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Title

Video Segments

Contents of DVDs

Algebra Applications DVDs
Linear Functions

ALGEBRA APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Introduction. 

An overview of the key topics to be covered in the video.

Segment 2: Cycling. 

Go on a tour of Italy through the mountains of Tuscany and apply students' understanding of slope.

Algebra concepts: slope, slope formula, slope-intercept form, linear functions

Segment 3: Oil Exploration.

A linear regression of oil consumption data over the past 25 years reveals an interesting pattern. How could new oil fields like ANWR help in breaking our dependence on foreign oil?

Algebra concepts: linear functions, linear regression

Segment 4: Exercise.

The maximum heart rate from aerobic exercise is a linear function dependent on age. Students are asked to develop a data table based on the function.

Algebra concepts: linear functions, data analysis

Algebra Applications DVDs
Quadratic Functions

ALGEBRA APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Introduction

An overview of the key topics to be covered in the video.

Segment 2: Pyrotechnics.

In this segment the basics of quadratic functions in standard form are developed visually and students are guided through the planning of a fireworks display.

Algebra concepts: quadratic functions in standard form, curve fitting

Segment 3: Forensics.

The distance a car travels even after the brakes are applied can be described through a quadratic function.  The total distance is known as the stopping distance and this segment analyzes the quadratic function. This is an equation that can be used by accident investigators.

Algebra concepts: Quadratic equations, quadratic functions, solving quadratic equations graphically

Segment 4: Medicine.

An analysis of CDC data reveals a number of quadratic models that doctors can use to monitor and growth and development of children.
Key concepts: Quadratic regression

Algebra Applications DVDs
Variables and Equations

ALGEBRA APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Introduction.

An overview of the key topics to be covered in the video.

Segment 2: Honey Production.

Analyzing statistics from honey bee production allows for a mathematical analysis of the so-called Colony Collapse Disorder.

Algebra concepts: variables, equations, formulas, ratios and proportions, and box and whisker plots

Segment 3: River Ratios.

Why do rivers meander instead of traveling in a straight line? In going from point A to point B, why should a river take the circuitous route it does instead of a direct path? In the process, the so-called Meander Ratio is explored. Students construct a mathematical model of a meandering river using the TI-Nspire. 

Algebra concepts: variables, equations, ratios, geometry and measurement, statistical mean, and data analysis

Algebra Applications DVDs
Inequalities

ALGEBRA APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Introduction.

An overview of the key topics to be covered in the video.

Segment 2: Hybrid cars.

The need for fuel-efficient cars makes hybrids a current favorite. An examination of the equations and inequalities that involve miles per gallon (mpg) for city and highway traffic reveals important information about hybrid cars and those with gasoline-powered engines.  Students use the Graphs and Geometry features of the TI-Nspire.
 

Algebra concepts: linear equations, functions, and inequalities, graphs of inequalities

Segment 3: Floods in Venice.

Venice experiences a great deal of flooding, and with the expected rise of sea levels over the next century, this ancient city is in peril.  Through a series of inequalities, students analyze the impact of flooding, rising sea levels, and sinking have on this grand, ancient city. Students use the Lists and Spreadsheets and the Program Editor features of the TI-Nspire.

Algebra concepts: inequalities

Algebra Applications DVDs
Functions and Relations

ALGEBRA APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Introduction.

Scientists use conic sections to map the trajectories of spacecraft in flight. The setting for this episode is a planned future flight to Mars.

Segment 2: Parabolic Paths.

The liftoff and pre-orbital path of the rock is described by a parabola. Students explore the properties of parabolas from the standpoint of the parametric equations that describe the horizontal and vertical directions of motion for the rocket.

Algebra concepts: conic sections, parabolas, functions, parametric equations

Segment 3: Circular Paths.

The path of a rocket orbiting the Earth can be modeled with the equation of a circle. Students explore the quadratic relation and the parametric equations that can be used to model the path of a spacecraft orbiting Earth.

Algebra concepts: conic sections, circles, equations of circles, functions

Segment 4: Elliptical Paths.

The planets orbiting the sun follow elliptical paths. In fact, the trajectory of a spacecraft traveling to Mars would also be elliptical. Students explore these various ellipses.

Algebra concepts: conic sections, ellipses, equations of ellipses, functions

Algebra Applications DVDs
Data Analysis

ALGEBRA APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Introduction

Students explore the dramatic events of 2008 related to the mortgage crisis.

Segment 2: What Is a Mortgage? 

The time value of money is at the basis of all loans. Students learn about the key factors that determine monthly mortgage payments and use the TI-Nspire to create an amortization table. This table is used throughout the rest of the program to explore different scenarios.

Algebra concepts: time value of money, data analysis

Segment 3: What Is a Subprime Mortgage?

Students use the amortization table to run probability simulations to determine possible loan defaults on subprime mortgages.

Algebra concepts: time value of money, data analysis

Segment 4: What Is an Adjustable Rate Mortgage?

Another factor in the mortgage crisis was the use of adjustable rate mortgages Students run a number of scenarios to test adjustable rate mortgages, while also taking into account the state of the housing market during the time of the mortgage crisis.

Algebra concepts: time value of money, data analysis

Algebra Applications DVDs
Exponential Functions

ALGEBRA APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Introduction. 

We visit ancient Greece to learn about the Platonic Solids. This provides an introduction to the more general topic of three-dimensional figures.

Segment 2: What Is an Earthquake?

The basic definition of an exponential function is shown in the intensity function for an earthquake. Students analyze data and perform an exponential regression based on data from the Sichuan earthquake.

Algebra concepts: exponential functions, inverse functions, logarithmic functions

Segment 3: How Is an Earthquake Measured?

An exponential model describes the intensity of an earthquake, while a logarithmic model describes the magnitude of an earthquake. In the process students learn about the inverse of an exponential function.

Algebra concepts: exponential functions, data analysis, logarithmic functions

Segment 4: What Is the Difference Between Intensity and Magnitude?

An earthquake is an example of a seismic wave. A wave can be modeled with a trigonometric function. Using the TI-Nspire, students link the amplitude to an exponential function to analyze the dramatic increase in intensity resulting from minor changes to magnitude.

Algebra concepts: exponential functions, trigonometric functions, composite functions

Algebra Applications DVDs
Logarithmic Functions

ALGEBRA APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: What Is a Logarithm?

The mathematical definition of a logarithm is the inverse of an exponential function, but why do we need to use logarithms?

Segment 2: Hearing Loss

Hearing loss. We live in a noisy world. In fact, prolonged exposure to noise can cause hearing loss. Students analyze the noise level at a rock concert and determine the ideal distance where the noise level is out of the harmful range.

Algebra concepts: logarithmic functions and equations, decibel scale

Segment 3: Tsunamis

In 1998 a devastating tsunami was triggered by a 7.0 magnitude earthquake off the coast of New Guinea. The amount of energy from this earthquake was equivalent to a thermonuclear explosion. Students analyze the energy outputs for different magnitude earthquakes.

Algebra concepts: logarithmic functions, logarithmic scale

Algebra Applications DVDs
Rational Functions

ALGEBRA APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Engineering

A submarine must withstand large amounts of water pressure; otherwise, a serious breach can occur. Rational functions are used to study the relationship between water pressure and volume. Students graph rational functions to study the forces at work with a submarine.

Algebra concepts: inverse variations, rational functions

Segment 2: Biology

All living things take up a certain amount of space, and therefore have volume. They also have a certain amount of surface area. The ratio of surface area to volume, which is a rational function, reveals important information about the organism. Students look at different graphs of these functions for different organisms.

Algebra concepts: rational functions, ratios, surface area, volume

Segment 3: The Hubble Telescope

The Hubble Telescope, like all telescopes, relies on the lens formula to focus an image. The lens formula results in a rational equation that can be solved for determining the settings on the lens.

Algebra concepts: lens formula, rational equations, functions

Algebra Applications DVDs
Systems of Equations

ALGEBRA APPLICATIONS DVDS: $39.99/SINGLE DISC.

Segment 1: Profit and Loss

Profit and loss are the key measures in a business. A system of equations that includes an equation for income and one for expenses can be used to determine profit and loss.

Algebra concepts: linear systems, linear functions, data analysis

Segment 2: Encryption

Secret codes and encryption are ideal examples of a system of equations.  In this activity, students encrypt and decrypt a message.

Algebra concepts: linear systems, matrices

Segment 3: Ballistic Missiles

A ballistic missile shield allows you to shoot incoming missiles out of the sky. Mathematically, this is an example of a quadratic system. Students graph such a system and find the points of intersection between two quadratic functions.

Algebra concepts: nonlinear functions