Illustrative Math Alignment: Grade 8 Unit 7

Overview

Overview

Overview

This collection from Media4Math on Integer and Rational Exponents offers a comprehensive set of examples on the topic of exponents. These examples gradually increase in complexity, covering a range of skills including integer and rational exponents, simplifying expressions, and applying exponent rules. Each example is supported by visual models to help simplify concepts, making it easier for students to understand the various properties of exponents.

Overview

Overview

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.

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

Related Resources

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

Topic

Equations

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

Related Resources

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

Topic

Inequalities

Topic

Equations

Topic

Equations

Topic

Equations

Description

The video introduces algebraic expressions and their ability to represent both known and unknown quantities. It defines variables as placeholders for unknowns and explains equations as relationships between two expressions. Key concepts include solving for variables and understanding the role of variables in equations. Key vocabulary includes variable, unknown quantity, and equation. The applications discussed include investigations into real-world scenarios such as honeybee populations and river geology.

Topic

Equations

Description

The video investigates the geometry of river meanders using the concept of the meander ratio, calculated as the ratio of a river’s sinuous length to its straight-line length. It uses a TI-Nspire calculator to simulate river paths and compute ratios. Key vocabulary includes meander ratio, sinuous length, and geometric modeling. Applications highlight the mathematical modeling of natural phenomena and the occurrence of pi in nature.

Topic

Equations

Description

This segment explores the impact of colony collapse disorder on honey production using statistical data. It introduces box and whisker plots and the calculation of mean as statistical tools to analyze honey yields. Key vocabulary includes colony collapse disorder, box plot, and mean. Applications include modeling bee population declines and their broader ecological and agricultural implications.

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.

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.

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.

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.

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.

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.

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.

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

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

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

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

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

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

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.

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.

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.

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.

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

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

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

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.