Course 1 Unit 1 - Patterns in Data
1st Edition

Patterns in Data is the first unit in Course 1 of the Contemporary Mathematics in Context program. This unit is the first of seven units in Courses 1- 4 that develop mathematical content from the Statistics and Probability strand of the curriculum. (See the descriptions of Course 1 Units.) Note that there are seven units and a capstone unit for this course. Units vary in length but are typically completed in 3 to 6 weeks.

Unit Overview

Patterns in Data is an introduction to data analysis. In this unit, students analyze data using graphical displays such as stem-and-leaf plots, number line plots, histograms, box plots, and scatterplots. They use visual patterns in the data and summary statistics such as mean, median, percentiles, and the interquartile range to describe distributions of data, to make decisions, to make comparisons, and to make predictions.

Objectives of the Unit
  • To use various graphical displays of data to uncover important patterns in the data set and interpret these patterns in the real-world context
  • To summarize and interpret sets of data using measures of center and variability
  • To compare sets of data using scatterplots and the line y = x, and to interpret these comparisons for the real-world contexts that gave rise to the data

Sample Overview

The sample material for Unit 1 consists of the first two investigations of Lesson 3, "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.

As you examine the sample investigations and lessons, you should note that lessons often span several days and that investigations may require more than one 50-minute class period to complete. (See Instructional Design.) The first two investigations and homework set will take approximately four 50-minute class periods for heterogeneously-grouped classes of ninth graders. Teachers will typically adjust the length of time spent on an investigation for classes above or below grade level or classes that have not completed rich middle school mathematics programs.

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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 common pattern as elaborated under Instructional Design.

How the Statistics and Probability Strand Continues

The second unit from the statistics and probability strand in Course 1 introduces students to simulation and to the idea of probability distributions.

In Course 2, students study the appropriate use of correlation and regression to describe bivariate association. Students will continue to develop their ability to understand situations involving chance by using simulations and mathematical analysis to construct probability distributions and study the following topics: multiplication rule for independent events, conditional probability, geometric distributions, expected value, rare events, summation notation, and an introduction to binomial distributions.

In Course 3, students study survey methods, sampling, sampling distributions, relationships between a sample and a population, confidence intervals, and margin of error. In Unit 5, Patterns in Variation, students extend their understanding of measurement of variation, use the normal distribution as a model of variation, study the Addition Rule for mutually exclusive events, and are introduced to probability and statistical inference involved in the control charts used in industry for statistical process control.

In Course 4, students extend their understanding of the binomial distribution and how the binomial distribution is used in statistical inference to test a single proportion and to compare two treatments in an experiment.

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