Students analyze contextual situations, focusing on single variable data and bivariate data, and are introduced to the concept of using data to make predictions and judgments about a situation.
In Unit 2: Statistics, students continue to analyze contextual situations, but in this unit, they focus on single variable data and then bivariate data. This is the first unit where students are introduced to the concept of using data to make predictions and judgments about a situation. Univariate data is described through shape, center, and spread by using mathematical calculations to support reasoning. Students begin to make judgments about whether data is consistent (analysis of spread) and whether mean or median is a better representation of a situation (center). Bivariate data is analyzed for whether the variables are related (correlation) and whether a linear model is the best function to fit a set of data (analysis of residuals), and students develop a linear model that can be used to predict future events. In Unit 2, students are introduced to the modeling cycle and complete a project on univariate data analysis and another on bivariate data analysis.
Unit 2 begins with analyzing and describing univariate data. Students expand on their knowledge of shape, center, and spread from 6th and 7th grade to further interpret and calculate measures of spread—learning about variance and standard deviation. Students capitalize on previous understandings of measures of center and different graphical representations to formalize their knowledge of which measures of center, shape, and spread are used in conjunction with one another, and how these help to inform the “big picture” of the data set they represent. A three-day project culminates study of this topic.
In Unit 2 students dive deeper into bivariate data—identifying categorical and numerical data, and choosing representations that match the data presented. Two-way tables are used to represent categorical data. Students calculate relative and conditional frequencies in two-way tables and expand on their understanding of the tool from 8th grade. Scatterplots are explored heavily in this unit, and students use what they know about association from 8th grade to connect to correlation in Algebra 1. Students base their understanding of regression on their previous learning about line of best fit. Also in this unit, students will learn to assess the validity of the model they have used (be it linear or another function) by using residuals. A three-day project culminates this topic, with a loose framework provided.
As Algebra 1 progresses, students will identify shapes of data sets according to the functions, and they will continue to bring in ideas about how to model data in line with functions. Students will explore S-ID.7 more heavily as they progress through the units of Algebra 1.
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descriptive statistics |
measures of center (mean, median) |
inferential statistics | spread (standard deviation, interquartile range) |
univariate data | shape (skew, symmetrical) |
bivariate data | normal distribution |
numerical data | outlier resistant |
categorical data | distribution |
sample | variance |
population | scatterplots |
statistical question | two-way frequency tables |
frequency graphs (histogram, bar graph, dot plot) | relative frequency |
box plot (box-and-whisker plot) | marginal frequency |
association | correlation (correlation coefficient) |
causation | residuals (residual plot) |
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Internalization of Standards via the Unit Assessment:
Internalization of Trajectory of Unit:
Unit-Specific Intellectual Prep:
This assessment accompanies Unit 2 and should be given on the suggested assessment day or after completing the unit.
HSS-ID.A.1
HSS-ID.A.2
HSS-IC.A.1
Describe statistics. Represent data in frequency graphs and identify the center of a data set.
HSS-ID.A.1
HSS-ID.A.2
Describe center and spread. Represent data in a box plot (box-and-whisker plot) and calculate the center and spread.
HSS-ID.A.1
Represent data in a histogram and calculate the center. Identify when the median and mean are not the same value.
HSS-ID.A.2
HSS-ID.A.3
Describe the shape of the data in box plots and histograms. Choose an appropriate measure of center (or an appropriate shape) based on the shape and the relationship between the mean and the median.
HSS-ID.A.3
HSS-ID.A.4
Calculate and interpret the spread (variance) of a data set.
HSS-ID.A.2
HSS-ID.A.4
Calculate the standard deviation and compare two symmetrical distributions based on the mean and standard deviation.
HSS-ID.A.2
HSS-ID.A.4
Interpret the standard deviation and interquartile range.
HSS-ID.A.4
Calculate population percentages using the standard deviation.
HSS-ID.A.2
Given summary statistics, describe the best measures of center and spread. Describe reasoning.
HSS-ID.A.1
HSS-ID.A.2
HSS-ID.A.3
HSS-ID.A.4
Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 1/3)
HSS-ID.A.1
HSS-ID.A.2
HSS-ID.A.3
HSS-ID.A.4
Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 2/3)
HSS-ID.A.1
HSS-ID.A.2
HSS-ID.A.3
HSS-ID.A.4
Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 3/3)
HSS-ID.B.5
Define categorical and numerical data. Create two-way tables to organize bivariate categorical data.
HSS-ID.B.5
Describe relative and relative conditional frequencies of two-way tables.
HSS-ID.B.6
Create scatterplots and identify function shapes in scatterplots.
HSS-ID.C.8
HSS-ID.C.9
Calculate, with technology, the correlation coefficient for a data set. Explain why correlation does not determine causation.
HSS-ID.B.6a
HSS-ID.B.6b
HSS-ID.C.7
Determine the function of best fit and create a linear equation from least squares regression using technology.
HSS-ID.B.6b
HSS-ID.B.6c
Use residuals to assess the strength of the model for a data set.
HSS-ID.B.6a
HSS-ID.C.7
HSS-ID.C.9
Describe the relationship between two quantitative variables in a contextual situation represented in a scatterplot using the correlation coefficient, least squares regression, and residuals as evidence.
HSS-ID.B.6
HSS-ID.C.7
HSS-ID.C.8
HSS-ID.C.9
Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 1/3)
HSS-ID.B.6
HSS-ID.C.7
HSS-ID.C.8
HSS-ID.C.9
Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 2/3)
HSS-ID.B.6
HSS-ID.C.7
HSS-ID.C.8
HSS-ID.C.9
Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 3/3)
Key: Major Cluster Supporting Cluster Additional Cluster
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