enVision Mathematics Topic 8
6th Grade; April – May (7 weeks); 4th Quarter
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Topic Title(s):
Display, Describe, and Summarize Data
Prepared Graduates:
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP4. Model with mathematics.
MP7. Look for and make use of structure.
Standard(s):
3. Data, Statistics, and Probability
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
6.SP.A. Statistics & Probability: Develop understanding of statistical variability.
Identify 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. (CCSS: 6.SP.A.1)
Demonstrate that a set of data collected to answer a statistical question has a distribution that can be described by its center, spread, and overall shape. (CCSS: 6.SP.A.2)
Explain 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. (CCSS: 6.SP.A.3)
6.SP.B. Statistics & Probability: Summarize and describe distributions.
Display numerical data in plots on a number line, including dot plots, histograms, and box plots. (CCSS: 6.SP.B.4)
Summarize numerical data sets in relation to their context, such as by: (CCSS: 6.SP.B.5)
Reporting the number of observations. (CCSS: 6.SP.B.5.a)
Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. (CCSS: 6.SP.B.5.b)
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. (CCSS: 6.SP.B.5.c)
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. (CCSS: 6.SP.B.5.d)
Identify statistical questions that require the collection of data representing multiple perspectives. (Civic/Interpersonal Skills: Global/Cultural Awareness)
Make sense of practical problems by turning them into statistical investigations. (MP1)
Reason abstractly and quantitatively with data collected from statistical investigations by describing the data’s center, spread, and shape.
Model variability in data collected to answer statistical questions and draw conclusions based on center, spread, and shape. (MP4)
Write informative texts describing statistical distributions, their measures, and how they relate to the context in which the data were gathered. (Entrepreneurial Skills: Literacy/Writing)
Move from context to abstraction and back to context while finding and using measures of center and variability and describing what they mean in the context of the data. (MP2)
Analyze data sets and draw conclusions based on the data display and measures of center and/or variability. (MP4)
Identify clusters, peaks, gaps, and symmetry, and describe the meaning of these and other patterns in data distributions. (MP7)
Inquiry Questions
What distinguishes a statistical question from a question that is not a statistical question?
Why do we have numerical measures for both the center of a data set and the variability of a data set?
How can different data displays communicate different meanings?
When is it better to use the mean as a measure of center? Why?
When is it better to use the median as a measure of center? Why?
How many values of a data set do you use to calculate the range? Interquartile range? Mean absolute deviation? How does this help to compare what these measures represent?
Coherence Connections
This expectation is in addition to the major work of the grade.
In previous grades, students represent and interpret data in dot plots/line plots, and use arithmetic to answer questions about the plots.
In previous grades, students represent and interpret data in dot plots and line plots.
In Grade 6, students summarize and describe data distributions using numerical measures of center and spread, and terms such as cluster, peak, gap, symmetry, skew, and outlier.
In Grade 6, this expectation connects with developing understanding of statistical variability.
In Grade 7, students use random sampling to draw inferences about a population and draw informal comparative inferences about two populations.
In high school, students summarize, represent, and interpret data on a single count or measurement variable (including standard deviation), and make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Academic Vocabulary & Language Expectations:
Statistical question, mean, median, mode, range, box plot, quartiles, frequency table, histogram, absolute deviation, mean absolute deviation (MAD), interquartile range (IQR), outlier, data distribution
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topic 8
Let's Investigate! Tasks
Let's Investigate! Let's Chat About Data (TE) (relates to Lesson 8-1)
5th-to-6th Grade Warm-Ups for Activating Prior Knowledge (Geoff Krall)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention: None since this Unit Plan is in addition to the major work of the grade
Coherence Map/Concept Progressions: 6.SP.A.2, 6.SP.B.4, 6.SP.B.5.c
enVision Mathematics 6-8 & Number Worlds Connections (for SVVSD Special Education teachers only)
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