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.

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.

Video Tutorial: Ratios and Proportions: Scale Drawings. In this video, we look at the properties of similar figures and use proportions to find lengths of corresponding sides.

Video Tutorial: Ratios and Proportions: Solving Proportions. In this video, we solve proportion problems algebraically.

Video Tutorial: Ratios and Proportions: What are Proportions?. In this video, we solve proportion problems using equivalent ratios.

Video Tutorial: Ratios and Rates: Converting Measurement Units. In this video, we show how to use conversion rates to convert from one unit of measurement to another. Students are shown how to create a conversion rate.

Video Tutorial: Ratios and Rates: Rates and Slopes of Lines. In this video we connect the concept of rate of change for a set of linear data to the concept of slope. We use the slope formula to find the rate of change.

Video Tutorial: Ratios and Rates: Rates from Data. In this video, we look at linear data sets that can be used to find the rate of change.

Video Tutorial: Ratios and Rates: Ratios as Decimals. In this video, students explore ratios whose terms are decimals. Students are shown techniques for simplifying these types of ratios in ;the context of solving real-world ratio problems.

Video Tutorial: Ratios and Percents: Calculating Percents. In this video, students will see the relationship between ratios, proportions, and percents. A percent formula is derived and used to solve several real-world percent problems.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. Let's look at an example.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. Let's look at an example.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

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 asymptote is a line that a graph approaches but never touches.

Description

Asymptotes are significant in the study of Rational Numbers, Expressions, Equations, and Functions. They help in understanding the behavior of graphs of rational functions, particularly as the values of the variables approach certain limits. Horizontal asymptotes indicate the value that the function approaches as the input grows infinitely large or small. Vertical asymptotes show the values that the function cannot take because they cause division by zero.

Topic

Rationals and Radicals

Definition

The conjugate of a radical expression is obtained by changing the sign between two terms in a binomial.

Description

In the context of Radical Numbers, Expressions, Equations, and Functions, the concept of conjugates is essential for simplifying expressions. When dealing with radicals, particularly in the denominator, multiplying by the conjugate can help to rationalize the expression. This process eliminates the radical from the denominator, making the expression easier to work with.

Topic

Rationals and Radicals

Definition

The cube root of a number is a value that, when multiplied by itself three times, gives the original number.

Description

The cube root is a fundamental concept in Radical Numbers, Expressions, Equations, and Functions. It is the inverse operation of raising a number to the power of three. Understanding cube roots is crucial for solving equations involving cubic terms and for simplifying radical expressions.

Cube roots also appear in various real-world applications, such as calculating volumes and in certain physics equations. They are an integral part of higher-level mathematics, including algebra and calculus.

Topic

Rationals and Radicals

Definition

An extraneous solution is a solution derived from an equation that is not a valid solution to the original equation.

Description

Extraneous solutions often arise in the context of Rational and Radical Equations. They are solutions that appear during the process of solving an equation but do not satisfy the original equation. This can happen when both sides of an equation are squared or when other operations introduce additional solutions.

Topic

Rationals and Radicals

Definition

Factoring a radical involves expressing it as a product of simpler expressions.

Description

Factoring radicals is a key technique in the study of Radical Numbers, Expressions, Equations, and Functions. It simplifies complex radical expressions, making them easier to work with. This process is essential for solving equations and for performing algebraic manipulations involving radicals.

Understanding how to factor radicals is also important for simplifying expressions in calculus and higher-level mathematics. It helps in breaking down complex problems into more manageable parts.

Topic

Rationals and Radicals

Definition

The fourth root of a number is a value that, when raised to the power of four, gives the original number.

Description

The fourth root is an important concept in Radical Numbers, Expressions, Equations, and Functions. It is the inverse operation of raising a number to the power of four. Understanding fourth roots is crucial for solving higher-degree equations and for simplifying radical expressions.

Fourth roots are also relevant in various scientific and engineering applications where higher-degree roots are required. They are a part of advanced mathematical studies, including algebra and calculus.