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Mathematics Core Curriculum Video Library
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1.

## Using Samples [electronic resource]

This program begins with an explanation of the difference between a Population and a Sample, and the reasons why samples are so important in estimating data relating to populations too large or too impractical to be measured in their entirety. The program emphasizes the need for random samples, explains how several random samples of the same size will vary, and then looks at ways of dealing with this variability, calculating the Standard Error of the Mean, and how to estimate the "95% Confidence Interval. The program goes on to show how, when dealing with quantitative data, you can calculate the size of the sample that is needed in order to achieve the precision required.
Online
2005; 1996
2.

## A Gift for Math [electronic resource]

Endowed with an elementary representation mechanism, the human brain is naturally predisposed toward mathematics. This program seeks to understand the biological basis of humankind's "gift for math"-and why, beyond that baseline computational ability, some people are capable of scaling the highest peaks of mathematical comprehension. Experiments with animals, studies of very young children, cases involving patients with brain injuries, and analysis of brain imaging data are included.
Online
2005; 2000
3.

## Probability [electronic resource]

What are the odds that a casino card dealer and a pair of Simon and Garfunkel wannabes know something about probability? This program begins by defining probability and sampling, experiments, simple and compound events, and sample space. Next, the formula for finding probability is analyzed, along with the composition of simple and compound events, mutually exclusive events, and complements of events. Finally, dependent and independent conditional events are discussed.
Online
2005; 2000
4.

## Reading a Ruler [electronic resource]: English and Metric Measurements

In the first lesson, the different forms of English measurement are discussed and displayed as they would appear on a ruler. The viewer also learns how to understand fractions when measuring and how to find exact measurements using a ruler. The second lesson deals with the metric system by introducing the meter and other metric measurements. Viewers learn how to read a meter stick, and common abbreviations of metric measurements are discussed. Viewers also learn how to convert measurements using the decimal point.
Online
2005; 1994
5.

## Measurement [electronic resource]: Long and Short of It

Emphasizing hands-on practice, this program is an excellent tool for introducing the basics of linear measurement: its history, terminology, systems, and practical applications. Using both customary and metric rulers, Measurement: The Long and the Short of It will guide your students through the process of taking measurements, performing related calculations using whole numbers and fractions, and arriving at answers they can feel confident with. By the time the program is over, students will understand exactly what measurement is-and why it's relevant to their lives. Includes a workbook. Correlates to all applicable state and national standards.Recommended for middle school, high school, and vocational/technical school.
Online
2006; 2007
6.

## Mathematics and Nature [electronic resource]

The shapes of natural things-trees and clouds, blades of grass and galaxies-seem countless. Closer observation shows that nature only presents a small number of fundamental shapes and that these basic shapes obey strict laws. This program explains a new science of natural forms that aims to understand the order of nature. We see that most natural phenomena, whether the movement of planets or the secretion of hormones, follow regular cycles. Attempts to describe the order of nature mathematically have led to a new geometry: fractal geometry.
Online
2005; 1990
7.

## Handling Variability [electronic resource]

This program examines the measurement of blood pressure to introduce the idea that multiple measurements may produce very variable results. The idea that measurement "errors," together with fluctuations in the parameters being measured, create variability is followed by an explanation of both Systematic and Random Error and the recognition of the need for statistical techniques to handle this variability in order to allow inferences to be drawn and decisions made.
Online
2005; 1996
8.

## Describing Data [electronic resource]

Beginning with an explanation of the difference between "qualitative" and "quantitative" data, this program goes on to explain various ways of presenting data, including Dot Plots, Bar Charts, and Histograms. The program also explains Summary Measures, Characteristic Values, and how to arrive at the Mode, Median, and Mean, with a discussion of their individual drawbacks and advantages. The program goes on to discuss handling the Spread of Distribution, and explains techniques for measuring Spread, including Quartiles, Inter-quartile Range, and Standard Deviation, and concludes with modeling using Normal Distribution.
Online
2005; 1996
9.

## Bivariate Data [electronic resource]: When y Depends on X

This program demonstrates how "qualitative" bivariate data can be visualized by using a modification of the simple Bar Chart. Quantitative data is dealt with by developing the Dot Plot into the Scatter Diagram, which allows any correlation to show itself in a linear relation. The program explains how this correlation can be modeled by calculating a "Line of Best Fit," how to calculate 95% Confidence Bands, and how to calculate a summary measure for any correlation called the Correlation Coefficient. Finally, the program explains how to deal with data that indicates a curved Line of Best Fit by either finding a way of re-plotting to provide a linear correlation or, alternatively, how to calculate a curved Line of Best Fit.
Online
2005; 1996
10.

## Graphs [electronic resource]

This video describes how to read, interpret, and evaluate data displayed in bar graphs, line graphs, and pie charts. Dramatized segments and computer animations illustrate ways to determine the financial advantages of a staggered breeding schedule at a dairy farm; allocate rack space in a CD store, based on regional and local sales figures; and decide whether an athlete's physical characteristics indicate competition as a sprinter or as a distance runner.
Online
2005; 1995
11.

## Decimals and Exponents [electronic resource]

This video describes how whole numbers and decimals are used in the monetary system, how to calculate costs in foreign currencies, and how to use exponents. Dramatized segments and computer animations focus on ways to determine the international value of U.S. dollars at a currency exchange; select chairs for an interior decorating job while staying within a budget; and calculate interstellar distances using scientific notation-and imagination.
Online
2005; 1995
12.

## Logical Reasoning [electronic resource]

This video describes how to recognize and apply inductive and deductive reasoning. Dramatized segments and computer animations involve determining a crime suspect's guilt or innocence based on clues from a series of convenience store robberies; finding a strategy for winning a game played with coins; and matching students to the sports or musical instruments they play as a part of a puzzle.
Online
2005; 1995
13.

## Measurement [electronic resource]

This video describes how to estimate costs of products and services, determine the circumference of an object and its effect on motion, and calculate area and volume. Dramatized segments and computer animations illustrate ways to use measurements taken from blueprints to estimate construction costs; determine tire sizes, which affect vehicle speed; and calculate a running track's circumference to fairly stagger the start lines.
Online
2005; 1995
14.

## Fractions [electronic resource]

This video describes the meaning of fractions and how to solve problems involving sums and products. Dramatized segments and computer animations focus on adjusting ingredient amounts to vary the yield of recipes at a bakery; deciding whether to hire an untrained worker at a bike shop by projecting overtime wages and short-term productivity loss; and learning to read musical notation including fractional measures.
Online
2005; 1995
15.

## Area and Volume [electronic resource]

This video describes how to calculate the area of rectangles and other shapes-both geometrical and irregular-and how to determine the volume of a rectangular solid. Dramatized segments and computer animations focus on calculating lawn dimensions at a sod farm; creatively redesigning a cereal box while retaining the original volume; and using the Pythagorean Theorem to work out the coverage area for a kitchen floor being tiled diagonally.
Online
2005; 1995
16.

## Geometry Basics [electronic resource]

This program presents the building blocks that every student of geometry needs to understand. Topics addressed include inductive and deductive reasoning; terminology such as points, lines, planes, and space; six core postulates; five essential theorems; and how to express theorems in their statement, converse, inverse, contrapositive, and biconditional forms.
Online
2005; 1999
17.

## Introduction to Statistics and the Relative Frequency Histogram [electronic resource]

After concisely defining the purpose of statistics, section one of this program uses Five-Card Charlie's Fuzzy Dice Cola to examine the concepts of population and sampling and to catalogue the elements of statistical problems. In section two, data derived from the National Martyr Competition provides an opportunity to set up a relative frequency histogram, which involves classes and their widths, boundaries, frequencies, and relative frequencies.
Online
2005; 2000
18.

## Hypothesis Testing, Types of Error, and Small Samples [electronic resource]

In this program, a helpful bunch of bullies comes to grips with and alternate hypotheses, the significance level, the test statistic, acceptance and rejection regions, one- and two-tailed tests, and Type I and Type II errors. The essentials of dealing with small samples-including t-distribution, the t-Value Formula, and degrees of freedom-are also tackled.
Online
2005; 2000
19.

## The Math Life [electronic resource]

Why did a magician become a mathematician? How can a person see in four dimensions? What does a mathematical proof have in common with a Picasso portrait? This elegant program brings to life the human dimension of mathematics through lively interviews with Freeman Dyson, David Mumford, Ingrid Daubechies, Persi Diaconis, Michael Freedman, Fan Chung Graham, Kate Okikiolu, Jennifer Tour Chayes, Peter Sarnak, Steven Strogatz, and seven other mathematicians. These captivating luminaries vividly communicate the excitement and wonder that fuel their work as they explore the world through its patterns, shapes, motions, and probabilities. Computer animations and analogies drawn from the visual arts are incorporated, to maximize accessibility to the fascinating concepts discussed. A Wendy Conq [...]
Online
2005; 2002