In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.
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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Statistical question
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1 - Recognize (Statistical question)
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3 - I recognize statistical questions.
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A. Statistical questions anticipate data variability and account for the variability in the answers.
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A.1 What is a statistical question?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Data descriptors
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2 - Understand (Data distribution)
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2 - I understand that data collected for a statistical question has a distribution that can be described by its center, spread and shape.
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A. Data collected to answer a statistical question has a distribution that can be described by its center, spread and overall shape.
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A.1 What is data distribution?
A.2 How can data distribution be described by its center?
A.3 How can data distribution be described by its spread?
A.4 How can data distribution be described by its overall shape?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Measures
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1 - Recognize (Measures with a single number)
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1 - I can recognize that the measure of center and the measure of variation of a numerical data set are both represented by a single number.
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A. The measure of center and the measure of variation of a numerical data set are both represented by a single number.
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A.1 What is the measure of center of a numerical data set?
A.2 What is the measure of variation for a numerical data set?
A.3 How do you find the single number that measures the center of a numerical data set?
A.4 How do you find the single number that gives the measure of variation of a numerical data set?
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Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Number line display e.g.
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3 - Display (Data with dot plots)
3 - Display (Data with histograms)
3 - Display (Data with box plots)
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3 - I can display numerical data with dot plots.
3 - I can display numerical data with histograms.
3 - I can display numerical data with box plots.
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A. One can display numerical data using dot plots, histograms and box plots.
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A.1 How does one display data with a dot plot?
A.2 How does one display data with a histogram?
A.3 How does one display data with a box plot?
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Summarize numerical data sets in relation to their context, such as by:
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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b. Attribute investigated
b. Measure
c. Measures
c. Measures of variability
c. Descriptors
d. Choice of Measure
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2 - Summarize (Data)
1 - Report (Number of observations[a])
2 - Describe (Nature of attribute[b])
2 - Describe (How attribute was measured [b])
2 - Describe (Unit of measurement [b])
1 - Give (Quantitative measures of center[c])
1 - Give (Quantitative measures of variability [c])
2 - Describe (Overall pattern[c])
2 - Describe (Striking deviations [c])
2 - Describe (Context of data collection[c])
6 - Relate (Choice of measures, shape of data and context of data gathered[d])
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2 - I can summarize numerical data sets in relation to their context.
1 - I can report the number of observations
2 - I can describe the nature of the attribute under investigation.[b]
2 - I can describe how the attribute was measured.[b]
2 - I can describe the attributes units of measurement.[b]
1 - I can give the quantitative measures of center. [c]
1 - I can give the quantitative measures of variability.[c]
2 - I can describe the overall pattern of the data collected.[c]
2 - I can describe any striking deviations.[c]
2 - I can describe the context in which the data were gathered.[c]
6 - I can relate my choice of measure of center, my choice of measure of variability, the shape of the data and the context in which the data were gathered.[d]
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A. One can summarize numerical data sets in relation to their context.
B. The number of observations should be reported when summarizing numerical data sets.
C. When summarizing numerical data one should describe how the attribute was measured and its units of measurement.
D. When summarizing numerical data, one should give quantitative measures of center, measures of variability, overall patterns, and striking deviations.
E. One should relate 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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A.1 How can one summarize numerical data sets in relation to their context?
B.2 How does one report the number of observations?
C.1 How does one describe the nature of the attribute under investigation?
C.2 How does one describe how an attribute was measured?
C.3 How does one describe the attributes units of measurement?
D.1 What are the quantitative measures of center?
D.2 How does one find the median of a data set?
D.3 How does one find the mean of a data set?
D.4 What are the quantitative measures of variability?
D.5 How does one find the interquartile range of a data set?
D.6 How does one find the mean absolute deviation for a data set?
D.7 How does one describe the overall pattern of the data collected?
D.8 What is a striking deviation?
D.9 How does one describe any striking deviations?
E.1 How does one describe the context in which the data were gathered?
E.2 How does one relate their choice of measures of center and variability to the shape of the data and the context in which that data were gathered?
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