Use the following Media4Math resources with this Illustrative Math lesson.
Thumbnail Image | Title | Body | Curriculum Topics |
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Math Clip Art--Angle Illustrations--Straight Angle--Unlabeled | Math Clip Art--Angle Illustrations--Straight Angle--Unlabeled
This is part of a collection of clip art images showing different types of angles. Each type of angle measure includes a labeled and unlabeled version. |
Angles and Applications of Angles and Planes | |
Math Clip Art--Angle Illustrations--Supplementary Angles--Labeled | Math Clip Art--Angle Illustrations--Supplementary Angles--Labeled
This is part of a collection of clip art images showing different types of angles. Each type of angle measure includes a labeled and unlabeled version. |
Angles and Applications of Angles and Planes | |
Math Clip Art--Angle Illustrations--Supplementary Angles--Unlabeled | Math Clip Art--Angle Illustrations--Supplementary Angles--Unlabeled
This is part of a collection of clip art images showing different types of angles. Each type of angle measure includes a labeled and unlabeled version. |
Angles and Applications of Angles and Planes | |
Definition--Rationals and Radicals--Cube Root | Cube RootTopicRationals and Radicals DefinitionThe cube root of a number is a value that, when multiplied by itself three times, gives the original number. DescriptionThe 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. |
Radical Expressions | |
Definition--Rationals and Radicals--Extraneous Solution | Extraneous SolutionTopicRationals and Radicals DefinitionAn extraneous solution is a solution derived from an equation that is not a valid solution to the original equation. DescriptionExtraneous 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. |
Rational Functions and Equations | |
Definition--Rationals and Radicals--Graphs of Rational Functions | Graphs of Rational FunctionsTopicRationals and Radicals DefinitionGraphs of rational functions are visual representations of equations involving rational expressions. DescriptionGraphs of rational functions are fundamental in the study of Rational Numbers, Expressions, Equations, and Functions. They help in understanding the behavior of these functions, including their asymptotes, intercepts, and regions of increase and decrease. |
Rational Functions and Equations | |
Definition--Rationals and Radicals--Inverse Variation | Inverse VariationTopicRationals and Radicals DefinitionInverse variation describes a relationship between two variables in which the product is a constant. When one variable increases, the other decreases proportionally. |
Rational Functions and Equations | |
Definition--Rationals and Radicals--Irrational Number 2 | Irrational Number 2TopicRationals and Radicals DefinitionAn irrational number is a number that cannot be expressed as a ratio of two integers. Its decimal form is non-repeating and non-terminating. |
Rational Expressions | |
Definition--Rationals and Radicals--nth Root | nth RootTopicRationals and Radicals DefinitionThe nth root of a number is a value that, when raised to the power of n, gives the original number. It is denoted as $$\sqrt[n]{a}$$ DescriptionThe nth Root is a fundamental concept in the study of Radical Numbers, Expressions, Equations, and Functions. It generalizes the idea of square roots and cube roots to any positive integer n. For example, the cube root of 8 is 2 because $$2^3 = 8$$ |
Radical Expressions | |
Definition--Order of Operations | Definition--Order of Operations
Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
A numerical expression includes numbers and operation symbols, addition, subtraction, multiplication, and division. Because addition is commutative, adding from left to right, or right to left, gives you the same result. The expressions 2 + 3 and 3 + 2 give the same result. But this isn't the case with all operations. Subtraction isn't commutative. |
Numerical Expressions and Variable Expressions | |
Definition--Ratios, Proportions, and Percents Concepts--Percent | PercentTopicRatios, Proportions, and Percents DefinitionA percent is a ratio that compares a number to 100. DescriptionPercentages are a fundamental concept in mathematics, representing a ratio out of 100. They are used in various applications, including finance, statistics, and everyday calculations such as discounts and interest rates. For example, if you score 45 out of 50 on a test, your percentage score is (45/50) × 100 = 90% |
Percents | |
Definition--Ratios, Proportions, and Percents Concepts--Proportional | ProportionalTopicRatios, Proportions, and Percents DefinitionProportional refers to the relationship between two quantities where their ratio is constant. DescriptionProportional relationships are fundamental in mathematics and science, describing how one quantity changes in relation to another. This concept is used in various fields, including physics, economics, and engineering. For example, if the speed of a car is proportional to the time it travels, doubling the time will double the distance covered. Understanding proportionality helps students solve complex problems and apply mathematical reasoning in real-world situations. |
Proportions | |
Definition--Rationals and Radicals--Radical Expression | Radical ExpressionTopicRationals and Radicals DefinitionA radical expression is an expression that contains a radical symbol, which indicates the root of a number. DescriptionRadical Expressions are a core component of Radical Numbers, Expressions, Equations, and Functions. These expressions involve roots, such as square roots, cube roots, or higher-order roots, and are denoted by the radical symbol (√). For example, the expression $$\sqrt{16}$$ |
Radical Expressions | |
Definition--Rationals and Radicals--Radical Function | Radical FunctionTopicRationals and Radicals DefinitionA radical function is a function that contains a radical expression with the independent variable in the radicand. DescriptionRadical Functions are a vital part of Radical Numbers, Expressions, Equations, and Functions. These functions involve radicals, such as square roots or cube roots, with the independent variable inside the radical. For example, the function $$f(x) = \sqrt{x}$$ |
Radical Expressions | |
Definition--Rationals and Radicals--Radical Symbol | Radical SymbolTopicRationals and Radicals DefinitionThe radical symbol (√) is used to denote the root of a number, such as a square root or cube root. DescriptionThe Radical Symbol is a fundamental notation in the study of Radical Numbers, Expressions, Equations, and Functions. This symbol (√) indicates the root of a number, with the most common being the square root. For example, the expression $$\sqrt{25}$$ |
Radical Expressions | |
Definition--Rationals and Radicals--Radicand | RadicandTopicRationals and Radicals DefinitionThe radicand is the number or expression inside the radical symbol that is being rooted. DescriptionThe Radicand is a key component in the study of Radical Numbers, Expressions, Equations, and Functions. It is the number or expression inside the radical symbol that is being rooted. For example, in the expression $$\sqrt{49}$$ |
Radical Expressions | |
Definition--Ratios, Proportions, and Percents Concepts--Rate | RateTopicRatios, Proportions, and Percents DefinitionA rate is a ratio that compares two quantities with different units. DescriptionRates are used to compare different quantities, such as speed (miles per hour) or price (cost per item). Understanding rates is essential for interpreting data and making informed decisions in various contexts, such as travel and budgeting. For instance, if a car travels 60 miles in 2 hours, the rate is 30 miles per hour. Learning about rates helps students analyze real-world situations and apply mathematical reasoning to everyday problems. |
Ratios and Rates | |
Definition--Ratios, Proportions, and Percents Concepts--Ratio | RatioTopicRatios, Proportions, and Percents DefinitionA ratio is a comparison of two quantities by division. DescriptionRatios are used to express the relationship between two quantities, providing a way to compare different amounts. They are fundamental in various fields, including mathematics, science, and finance. For example, the ratio of 4 to 5 can be written as 4:5 or 4/5. Understanding ratios helps students analyze data, solve problems, and make informed decisions in real-world situations. |
Ratios and Rates | |
Definition--Rationals and Radicals--Rational Expressions | Rational ExpressionsTopicRationals and Radicals DefinitionRational expressions are fractions in which the numerator and/or the denominator are polynomials. DescriptionRational 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 $$x \neq 1$$ |
Rational Expressions | |
Definition--Rationals and Radicals--Rational Functions | Rational FunctionsTopicRationals and Radicals DefinitionRational functions are functions that are the ratio of two polynomials. DescriptionRational Functions are a key concept in the study of Rational Numbers, Expressions, Equations, and Functions. These functions are the ratio of two polynomials, such as $$f(x) = \frac{P(x)}{Q(x)}$$ where P(x) and Q(x) are polynomials. Understanding rational functions involves analyzing their behavior, including identifying asymptotes, intercepts, and discontinuities. For example, the function $$f(x) = \frac{1}{x}$$ |
Rational Functions and Equations | |
Definition--Rationals and Radicals--Rational Numbers | Rational NumbersTopicRationals and Radicals DefinitionRational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero. |
Rational Functions and Equations | |
Definition--Ratios, Proportions, and Percents Concepts--Scale Drawing | Scale DrawingTopicRatios, Proportions, and Percents DefinitionA scale drawing is a representation of an object or structure with dimensions proportional to the actual object or structure. DescriptionScale drawings are essential in fields like architecture, engineering, and cartography, where accurate representations of large objects or areas are needed. For example, an architect might create a scale drawing of a building where 1 inch on the drawing represents 10 feet in reality. This allows for detailed planning and visualization without needing a full-sized model. |
Proportions | |
Definition--Ratios, Proportions, and Percents Concepts--Solving Proportions | Solving ProportionsTopicRatios, Proportions, and Percents DefinitionSolving proportions involves finding the value of a variable that makes two ratios equal. DescriptionSolving proportions is a key skill in algebra and is used in various applications, such as scaling recipes, converting units, and solving real-world problems. For example, if you know that 2/3 = x/6 you can solve for x by cross-multiplying to get 2 * 6 = 3 * x leading to x = 4 |
Proportions | |
Definition--Rationals and Radicals--Square Root | Square RootTopicRationals and Radicals DefinitionThe square root of a number is a value that, when multiplied by itself, gives the number. It is denoted by the radical symbol √. |
Radical Expressions | |
INSTRUCTIONAL RESOURCE: Tutorial: Adding and Subtracting Rational Numbers | INSTRUCTIONAL RESOURCE: Tutorial: Adding and Subtracting Rational Numbers
In this Slide Show, learn how to add and subtract rational numbers. Includes links to several Media4Math videos and a math game. This is part of a collection of tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file.Library of Instructional ResourcesTo see the complete library of Instructional Resources , click on this link. |
Rational Expressions and Rational Functions and Equations | |
Instructional Resource: Applications of Linear Functions: Speed and acceleration | In this Slide Show, apply concepts of linear functions to the context of speed and acceleration. Note: The download is a PPT file. Related ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN |
Applications of Linear Functions | |
INSTRUCTIONAL RESOURCE: Desmos Tutorial: Matching Coordinates to Rational Functions | INSTRUCTIONAL RESOURCE: Desmos Tutorial: Matching Coordinates to Rational Functions
In this Slide Show, use the Desmos graphing calculator to explore rational functions. To see the complete collection of Desmos Resources click on this link. Note: The download is a PPT file. This is part of a collection of Desmos tutorials on a variety of math topics. To see the complete collection of these resources, click on this link.Library of Instructional ResourcesTo see the complete library of Instructional Resources , click on this link. |
Rational Functions and Equations | |
Math in the News: Issue 50--March Madness Made Rational | Math in the News: Issue 50--March Madness Made Rational
March 2012. In this issue we look at March Madness mathematically. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis | |
Math in the News: Issue 59--The Butterfly Migration | Math in the News: Issue 59--The Butterfly Migration
September 2012. In this issue of Math in the News we look at the great Monarch butterfly migration. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis | |
Math in the News: Issue 61--The Butterfly Migration Update | Math in the News: Issue 61--The Butterfly Migration Update
September 2012. In this issue of Math in the News we look at the Monarch Butterfly Migration with new data since our last investigation of it. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis | |
VIDEO: Algebra Applications: Rational Functions | VIDEO: Algebra Applications: Rational Functions
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. |
Rational Expressions and Rational Functions and Equations | |
VIDEO: Algebra Applications: Rational Functions, 1 | VIDEO: Algebra Applications: Rational Functions, Segment 1: Submarines
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. This is part of a collection of videos from the Algebra Applications video series on the topic of Rational Functions. |
Rational Expressions and Rational Functions and Equations | |
VIDEO: Algebra Applications: Rational Functions, 2 | VIDEO: Algebra Applications: 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. This is part of a collection of videos from the Algebra Applications video series on the topic of Rational Functions. |
Rational Expressions and Rational Functions and Equations | |
VIDEO: Algebra Applications: Rational Functions, 3 | VIDEO: Algebra Applications: Rational Functions, Segment 3: Hubble Telescope
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. This is part of a collection of videos from the Algebra Applications video series on the topic of Rational Functions. |
Rational Expressions and Rational Functions and Equations | |
VIDEO: Algebra Nspirations: Data Analysis and Probability | VIDEO: Algebra Nspirations: Data Analysis and Probability
What are the two meanings of statistics? What does it really mean that an event has a 50% probability of occurring? Why are data analysis and probability always taught together? Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video answers these questions and addresses fundamental concepts such as the law of large numbers and the notion of regression analysis. Both engaging investigations are based on true stories and real data, utilize different Nspire applications, and model the seamless connection among various problem representations. Concepts explored: statistics, data analysis, regression analysis. |
Data Analysis and Data Gathering | |
VIDEO: Algebra Nspirations: Data Analysis and Probability, 1 | VIDEO: Algebra Nspirations: Data Analysis and Probability, Segment 1
What are the two meanings of statistics? What does it really mean that an event has a 50% probability of occurring? Why are data analysis and probability always taught together? Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video answers these questions and addresses fundamental concepts such as the law of large numbers and the notion of regression analysis. Both engaging investigations are based on true stories and real data, utilize different Nspire applications, and model the seamless connection among various problem representations. Concepts explored: statistics, data analysis, regression analysis. |
Data Analysis and Data Gathering | |
VIDEO: Algebra Nspirations: Data Analysis and Probability, 2 | VIDEO: Algebra Nspirations: Data Analysis and Probability, Segment 2
What are the two meanings of statistics? What does it really mean that an event has a 50% probability of occurring? Why are data analysis and probability always taught together? Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video answers these questions and addresses fundamental concepts such as the law of large numbers and the notion of regression analysis. Both engaging investigations are based on true stories and real data, utilize different Nspire applications, and model the seamless connection among various problem representations. Concepts explored: statistics, data analysis, regression analysis. |
Data Analysis and Data Gathering | |
VIDEO: Algebra Nspirations: Data Analysis and Probability, 3 | VIDEO: Algebra Nspirations: Data Analysis and Probability, Segment 3
What are the two meanings of statistics? What does it really mean that an event has a 50% probability of occurring? Why are data analysis and probability always taught together? Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video answers these questions and addresses fundamental concepts such as the law of large numbers and the notion of regression analysis. Both engaging investigations are based on true stories and real data, utilize different Nspire applications, and model the seamless connection among various problem representations. Concepts explored: statistics, data analysis, regression analysis. |
Data Analysis and Data Gathering | |
VIDEO: Algebra Nspirations: Data Analysis and Probability, 4 | VIDEO: Algebra Nspirations: Data Analysis and Probability, Segment 4
What are the two meanings of statistics? What does it really mean that an event has a 50% probability of occurring? Why are data analysis and probability always taught together? Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video answers these questions and addresses fundamental concepts such as the law of large numbers and the notion of regression analysis. Both engaging investigations are based on true stories and real data, utilize different Nspire applications, and model the seamless connection among various problem representations. Concepts explored: statistics, data analysis, regression analysis. |
Data Analysis and Data Gathering | |
VIDEO: Algebra Nspirations: Variables and Equations | VIDEO: Algebra Nspirations: Variables and Equations
Ever since the mathematics of the Babylonians, equations have played a central role in the development of algebra. Written and hosted by internationally acclaimed mathematics educator Dr. Monica Neagoy, this video traces the history and evolution of equations. It explores the two principal equations encountered in an introductory algebra course--linear and quadratic--in an engaging way. The foundations of algebra are explored and fundamental questions about the nature of algebra are answered. In addition, problems involving linear and quadratic equations are solved using the TI-Nspire graphing calculator. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. |
Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions | |
VIDEO: Algebra Nspirations: Variables and Equations, 1 | VIDEO: Algebra Nspirations: Variables and Equations, Segment 1
In this Investigation we get a historical overview of equations. This video is Segment 1 of a 2 segment series related to Variables and Equations. |
Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions | |
VIDEO: Algebra Nspirations: Variables and Equations, 2 | VIDEO: Algebra Nspirations: Variables and Equations, Segment 2
In this Math Lab a hands-on activity has students comparing the diameter of a circle and its circumference. This video is Segment 2 of a 2 segment series related to Variables and Equations. |
Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions | |
VIDEO: Algebra Nspirations: Variables and Equations, 3 | VIDEO: Algebra Nspirations: Variables and Equations, Segment 3
Watch this video about variables and equations. (The transcript is included.) Video Transcript
From the mathematics of old Babylon and Egypt, to the mathematics of ancient Greece, China, India, the Islamic world, and all the way up to the Renaissance and the present, equations have played a central role in the development of algebra. But algebraic equations haven't always been written in present day symbolic form. |
Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions | |
VIDEO: Algebra Nspirations: Variables and Equations, 4 | VIDEO: Algebra Nspirations: Variables and Equations, Segment 4
In this Math Lab we look at an area model for expanding the product of two binomials. This video is Segment 4 of a 4-segment series related to Variables and Equations. |
Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions | |
VIDEO: Algebra Nspirations: Exponents | VIDEO: Algebra Nspirations: Exponents and Exponential Functions
Almost everyone has an intuitive understanding that exponential growth means rapid growth. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video builds on students' intuitive notions, explores exponential notation, and analyzes properties of exponential function graphs, with the help of TI-Nspire features such as sliders and graph transformations. Using exponential functions to model finance applications and a Newton’s law of cooling problem further help students build a solid foundation for these fundamental algebraic concepts. Concepts explored: functions, exponents, exponential functions. —PRESS PREVIEW TO SEE THE VIDEO—This is part of a collection of videos from the Algebra Applications video series on the topic of Exponential Functions. |
Applications of Exponential and Logarithmic Functions, Exponential and Logarithmic Functions and Equations and Graphs of Exponential and Logarithmic Functions | |
VIDEO: Algebra Nspirations: Exponents, 1 | VIDEO: Algebra Nspirations: Exponents and Exponential Functions, Segment 1
In this episode of Algebra Applications, students explore earthquakes using exponential models. In particular, students analyze the earthquake that struck the Sichuan Province in China in 2008, months before the Beijing Olympics. This dramatic, real-world example allows students to apply their understanding of exponential functions and their inverses, along with data analysis and periodic function analysis. —PRESS PREVIEW TO SEE THE VIDEO—This is part of a collection of videos from the Algebra Applications video series on the topic of Exponential Functions. |
Applications of Exponential and Logarithmic Functions, Exponential and Logarithmic Functions and Equations and Graphs of Exponential and Logarithmic Functions | |
VIDEO: Algebra Nspirations: Exponents, 2 | VIDEO: Algebra Nspirations: Exponents and Exponential Functions, Segment 2
In this episode of Algebra Applications, students explore earthquakes using exponential models. In particular, students analyze the earthquake that struck the Sichuan Province in China in 2008, months before the Beijing Olympics. This dramatic, real-world example allows students to apply their understanding of exponential functions and their inverses, along with data analysis and periodic function analysis. —PRESS PREVIEW TO SEE THE VIDEO—This is part of a collection of videos from the Algebra Applications video series on the topic of Exponential Functions. |
Applications of Exponential and Logarithmic Functions, Exponential and Logarithmic Functions and Equations and Graphs of Exponential and Logarithmic Functions | |
VIDEO: Algebra Nspirations: Exponents, 3 | VIDEO: Algebra Nspirations: Exponents and Exponential Functions, Segment 3
In this episode of Algebra Applications, students explore earthquakes using exponential models. In particular, students analyze the earthquake that struck the Sichuan Province in China in 2008, months before the Beijing Olympics. This dramatic, real-world example allows students to apply their understanding of exponential functions and their inverses, along with data analysis and periodic function analysis. —PRESS PREVIEW TO SEE THE VIDEO—This is part of a collection of videos from the Algebra Applications video series on the topic of Exponential Functions. |
Applications of Exponential and Logarithmic Functions, Exponential and Logarithmic Functions and Equations and Graphs of Exponential and Logarithmic Functions | |
VIDEO: Algebra Nspirations: Exponents, 4 | VIDEO: Algebra Nspirations: Exponents and Exponential Functions, Segment 4
In this episode of Algebra Applications, students explore earthquakes using exponential models. In particular, students analyze the earthquake that struck the Sichuan Province in China in 2008, months before the Beijing Olympics. This dramatic, real-world example allows students to apply their understanding of exponential functions and their inverses, along with data analysis and periodic function analysis. —PRESS PREVIEW TO SEE THE VIDEO—This is part of a collection of videos from the Algebra Applications video series on the topic of Exponential Functions. |
Applications of Exponential and Logarithmic Functions, Exponential and Logarithmic Functions and Equations and Graphs of Exponential and Logarithmic Functions | |
VIDEO: Algebra Nspirations: Functions and Relations | VIDEO: Algebra Nspirations: Functions and Relations
Functions are relationships between quantities that change. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video explores the definition of a function, its vocabulary and notations, and distinguishes the concept of function from a general relation. Multiple representations of functions are provided using the TI-Nspire, while dynamic visuals and scenarios put them into real-world contexts. Concepts explored: functions, relations, equations, quadratic functions, linear functions, multiple representations. |
Applications of Functions and Relations, Quadratic Equations and Functions and Relations and Functions |