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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 7

Exponents and Scientific Notation

Lesson 3: Powers of Powers of 10

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Math Worksheets Math Worksheet Collection: Scientific Notation

Overview

This collection aggregates all the math worksheets around the topic of Scientific Notation. There are a total of 40 worksheets. Each worksheet includes an answer key. This collection of resources is made up of downloadable PDF files that you can easily incorporate into your instruction.

 

To download the full set of these resources, click on this link.

 

Numerical Expressions
Collection Math Quiz Collection: The Laws of Exponents

Overview

This collection aggregates all the math quizzes on this topic: The Laws of Exponents. There are a total of 3 resources. This collection of quizzes is made up of downloadable PDFs. To download the full set of these resources, click on this link.

 

Laws of Exponents
Math Examples Math Examples Collection: Integer and Rational Exponents

Overview

This collection aggregates all the math examples around the topic of Integer and Rational Exponents. There are a total of 15 images. This collection of resources is made up of downloadable PNG files that you can easily incorporate into a presentation.

 

To download the full set of these resources, click on this link.

 

Numerical Expressions
Exponential Collection Math Definitions Collection: Exponential and Logarithmic Vocabulary

Overview

This collection aggregates all the definition image cards around the topic of Exponential and Logarithmic vocabulary. There are a total of 11 terms. This collection of resources is made up of downloadable PNG files that you can easily incorporate into a presentation.

 

 

 

Applications of Exponential and Logarithmic Functions
Math in the News Math in the News Collection: Applications of Numerical and Algebraic Expressions

Overview

This is a collection of Math in the News stories that focus on the topic of Numerical and Algebraic Expressions.

 

 

 
Numerical Expressions and Variable Expressions
Math Examples Math Examples Collection: The Laws of Exponents

Overview

This comprehensive collection of 24 Math Examples focuses on the Laws of Exponents, providing educators with a rich resource to enhance their lesson plans. This set of downloadable images covers a wide range of skills related to exponent manipulation.

Laws of Exponents
Algebra Applications Teacher's Guide: Equations Algebra Applications Teacher's Guide: Equations Algebra Applications Teacher's Guide: Equations

This is the Teacher's Guide that accompanies Algebra Applications: Equations.

This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Applications of Equations and Inequalities
VIDEO: Algebra Applications: Variables and Equations VIDEO: Algebra Applications: Variables and Equations VIDEO: Algebra Applications: Variables and Equations

In this episode of Algebra Applications, two real-world explorations are developed: Biology. Analyzing statistics from honey bee production allows for a mathematical analysis of the so-called Colony Collapse Disorder. Geology. Why do rivers meander instead of traveling in a straight line? In this segment the geological forces that account for a river's motion are explained.

This is part of a collection of videos from the Algebra Applications video series on the topic of Variables and Equations.

Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions
Algebra Nspirations Teacher's Guide: Variables and Equations Algebra Nspirations Teacher's Guide: Variables and Equations Algebra Nspirations Teacher's Guide: Variables and Equations

This is the Teacher's Guide that accompanies Algebra Nspirations: Variables and Equations.

This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Applications of Equations and Inequalities
VIDEO: Algebra Nspirations: Inequalities VIDEO: Algebra Nspirations: Inequalities VIDEO: Algebra Nspirations: Inequalities

Used in just about any industry, inequalities, like equations, are fundamental building blocks of algebra. Written and hosted by internationally acclaimed mathematics educator Dr. Monica Neagoy, this video explores inequalities--concepts, properties, solutions, and notations--connects them to real-world contexts, and uses the TI-Nspire to make the algebra meaningful. The focus of this program is on linear inequalities in one and two variables. Concepts explored: Equations, inequalities.

Applications of Equations and Inequalities and Inequalities
VIDEO: Algebra Nspirations: Variables and Equations 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
Closed Captioned Video: Algebra Applications: Variables and Equations Closed Captioned Video: Algebra Applications: Variables and Equations Closed Captioned Video: Algebra Applications: Variables and Equations

In this episode of Algebra Applications, two real-world explorations are developed: Biology. Analyzing statistics from honey bee production allows for a mathematical analysis of the so-called Colony Collapse Disorder. Geology. Why do rivers meander instead of traveling in a straight line? In this segment the geological forces that account for a river’s motion are explained.

Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions
Closed Captioned Video: Algebra Applications: Variables and Equations, Segment 1: Introduction Closed Captioned Video: Algebra Applications: Variables and Equations, 1 Closed Captioned Video: Algebra Applications: Variables and Equations, Segment 1: Introduction

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

Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions
Closed Captioned Video: Algebra Applications: Variables and Equations, Segment 2: Honey Production Closed Captioned Video: Algebra Applications: Variables and Equations, 2 Closed Captioned Video: Algebra Applications: Variables and Equations, Segment 2: Honey Production

Honey bees not only produce a tasty treat, they also help pollinate flowering plants that provide much of the food throughout the world. So, when in 2006 bee colonies started dying out, scientists recognized a serious problem. Analyzing statistics from honey bee production allows for a mathematical analysis of the so-called Colony Collapse Disorder.

Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions
Closed Captioned Video: Algebra Applications: Variables and Equations, Segment 3: River Ratios Closed Captioned Video: Algebra Applications: Variables and Equations, 3 Closed Captioned Video: Algebra Applications: Variables and Equations, 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? Furthermore, what information can the ratio of the river’s length to its straight-line distance tell us? In this segment the geological forces that account for a river’s motion are explained. In the process, the so-called Meander Ratio is explored. Students construct a mathematical model of a meandering river using the TI-Nspire. Having built the model, students then use it to generate data to find the average of many Meander Ratios. The results show that on average the Meander Ratio is equal to pi.

Applications of Equations and Inequalities, Variables and Unknowns, Variable Expressions and Applications of Ratios, Proportions, and Percents
Closed Captioned Video: Algebra Nspirations: Inequalities Closed Captioned Video: Algebra Nspirations: Inequalities Closed Captioned Video: Algebra Nspirations: Inequalities

Used in just about any industry, inequalities, like equations, are fundamental building blocks of algebra. Written and hosted by internationally acclaimed mathematics educator Dr. Monica Neagoy, this video explores inequalities—concepts, properties, solutions, and notations— connects them to real-world contexts, and uses the TI-Nspire to make the algebra meaningful. The focus of this program is on linear inequalities in one and two variables. Concepts explored: Equations, inequalities.

Applications of Equations and Inequalities and Inequalities
Closed Captioned Video: Algebra Nspirations: Inequalities, Segment 1 Closed Captioned Video: Algebra Nspirations: Inequalities, 1 Closed Captioned Video: Algebra Nspirations: Inequalities, Segment 1

In this Investigation we explore linear inequalities in one variable. This video is Segment 1 of a 4 segment series related to Algebra Nspirations: Inequalities. Segments 1 and 2 are grouped together.

Applications of Equations and Inequalities and Inequalities
Closed Captioned Video: Algebra Nspirations: Inequalities, Segment 3 Closed Captioned Video: Algebra Nspirations: Inequalities, 3 Closed Captioned Video: Algebra Nspirations: Inequalities, Segment 3

In this Investigation we look at linear inequalities in two variables. This video is Segment 3 of a 4 segment series related to Algebra Nspirations: Inequalities. Segments 3 and 4 are grouped together.

Applications of Equations and Inequalities and Inequalities
Closed Captioned Video: Algebra Nspirations: Variables and Equations Closed Captioned Video: Algebra Nspirations: Variables and Equations Closed Captioned 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
Closed Captioned Video: Algebra Nspirations: Variables and Equations, Segment 1 Closed Captioned Video: Algebra Nspirations: Variables and Equations, 1 Closed Captioned 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
Closed Captioned Video: Algebra Nspirations: Variables and Equations, Segment 3 Closed Captioned Video: Algebra Nspirations: Variables and Equations, 3 Closed Captioned Video: Algebra Nspirations: Variables and Equations, Segment 3

In this Investigation we solve linear and quadratic equations. This video is Segment 3 of a 4 segment series related to Variables and Equations. Segments 3 and 4 are grouped together.

Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions
Closed Captioned Video: Algebra Tiles: Modeling Equations Using Algebra Tiles Closed Captioned Video: Algebra Tiles: Modeling Equations Using Algebra Tiles Closed Captioned Video: Algebra Tiles: Modeling Equations Using Algebra Tiles

Description

Video Tutorial: Algebra Tiles: Modeling Equations Using Algebra Tiles. In this tutorial, review the basic definition of what algebra tiles are and how they are used. Then the video focuses on how to model equations using algebra tiles.

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.

Algebra Tiles--Expressions and Equations
Closed Captioned Video: Anatomy of an Equation: One-Step Addition Equations Closed Captioned Video: Anatomy of an Equation: One-Step Addition Equations Closed Captioned Video: Anatomy of an Equation: One-Step Addition Equations

In this video learn the mechanics of solving one-step equations involving addition. .

Solving One-Step Equations
Closed Captioned Video: Anatomy of an Equation: One-Step Addition Equations 2 Closed Captioned Video: Anatomy of an Equation: One-Step Addition Equations 2 Closed Captioned Video: Anatomy of an Equation: One-Step Addition Equations 2

In this video learn the mechanics of solving one-step equations involving addition. .

Solving One-Step Equations
Closed Captioned Video: Anatomy of an Equation: One-Step Division Equations Closed Captioned Video: Anatomy of an Equation: One-Step Division Equations Closed Captioned Video: Anatomy of an Equation: One-Step Division Equations

In this video learn the mechanics of solving one-step equations involving division. .

Solving One-Step Equations
Closed Captioned Video: Anatomy of an Equation: One-Step Multiplication Equations Closed Captioned Video: Anatomy of an Equation: One-Step Multiplication Equations Closed Captioned Video: Anatomy of an Equation: One-Step Multiplication Equations

In this video learn the mechanics of solving one-step equations involving multiplication. .

Solving One-Step Equations
Closed Captioned Video: Anatomy of an Equation: One-Step Subtraction Equations Closed Captioned Video: Anatomy of an Equation: One-Step Subtraction Equations Closed Captioned Video: Anatomy of an Equation: One-Step Subtraction Equations

In this video learn the mechanics of solving one-step equations involving subtraction. .

Solving One-Step Equations
Closed Captioned Video: Anatomy of an Equation: One-Step Subtraction Equations 2 Closed Captioned Video: Anatomy of an Equation: One-Step Subtraction Equations 2 Closed Captioned Video: Anatomy of an Equation: One-Step Subtraction Equations 2

In this video learn the mechanics of solving one-step equations involving subtraction. .

Solving One-Step Equations
Closed Captioned Video: One-Step Equations: Addition Closed Captioned Video: One-Step Equations: Addition Closed Captioned Video: One-Step Equations: Addition

Video Tutorial: One-Step Equations: Addition. In this video, get an overview of one-step equations and how to solve them. In particular, look at one-step addition equations.

Solving One-Step Equations
Closed Captioned Video: One-Step Equations: Division Closed Captioned Video: One-Step Equations: Division Closed Captioned Video: One-Step Equations: Division

Video Tutorial: One-Step Equations: Division. In this video, students get an overview of one-step equations and how to solve them. In particular, look at one-step division equations.

Solving One-Step Equations
Closed Captioned Video: One-Step Equations: Multiplication Closed Captioned Video: One-Step Equations: Multiplication Closed Captioned Video: One-Step Equations: Multiplication

Video Tutorial: One-Step Equations: Multiplication. In this video, students get an overview of one-step equations and how to solve them. In particular, look at one-step multiplication equations.

Solving One-Step Equations
Closed Captioned Video: One-Step Equations: Subtraction Closed Captioned Video: One-Step Equations: Subtraction Closed Captioned Video: One-Step Equations: Subtraction

Video Tutorial: One-Step Equations: Subtraction. In this video, students get an overview of one-step equations and how to solve them. In particular, look at one-step subtraction equations.

Solving One-Step Equations
Closed Captioned Video: Overview of Variables and Equations Closed Captioned Video: Overview of Variables and Equations Closed Captioned Video: Overview of Variables and Equations

In this video segment, get an overview of variables and equations, along with the evolution of algebraic notation.

Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions
Closed Captioned Video: Two-Step Equations: Division and Addition Closed Captioned Video: Two-Step Equations: Division and Addition Closed Captioned Video: Two-Step Equations: Division and Addition

Video Tutorial: Two-Step Equations: Division and Addition. In this video, we will solve a two-step equation that involves division and addition.

Solving Two-Step Equations
Closed Captioned Video: Two-Step Equations: Division and Subtraction Closed Captioned Video: Two-Step Equations: Division and Subtraction Closed Captioned Video: Two-Step Equations: Division and Subtraction

Video Tutorial: Two-Step Equations: Division and Subtraction. In this video, we will solve a two-step equation that involves division and subtraction.

Solving Two-Step Equations
Closed Captioned Video: Two-Step Equations: Multiplication and Addition Closed Captioned Video: Two-Step Equations: Multiplication and Addition Closed Captioned Video: Two-Step Equations: Multiplication and Addition

Video Tutorial: Two-Step Equations: Multiplication and Addition. In this video, we will solve a two-step equation that involves multiplication and addition.

Solving Two-Step Equations
Closed Captioned Video: Two-Step Equations: Multiplication and Subtraction Closed Captioned Video: Two-Step Equations: Multiplication and Subtraction Closed Captioned Video: Two-Step Equations: Multiplication and Subtraction

Video Tutorial: Two-Step Equations: Multiplication and Subtraction. In this video, we will solve a two-step equation that involves multiplication and subtraction.

Solving Two-Step Equations
Definition--Equation Concepts--"Not Equal To" Definition--Equation Concepts--"Not Equal To" Not Equal To

Topic

Equations

Definition

The "Not Equal To" symbol (≠) is used to indicate that two values are not equal.

Description

The "Not Equal To" symbol is crucial in mathematics as it denotes inequality between two expressions. This symbol is used in various mathematical contexts, such as solving inequalities, comparing numbers, and expressing conditions in algebraic equations. For example, in the inequality 𝑥 ≠ 5, it means that x can be any number except 5.

Numerical and Algebraic Expressions
Definition--Equation Concepts--Addition Property of Equality Definition--Equation Concepts--Addition Property of Equality Addition Property of Equality

Topic

Equations

Definition

The Addition Property of Equality states that if you add the same value to both sides of an equation, the equality remains true.

Description

The Addition Property of Equality is a fundamental principle in algebra. It asserts that for any real numbers a, b, and c, if a = b, then a + c = b + c. This property is used to solve equations and maintain balance. For example, to solve x − 3 = 7, you add 3 to both sides to get x = 10.

Applications of Equations and Inequalities
Definition--Equation Concepts--Algebraic Equation Definition--Equation Concepts--Algebraic Equation Algebraic Equation

Topic

Equations

Definition

An algebraic equation is a mathematical statement that shows the equality of two algebraic expressions. It's also another way of referring to a polynomial equation.

Description

Algebraic equations are central to algebra and involve variables, constants, and arithmetic operations. They are used to represent relationships and solve problems. For instance, the equation 2x + 3 = 7 can be solved to find x. Algebraic equations come in various forms, including linear, quadratic, and polynomial equations.

Applications of Equations and Inequalities
Definition--Equation Concepts--Algebraic Expression Definition--Equation Concepts--Algebraic Expression Algebraic Expression

Topic

Equations

Definition

An algebraic expression is a combination of variables, constants, and arithmetic operations, without an equality sign.

Description

Algebraic expressions are fundamental components of algebra. They represent quantities and relationships without asserting equality. Examples include 3x + 4 and 5y − 2. Unlike equations, expressions cannot be solved but can be simplified or evaluated for given variable values.

Numerical and Algebraic Expressions
Definition--Equation Concepts--Assigning Values to Variables Definition--Equation Concepts--Assigning Values to Variables Assigning Values to Variables

Topic

Equations

Definition

Assigning values to variables involves giving specific values to variables in an equation or expression.

Description

Assigning values to variables is a fundamental process in algebra. It involves substituting variables with specific numbers to evaluate expressions or solve equations. For example, in the equation 

y = 2x + 3

assigning x = 4 gives y = 11.

Variable Expressions
Definition--Equation Concepts--Conditional Equation Definition--Equation Concepts--Conditional Equation Conditional Equation

Topic

Equations

Definition

A conditional equation is true only for specific values of the variable(s).

Description

Conditional equations are equations that hold true only under certain conditions or for specific variable values. For example, the equation 

x2 = 4 

is true only when x = 2 or x = −2. These equations contrast with identities, which are true for all variable values.

Applications of Equations and Inequalities
Definition--Equation Concepts--Constant Term Definition--Equation Concepts--Constant Term Constant Term

Topic

Equations

Definition

A constant term is a term in an algebraic expression that does not contain any variables.

Description

Constant terms are fixed values in algebraic expressions and equations. They do not change because they lack variables. For example, in the expression 

3x + 4

the number 4 is a constant term. Constant terms are essential in forming and solving equations.

Variables and Unknowns
Definition--Equation Concepts--Division Property of Equality Definition--Equation Concepts--Division Property of Equality Division Property of Equality

Topic

Equations

Definition

The Division Property of Equality states that if you divide both sides of an equation by the same nonzero value, the equality remains true.

Description

The Division Property of Equality is a key principle in algebra. It states that for any real numbers a, b, and c (where 𝑐 ≠ 0), if 

a = b, then a ÷ c​ = b ÷ c 

This property is used to solve equations by isolating variables. For example, to solve 

3x = 12

divide both sides by 3 to get x = 4.

Applications of Equations and Inequalities
Definition--Equation Concepts--Equality Definition--Equation Concepts--Equality Equality

Topic

Equations

Definition

Equality is a mathematical statement that asserts that two expressions are equal.

Description

Equality is a foundational concept in mathematics. It indicates that two expressions have the same value, represented by the symbol "=". For example, in the equation 2 + 3 = 5, both sides are equal. Equality is used to form equations and solve problems.

In real-world applications, equality is used in accounting, engineering, and data analysis to ensure balance and accuracy. Understanding equality helps students develop logical reasoning and problem-solving skills.

Applications of Equations and Inequalities
Definition--Equation Concepts--Equation Definition--Equation Concepts--Equation Equation

Topic

Equations

Definition

An equation is a mathematical statement that asserts the equality of two expressions.

Description

Equations are central to mathematics, representing relationships between quantities. They consist of two expressions separated by an equals sign. For example, 

2x + 3 = 7

is an equation that can be solved to find x. Equations can be linear, quadratic, or polynomial, among others.

Applications of Equations and Inequalities
Definition--Equation Concepts--Equations in One Variable Definition--Equation Concepts--Equations in One Variable Equations in One Variable

Topic

Equations

Definition

Equations in one variable involve a single variable and can be solved to find its value.

Description

Equations in one variable are fundamental in algebra. They typically take the form of ax + b = 0, where x is the variable. Solving these equations involves isolating the variable to determine its value. For example, solving 

2x + 3 = 7 

yields 

x = 2

Applications of Equations and Inequalities
Definition--Equation Concepts--Equations in Two Variables Definition--Equation Concepts--Equations in Two Variables Equations in Two Variables

Topic

Equations

Definition

Equations in two variables involve two variables and describe a relationship between them.

Description

Equations in two variables are essential in algebra and coordinate geometry. They typically take the form of 

ax + by = c

and represent lines in a coordinate plane. For example, the equation 

2x + 3y = 6

can be graphed as a line.

Applications of Equations and Inequalities
Definition--Equation Concepts--Equivalent Equations Definition--Equation Concepts--Equivalent Equations Equivalent Equations

Topic

Equations

Definition

Equivalent equations are equations that have the same solutions.

Description

Equivalent equations are a key concept in algebra. They may look different but yield the same solutions. For instance, 

2x + 3 = 7

and 

4x + 6 = 14

are equivalent because both have the solution x = 2. Transformations such as addition, subtraction, multiplication, or division can produce equivalent equations.

Applications of Equations and Inequalities