2014-2015 Curriculum Blueprint ... Course: MJ1 Unit #13 Analyzing Data:

2014-2015 Curriculum Blueprint
Grade: 6
Course: MJ1
Approximate Time:
10 Days
Unit #13 Analyzing Data:
Learning Goal
Students will be able to understand that data can be displayed using number lines, dot plots,
histograms and box plots. Students will use these representations to summarize and describe data
distributions using the appropriate measures of central tendency and variability with justification.
Link to Learning Scale: Measurement, Data, Statistics, & Probability
Essential Question(s)
How can you display a set of numerical data?
Why do we organize data in tables and graphs?
How is describing and summarizing data used in the real world?
In what type of real world situation would “mean’ not be the best representation of the data?
How do the concepts of central tendency and variability allow you to interpret the data
collected, organized and displayed?
 How do you decide which measure of central tendency provides the best representation of the
data?
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Unit Overview
This unit builds on the understanding developed in the previous unit as students represent
and analyze data sets and determine the measures of variability and center.
Summarizing and describing distributions requires that students use appropriate statistical
measures strategically (MP.5) and attend to precision in finding and applying those
measures (MP.6). 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 requires that students
construct and critique arguments (MP.3). Students look for and apply regularity in repeated
reasoning when they explore how adding or removing data points from a data set effects the
measures of center and variability (MP.8).
Focus Standards
Bullets are the deconstructed standards These should be used to develop concise learning
statements/daily objectives/scales. 6th Grade Math Test Item Specifications
Vertical Progression:
http://www.turnonccmath.net/ K-8 Learning Trajectories (This could be used to determine
remediation needs or enrichment opportunities)
MAFS.6.SP.2.4 (DOK 2)
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
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Identify the components of dot plots, histograms, and box plots.
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Find the median, quartile and interquartile range of a set of data.
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Analyze a set of data to determine its variance.
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Create a dot plot to display a set of numerical data.
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Create a histogram to display a set of numerical data.
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Create a box plot to display a set of numerical data.
5th Grade- Students work with data on a bar graph, picture graph, line plot, and first quadrant of a
coordinate plane.
MAFS.6.SP.2.5 a, b, c, d (DOK 3)
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.
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Organize and display data in tables and graphs.
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Report the number of observations in a data set or display.
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Describe the data being collected, including how it was measured and its units of
measurement.
7th Grade- Students will use measures of center and measures of variability for numerical data
from random samples to draw informal comparative inferences about two populations.
Unit Sequence
Be selective in choosing problems aligned to the
standards within each lesson
Creating a Dot Plot
 EngageNY Module 6: Lesson 3 (Page 27)
Creating & Describing a Histogram
 EngageNY Module 6: Lesson 4/5 (Page 35)
Understanding & Describing Mean Absolute
Deviation
 EngageNY Module 6: Lesson 9 -11 (Page 91)
Describe the Center of Distribution Using Median
 EngageNY Module 6: Lesson 12 (Page 137)
Describing Variability Using the Interquartile
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Essential Vocabulary
Dot Plot
Box Plot
Histograms
Mean
Median
Quartile
Interquartile
Set of Data
Interquartile Range (IQR)
Mean Absolute Deviation
Measures of Center
Measures of Variance
Measures of Central Tendency
Outliers
Skew
2014-2015 Curriculum Blueprint
Grade: 6
Course: MJ1
Unit #13 Analyzing Data:
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Calculate quantitative measures of center.
Calculate quantitative measures of variance.
Identify outliers.
Determine the effect of outliers on quantitative measures of a set of data.
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.
Mathematical Practice Standards
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.3.1: Construct viable arguments and critique the reasoning of others.
MAFS.K12.MP.5.1: Use appropriate tools strategically.
MAFS.K12.MP.6.1: Attend to precision.
MAFS.K12.MP.8.1: Look for and express regularity in repeated reasoning.
Range
 EngageNY Module 6: Lesson 13 (Page 148)
Summarizing a Distribution Using Box Plot
 EngageNY Module 6: Lesson 14/15 (Page
156)
Understanding Box Plots
 EngageNY Module 6: Lesson 16 (Page 177)
Describing Center, Variability, & Shape of a
Distribution from a Graph
 EngageNY Module 6: Lesson 20 (Page 219)
Summarizing a Data Distribution by Describing
Center, Variability, & Shape
 EngageNY Module 6: Lesson 21 (Page 228)
Supplemental Resources
6th Grade Common Core Flip Book A user-friendly
resource for understanding the specifications of
the Common Core Standards.
Approximate Time:
10 Days
Higher Order Questions/Stems
 Why did you choose ___________ to display
the set of data?
 Which measure would best represent the
data set?
 Which measure would give you the
highest/lowest value?
 What would happen to the
mean/median/range if…?
 Describe the different ways that data can be
displayed.
 When a new value is added to a data set, is
it possible that the mean/median will not
change? Explain your answer.
Writing Connections
 Create a data display based on a set of data.
Explain some observations that can be
made from the data display?
 Describe a real world situation in which
mean would not be the best representation
of the data?
 Explain how an outlier, high and low, would
impact the mean, median, mode and range
of a data set.
 Explain which measure, the mean, median,
mode or range, is most likely to be affected
if a new item much greater than/much less
than the others is added to a set.
EngageNY Grade 6 Module 6 – Word documents
can be found using this link
o Teacher Materials - The teacher materials
consist of scripted lessons, instructional
strategies, and structured plans.
o Student Materials - The student materials
consist of the student pages for each lesson in
this Module.
o Copy Ready Materials - A collection of the
Writing Template Tasks These template tasks
module assessments, lesson exit tickets and are designed from the Mathematical Practice
fluency exercises from the teacher materials. Standards. When filled in, these templates
become teaching tasks that create opportunities
Georgia Unit 6: Statistics Tasks aligned to
for teaching literacy skills in mathematics.
standards 6.SP.2.4 and 6.SP.2.5:
Link to Problem Solving Rubric
 What is a Statistical Question? – Page 15
Link to Webb’s DOK Guide
North Carolina Lessons for Learning –
Performance tasks aligned to 6.SP.2.5
o How Mad Are You (page 30)
o Shakespeare vs. Rowling (page 36)
2014-2015 Curriculum Blueprint
Grade: 6
Course: MJ1
Unit #13 Analyzing Data:
Math Formative Assessment System (MFAS)
These formative assessments could be used
before instructing a lesson on similar content to
help formulate small groups or they may be used
however PLCs see best for their students. Each
formative assessment comes with a rubric and
instructional implications based on the level of
student understanding.
MARS Classroom Challenge: Representing Data
Using Grouped Frequency Graphs and Box Plots–
A formative assessment lesson to assess how
well students are able to interpret frequency
graphs that use grouped data and their
associated box plots. In particular this unit aims
to identify and help students who have difficulty
interpreting information from frequency graphs
and box plots; such as minimum and maximum
values, medians and quartiles.
Illustrative Mathematics – 6th grade tasks
developed at the University of Arizona for the
CCSS.
EngageNY Module 6: Lesson 18 (page 195):
Extension opportunity for Connecting Graphical
Representations and Numerical Summaries
EngageNY Module 6: Lesson 19 (page 208)
Extension opportunity for Comparing Data
Distributions
RTTT Item Specifications (page 29)
Teaching Channel Video 2 min video with focus
on Improving Participation with Talk Moves
(Personalized Learning Opportunity).
Approximate Time:
10 Days