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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 6 Unit 9

Putting it All Together

Lesson 4: How Do We Choose?

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topics
Math Clip Art--Straight Angle--Unlabeled 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--Supplementary Angles--Labeled 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--Supplementary Angles--Unlabeled 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 Definition--Rationals and Radicals--Cube Root Cube Root

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.

Radical Expressions
Definition--Rationals and Radicals--Extraneous Solution Definition--Rationals and Radicals--Extraneous Solution Extraneous Solution

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.

Rational Functions and Equations
Definition--Rationals and Radicals--Graphs of Rational Functions Definition--Rationals and Radicals--Graphs of Rational Functions Graphs of Rational Functions

Topic

Rationals and Radicals

Definition

Graphs of rational functions are visual representations of equations involving rational expressions.

Description

Graphs 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 Definition--Rationals and Radicals--Inverse Variation Inverse Variation

Topic

Rationals and Radicals

Definition

Inverse 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 Definition--Rationals and Radicals--Irrational Number 2 Irrational Number 2

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.

Rational Expressions
Definition--Rationals and Radicals--nth Root Definition--Rationals and Radicals--nth Root nth Root

Topic

Rationals and Radicals

Definition

The nth root of a number is a value that, when raised to the power of n, gives the original number. It is denoted as $$\sqrt[n]{a}$$

Description

The 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--OrderOfOperations.jpg 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 Definition--Ratios, Proportions, and Percents Concepts--Percent Percent

Topic

Ratios, Proportions, and Percents

Definition

A percent is a ratio that compares a number to 100.

Description

Percentages 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 Definition--Ratios, Proportions, and Percents Concepts--Proportional Proportional

Topic

Ratios, Proportions, and Percents

Definition

Proportional refers to the relationship between two quantities where their ratio is constant.

Description

Proportional 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 Definition--Rationals and Radicals--Radical Expression Radical Expression

Topic

Rationals and Radicals

Definition

A radical expression is an expression that contains a radical symbol, which indicates the root of a number.

Description

Radical 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 Definition--Rationals and Radicals--Radical Function Radical Function

Topic

Rationals and Radicals

Definition

A radical function is a function that contains a radical expression with the independent variable in the radicand.

Description

Radical 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 Definition--Rationals and Radicals--Radical Symbol Radical Symbol

Topic

Rationals and Radicals

Definition

The radical symbol (√) is used to denote the root of a number, such as a square root or cube root.

Description

The 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 Definition--Rationals and Radicals--Radicand Radicand

Topic

Rationals and Radicals

Definition

The radicand is the number or expression inside the radical symbol that is being rooted.

Description

The 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 Definition--Ratios, Proportions, and Percents Concepts--Rate Rate

Topic

Ratios, Proportions, and Percents

Definition

A rate is a ratio that compares two quantities with different units.

Description

Rates 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 Definition--Ratios, Proportions, and Percents Concepts--Ratio Ratio

Topic

Ratios, Proportions, and Percents

Definition

A ratio is a comparison of two quantities by division.

Description

Ratios 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 Definition--Rationals and Radicals--Rational Expressions Rational Expressions

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 

$$x \neq 1$$

Rational Expressions
Definition--Rationals and Radicals--Rational Functions Definition--Rationals and Radicals--Rational Functions Rational Functions

Topic

Rationals and Radicals

Definition

Rational functions are functions that are the ratio of two polynomials.

Description

Rational 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 Definition--Rationals and Radicals--Rational Numbers Rational Numbers

Topic

Rationals and Radicals

Definition

Rational 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 Definition--Ratios, Proportions, and Percents Concepts--Scale Drawing Scale Drawing

Topic

Ratios, Proportions, and Percents

Definition

A scale drawing is a representation of an object or structure with dimensions proportional to the actual object or structure.

Description

Scale 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 Definition--Ratios, Proportions, and Percents Concepts--Solving Proportions Solving Proportions

Topic

Ratios, Proportions, and Percents

Definition

Solving proportions involves finding the value of a variable that makes two ratios equal.

Description

Solving 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 Definition--Rationals and Radicals--Square Root Square Root

Topic

Rationals and Radicals

Definition

The 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 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 Resources

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

Rational Expressions and Rational Functions and Equations
PowerPointPresentations.jpg 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 Resources

To 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 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 Resources

To 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 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 Resources

To 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 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 Resources

To 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 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 Resources

To 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 VIDEO: Algebra Applications: Rational Functions

Topic

Rational Functions

Rational Expressions and Rational Functions and Equations
VIDEO: Algebra Applications: Rational Functions, Segment 1: Submarines VIDEO: Algebra Applications: Rational Functions, 1 VIDEO: Algebra Applications: Rational Functions, 1

Topic

Rational Functions

Description

Explains submarine pressure and volume relationships using rational functions, illustrating depth impacts on vessel integrity and scuba safety.

Relevance: This video provides a practical perspective on Rational Functions, making abstract concepts more accessible through real-world applications.

Rational Expressions and Rational Functions and Equations
VIDEO: Algebra Applications: Rational Functions, Segment 2: Biology VIDEO: Algebra Applications: Rational Functions, 2 VIDEO: Algebra Applications: Rational Functions, 2

Topic

Rational Functions

Description

Examines surface area to volume ratios in animals using rational functions, connecting these ratios to evolutionary adaptations in different climates.

Relevance: This video provides a practical perspective on Rational Functions, making abstract concepts more accessible through real-world applications.

Rational Expressions and Rational Functions and Equations
VIDEO: Algebra Applications: Rational Functions, Segment 3: Hubble Telescope VIDEO: Algebra Applications: Rational Functions, 3 VIDEO: Algebra Applications: Rational Functions, 3

Topic

Rational Functions

Description

Demonstrates the optics of the Hubble telescope through rational functions, analyzing lens properties and asymptotes for image clarity.

Relevance: This video provides a practical perspective on Rational Functions, making abstract concepts more accessible through real-world applications.

Rational Expressions and Rational Functions and Equations
VIDEO: Algebra Nspirations: Data Analysis and Probability VIDEO: Algebra Nspirations: Data Analysis and Probability VIDEO: Algebra Nspirations: Data Analysis and Probability

Topic

Data Analysis

Data Analysis and Data Gathering
VIDEO: Algebra Nspirations: Data Analysis and Probability, Segment 1 VIDEO: Algebra Nspirations: Data Analysis and Probability, 1 VIDEO: Algebra Nspirations: Data Analysis and Probability, 1

Topic

Data Analysis

Description

This video introduces probability and statistics, differentiating between the two fields through historical context and practical applications. Concepts like the law of large numbers and randomness are explored using tools like the TI-Nspire. Key vocabulary includes probability, randomness, statistics, and law of large numbers. Applications include analyzing probabilities in real-world scenarios such as lightning strikes and coin flips.

Data Analysis and Data Gathering
VIDEO: Algebra Nspirations: Data Analysis and Probability, Segment 2 VIDEO: Algebra Nspirations: Data Analysis and Probability, 2 VIDEO: Algebra Nspirations: Data Analysis and Probability, 2

Topic

Data Analysis

Description

In this Math Lab video, students explore the probability distribution from tossing two coins.

This video provides an in-depth look at Data Analysis by exploring real-world applications. It delves into in this math lab video, students explore the probability distribution from tossing two coins.

The relevance of this video to the topic lies in its ability to connect theoretical concepts to practical scenarios. Students will gain insights into how these mathematical ideas are applied in data analysis.

Data Analysis and Data Gathering
VIDEO: Algebra Nspirations: Data Analysis and Probability, Segment 3 VIDEO: Algebra Nspirations: Data Analysis and Probability, 3 VIDEO: Algebra Nspirations: Data Analysis and Probability, 3

Topic

Data Analysis

Description

Building on Part 1, this video focuses on statistical representation and interpretation. Concepts include univariate and bivariate data, regression, and data visualization techniques like bar graphs and scatter plots. Applications include analyzing dog breeds and wolf population trends using data models. Key terms include univariate, bivariate, regression, and scatter plot.

Data Analysis and Data Gathering
VIDEO: Algebra Nspirations: Data Analysis and Probability, Segment 4 VIDEO: Algebra Nspirations: Data Analysis and Probability, 4 VIDEO: Algebra Nspirations: Data Analysis and Probability, 4

Topic

Data Analysis

Description

In this Math Lab video, students explore population data.

This video provides an in-depth look at Data Analysis by exploring real-world applications. It delves into in this math lab video, students explore population data.

The relevance of this video to the topic lies in its ability to connect theoretical concepts to practical scenarios. Students will gain insights into how these mathematical ideas are applied in data analysis.

Data Analysis and Data Gathering
VIDEO: Algebra Nspirations: Variables and Equations VIDEO: Algebra Nspirations: Variables and Equations VIDEO: Algebra Nspirations: Variables and Equations

Topic

Equations

Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions
VIDEO: Algebra Nspirations: Variables and Equations, Segment 1 VIDEO: Algebra Nspirations: Variables and Equations, 1 VIDEO: Algebra Nspirations: Variables and Equations, 1

Topic

Equations

Description

This video covers the historical evolution of equations, the role of variables, constants, and parameters, and introduces linear and quadratic equations. Key vocabulary includes symbolic algebra, parameter, variable, and constants. Real-world applications are introduced through general problem-solving using linear equations, like solving for unknowns in financial contexts.

Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions
VIDEO: Algebra Nspirations: Variables and Equations, Segment 2 VIDEO: Algebra Nspirations: Variables and Equations, 2 VIDEO: Algebra Nspirations: Variables and Equations, 2

Topic

Equations

Description

In this Math Lab explore the linear relationship between the circumference and diameter of a circle.

Relevance to the Topic: This video is a valuable resource for understanding the topic of Equations. It connects theoretical concepts with practical applications, offering insights that make learning engaging and relatable.

Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions
VIDEO: Algebra Nspirations: Variables and Equations, Segment 3 VIDEO: Algebra Nspirations: Variables and Equations, 3 VIDEO: Algebra Nspirations: Variables and Equations, 3

Topic

Equations

Description

Expanding on Part 1, this video demonstrates solving linear equations algebraically and dynamically using TI-Nspire technology. Applications include walk-a-thons and bike-a-thons, illustrating linear relationships in practical contexts. Key vocabulary includes linear equation, function, and symbolic representation.

Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions
VIDEO: Algebra Nspirations: Variables and Equations, Segment 4 VIDEO: Algebra Nspirations: Variables and Equations, 4 VIDEO: Algebra Nspirations: Variables and Equations, 4

Topic

Equations

Description

In this Math Lab, use a visual model to find the square of a binomial.

Relevance to the Topic: This video is a valuable resource for understanding the topic of Equations. It connects theoretical concepts with practical applications, offering insights that make learning engaging and relatable.

Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions
VIDEO: Algebra Nspirations: Exponents and Exponential Functions VIDEO: Algebra Nspirations: Exponents VIDEO: Algebra Nspirations: Exponents

Topic

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 and Exponential Functions, Segment 1 VIDEO: Algebra Nspirations: Exponents, 1 VIDEO: Algebra Nspirations: Exponents, 1

Topic

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 and Exponential Functions, Segment 2 VIDEO: Algebra Nspirations: Exponents, 2 VIDEO: Algebra Nspirations: Exponents, 2

Topic

Exponential Functions

Description

In this Math Lab explore a quadratic graph and an exponential graph and analyze their respective equations.

This video is relevant to the topic of Exponential Functions as it provides a detailed exploration of key concepts and their applications. By presenting clear and practical examples, it helps students understand and apply mathematical principles effectively.

Applications of Exponential and Logarithmic Functions, Exponential and Logarithmic Functions and Equations and Graphs of Exponential and Logarithmic Functions
VIDEO: Algebra Nspirations: Exponents and Exponential Functions, Segment 3 VIDEO: Algebra Nspirations: Exponents, 3 VIDEO: Algebra Nspirations: Exponents, 3

Topic

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 and Exponential Functions, Segment 4 VIDEO: Algebra Nspirations: Exponents, 4 VIDEO: Algebra Nspirations: Exponents, 4

Topic

Exponential Functions

Description

In this Math Lab explore cooling curves expressed as exponential functions.

This video is relevant to the topic of Exponential Functions as it provides a detailed exploration of key concepts and their applications. By presenting clear and practical examples, it helps students understand and apply mathematical principles effectively.

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 VIDEO: Algebra Nspirations: Functions and Relations

Topic

Functions and Relations

Applications of Functions and Relations, Quadratic Equations and Functions and Relations and Functions