unit?
6.NS.3
Fluently add, subtract, multiply, and divide multi-digit decimals
using the standard algorithm for each operation.
6.NS.4
Find the greatest common factor of two whole numbers less than
or equal to 100 and the least common multiple of two whole
numbers less than or equal to 12. Use the distributive property to
express a sum of two whole numbers 1–100 with a common factor
as a multiple of a sum of two whole numbers with no common
factor. For example, express 36 + 8 as 4 (9 + 2).
I am learning to….
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Curriculum and Instruction
Recognize that data can have variability
Recognize a statistical question (examples versus non-examples)
Know that a set of data has a distribution.
Describe a set of data by its center, e.g., mean and median.
Describe a set of data by its spread and overall shape, e.g., by
identifying data clusters, peaks, gaps, and symmetry.
Recognize there are measures of central tendency for a data set, e.g.,
mean, median, mode.
Recognize there are measures of variances for a data set, e.g., range,
interquartile range, mean absolute deviation.
Recognize measures of central tendency for a data set summarizes
the data with a single number.
Recognize measures of variation for a data set describes how its
values vary with a single number.
Identify the components of dot plots, histograms, and box plots.
Find the median, quartile and interquartile range of a set of data.
Analyze a set of data to determine its variance.
Create a dot plot to display a set of numerical data.
Create a histogram to display a set of numerical data
Create a box plot to display a set of numerical data.
Organize and display data in tables and graphs.
Report the number of observations in a data set of display.
Describe the data being collected, including how it was measured
and its units of measurement.
Calculate quantitative measures of center, e.g., mean, median,
mode.
Calculate quantitative measures of variance, e.g., range, interquartile
range, mean absolute deviation.
Identify outliers.
Determine the effect of outliers on quantitative measures of a set of
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
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Essential Vocabulary
What vocabulary must
students know to
understand and
communicate effectively
about this content?
Curriculum and Instruction
data, e.g., mean, median, mode, range, interquartile range, mean
absolute deviation.
Choose the appropriate measure of central tendency to represent the
data.
Analyze the shape of the data distribution and the context in which
the data were gathered to choose the appropriate measures of
central tendency and variability and justify why this measure is
appropriate in terms of the context.
Essential Vocabulary
Box Plot
Cluster
Distribution
Dot plot
Quartile (First/Lower and Third/Upper)
Frequency table
Gap
Histogram
Interquartile Range
Line plot
Lower extreme
Maximum
Mean
Mean Absolute Deviation
Measure of Center
Measure of Variability
Median
Minimum
Mode
Outlier
Range
Skewed Data
Spread
Statistical Question
Statistical Variability
Statistics
Upper Extreme
Supporting Vocabulary
Bar graph
Interval
Number line
Plot
Table
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
Resources/Activities
Resources/Activities
What resources could we
use to best teach this unit?
https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_6_6thGrade_Unit6.pdf
The following website is a website with lessons to address CCSS:
https://www.engageny.org/resource/grade-6-mathematics
http://www.insidemathematics.org/common-core-resources/mathematicalcontent-standards/standards-by-grade/6th-grade
http://www.mathchimp.com/6th-grade-math-resources
Newspaper and magazine graphs for analysis of the spread, shape and
variation of data from the National Council of Teachers of Mathematics,
Illuminations: Numerical and Categorical Data. In this unit of three lessons,
students formulate and refine questions, and collect, display and analyze
data. (ORC # 391, 392, 393)
Data Analysis and Probability Virtual Manipulatives Grades 6-8
#5048 Students can use the appropriate applet from this page of virtual
manipulatives to create graphical displays of the data set. This provides an
important visual display of the data without requiring students to spend time
hand-drawing the display. Classroom time can then be spent discussing the
patterns and variability of the data. Guidelines for Assessment and
Instruction in Statistics Education (GAISE) Report, American Statistics
Association
http://www.illustrativemathematics.org/6
http://commoncoretools.me/tools/
http://www.opusmath.com/common-core
Students can use applets to create data displays. Examples of applets
include the Box Plot Tool and Histogram Tool on NCTM’s Illuminations.
Box Plot Tool - http://illuminations.nctm.org/ActivityDetail.aspx?ID=77
Histogram Tool -- http://illuminations.nctm.org/ActivityDetail.aspx?ID=78
Curriculum and Instruction
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
Remember there are other sources in your school that may not be listed on
this resources list due to variation in each individual school. If you have a
good resource that you would be willing to share, please let Mendy Mills
know so that she can share with other math teachers.
[email protected]
Curriculum and Instruction
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Curriculum and Instruction
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