Course 1 Unit 2 - Patterns in Data

Patterns in Data is the second unit in Course 1 of the Core-Plus Mathematics program. This unit is the first of five units in Courses 1-3 that develop mathematical content from the statistics and probability strand of the curriculum. (See the descriptions of Course 1 Units.)

Unit Overview
Patterns in Data provides an introduction to the analysis of univariate (one-variable) data. Throughout this unit, students will be developing tools and strategies that will help them make sense of data and communicate their conclusions. The focus will be on displaying data (to observe shape, center, and variability/spread) and then computing and interpreting summary statistics such as measures of center (mean, median, and mode) and measures of variability (range, interquartile range, and standard deviation).
     Data analysis has been called the art of letting the data speak for themselves. This means that there is an emphasis on constructing graphical displays (plots) of the data that reveal the shape of the distribution and any patterns that might not be visible in a numerical listing or from summary statistics. Useful graphical displays included in this unit are dot plots, stemplots, histograms, and box plots.
     In Unit 3, students will learn some basics of handling bivariate (two-variable) data: first, plot the data on a scatterplot and, if there is a linear pattern, summarize by fitting a regression line.

Objectives of the Unit
  • Use various graphical displays of data to reveal important patterns in a data set and interpret those patterns in the context of the data
  • Compute measures of center and variability for sets of data and interpret the meaning of those statistics
  • Transform distributions by adding a constant or by multiplying by a positive constant and recognize how those transformations affect the shape, center, and spread of distributions

Sample Overview
The sample material for Unit 2 consists of the first two of four investigations of Lesson 2, "Variability." Understanding, measuring, and describing variability is a central theme throughout the curriculum. In these two investigations, students examine variability using the five-number summary and box plots.

View Sample Material
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Instructional Design
Throughout the curriculum, interesting problem contexts serve as the foundation for instruction. As lessons unfold around these problem situations, classroom instruction tends to follow a four-phase cycle of classroom activities—Launch, Explore, Share and Summarize, and Apply. This instructional model is elaborated under Instructional Design.

How the Statistics and Probability Strand Continues
The second unit from the statistics and probability strand in Course 1, Patterns in Chance, introduces students to sample spaces, probability distributions, the Addition Rule, simulation, and geometric probability. Important probabilistic concepts explored include mutually exclusive events and the Law of Large Numbers.
     In Course 2 Unit 4, Regression and Correlation, students study the appropriate use of correlation and regression to describe bivariate association. Students will continue to develop their ability to understand and visualize situations involving chance (in Unit 8, Probability Distributions) by using simulations and mathematical analysis to construct probability distributions. They study the following topics: Multiplication Rule, independent and dependent events, conditional probability, probability distributions and their graphs, waiting-time or geometric distributions, expected value, and rare events.
     In Course 3 Unit 1, Reasoning and Proof, students are introduced to more formal statistical reasoning. Students study inductive and deductive reasoning strategies; principles of logical reasoning—Affirming the Hypothesis and Chaining Implications; the relation among angles formed by two intersecting lines or by two parallel lines and a transversal; rules for transforming algebraic expressions and equations; design of experiments including the role of randomization, control groups, and blinding; sampling distributions; randomization tests; and statistical significance. In Unit 4, Samples and Variation, students extend their understanding of measurement of variation, use the normal distribution as a model of variation, are introduced to the binomial distribution and its use in decision making, and are introduced to probability and statistical inference involved in the control charts used in industry for statistical process control. (See the CPMP Courses 1-4 descriptions.)

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