Illustrative Math Alignment: Grade 7 Unit 5

Overview

In this episode of Algebra Applications, students explore various scenarios that can be explained through the use of rational functions. Such disparate phenomena as submarines, photography, and the appearance of certain organisms can be explained through rational function models.

This is part of a collection of videos from the Algebra Applications video series on the topic of Rational Functions.

In this TI Nspire tutorial for the TI-Nspire CAS, the Calculator Window is used to combine and simplify rational expressions. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .

In this episode of Algebra Applications, students explore various scenarios that can be explained through the use of rational functions. Such disparate phenomena as submarines, photography, and the appearance of certain organisms can be explained through rational function models.

In spite of their massive size, submarines are precision instruments. 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.

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.

The Hubble Telescope has transformed how we view the universe. We learn about the lens formula and how it is used in the construction of telescopes.

After briefly reviewing the concept of inverse variation, this video explores Boyle’s law, a real world example of an inversely proportional relationship between pressure and volume of a gas. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, it goes on to examine similarities and differences among rational functions and numbers. Finally, it takes a look at rational functions graphs and ends with a delightful example merging Euclidean and analytic geometry, thanks to the TI-Nspire technology. Concepts explored: functions, rational expressions, rational functions, asymptotes

In this Investigation we look at an application of rational functions: Boyle's Law. This video is Segment 1 of a 4 segment series related to Algebra Nspirations: Rational Functions and Expressions. Segments 1 and 2 are grouped together.

In this Investigation we look at graphs of rational functions. This video is Segment 3 of a 4 segment series related to Algebra Nspirations: Rational Functions and Expressions. Segments 3 and 4 are grouped together.

Description

This is part of a collection of video tutorials the topic of Algebra Tiles.This series of videos describes what algebra tiles are and how they can be used to model numbers, operations, expressions, and equations. Use this series if you are incorporating the use of algebra tiles in your instruction.

The following section reviews the basics of algebra tiles. Use this material as background material, and also as a supplement to the video series.

In this TI Nspire tutorial for the TI-Nspire CAS, the Calculator Window is used to multiply rational expressions. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

In this TI Nspire tutorial for the TI-Nspire CAS, the Calculator Window is used to combine and simplify rational expressions. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .

Topic

Rationals and Radicals

Definition

An irrational number is a number that cannot be expressed as a ratio of two integers. Its decimal form is non-repeating and non-terminating.

Topic

Rationals and Radicals

Definition

An irrational number is a number that cannot be expressed as a ratio of two integers. Its decimal form is non-repeating and non-terminating.

Topic

Rationals and Radicals

Definition

The laws of rational exponents describe how to handle exponents that are fractions, including rules for multiplication, division, and raising a power to a power.

Description

The Laws of Rational Exponents are vital in the study of Rational Numbers, Expressions, Equations, and Functions. These laws provide a framework for simplifying expressions involving exponents that are fractions. For example, the law

 $$a^{m/n} = \sqrt[n]{a^m}$$ 

Topic

Rationals and Radicals

Definition

Partial fraction decomposition is a method used to express a rational expression as a sum of simpler fractions.

Description

Partial Fraction Decomposition is a powerful tool in the study of Rational Numbers, Expressions, Equations, and Functions. It involves breaking down a complex rational expression into a sum of simpler fractions, which are easier to integrate or differentiate. For example, the rational function 

$$\frac{2x+3}{(x+1)(x-2)}$$

can be decomposed into 

Topic

Rationals and Radicals

Definition

A rational exponent is an exponent that is a fraction, where the numerator indicates the power and the denominator indicates the root.

Description

Rational Exponents are a crucial concept in the study of Rational Numbers, Expressions, Equations, and Functions. These exponents are fractions, where the numerator indicates the power and the denominator indicates the root. For example, the expression 

$$a^{m/n}$$

can be rewritten as 

$$\sqrt[n]{a^m}$$

Topic

Rationals and Radicals

Definition

Rational expressions are fractions in which the numerator and/or the denominator are polynomials.

Description

Rational Expressions are a fundamental aspect of Rational Numbers, Expressions, Equations, and Functions. These expressions are fractions where the numerator and/or the denominator are polynomials. Simplifying rational expressions often involves factoring the polynomials and canceling common factors. For example, the rational expression 

$$\frac{x^2 - 1}{x - 1}$$

can be simplified to x + 1, provided that 

$$x \neq 1$$

Topic

Rationals and Radicals

Definition

Simplifying a rational expression involves reducing the fraction to its lowest terms by factoring both the numerator and denominator and canceling common factors.

Description

Simplifying a Rational Expression is a crucial skill in the study of Rational Numbers, Expressions, Equations, and Functions. This process involves reducing a rational expression to its simplest form by factoring both the numerator and denominator and canceling common factors. For example, simplifying 

$$\frac{x^2 - 1}{x - 1}$$

results in x + 1 for 

In this Slide Show, learn how to add and subtract rational numbers. Includes links to several Media4Math videos and a math game.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

This set of tutorials provides 12 examples of multiplying integers.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

The complete set of 28 examples that make up this set of tutorials.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

This set of tutorials provides 28 examples of rational functions in tabular and graph form.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

In this tutorial students learn about rational expressions and use the properties of fractions to combine them.

—Press PREVIEW to see the tutorial—

Use this Jeopardy-style math game to review integer operations. This Jeopardy game has a bank of hundreds of questions for thousands of unique game experiences. Best viewed in Chrome. To see the complete set of Math Games and Puzzles, click on this link.

Related Resources

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library