Illustrative Math Alignment: Grade 6 Unit 1

Media4Math Classroom's SAT Math Prep series provide a thorough review of key math topics covered on the SAT. These modules review the key skills that are tested on the SAT with a two-pronged approach:

In this module there is a complete review of the topic of quadratic functions and equations. This module covers four key areas:

Students are given ample opportunities to review and test their understanding of the basics of these areas, before moving on to the more rigorous types of questions they can expect to see on the SAT.

Your students may know how to solve equations (or not), but do they know the underlying mathematical processes and properties involved in solving them? Do they have sufficient vocabulary to explain their steps in solving an equation?

More than memorizing an algorithm, the ability to define and use the properties of equality, as well as other key parts of the equation-solving process are essential for mathematical competence. The ability to analyze and use logical reasoning are skills that go beyond the math classroom.

In this module, students learn the basics of the equation-solving process. These principles apply to any equation a student is solving and provide a needed foundational reinforcement for students.

In this module students learn how to solve two-step equations. Students are shown how to solve these equations using the Properties of Equality (Addition, Subtraction, Multiplication, and Division).

Specifically, students work with the following equation types:

Just as important as solving these equations, students are shown how to recognize such equations. It's in the recognition of the equation type that students can reason their way to the solution, by deciding which of the Properties of Equality to use.

Your students may know how to solve equations (or not), but do they know the underlying mathematical processes and properties involved in solving them? Do they have sufficient vocabulary to explain their steps in solving an equation?

More than memorizing an algorithm, the ability to define and use the properties of equality, as well as other key parts of the equation-solving process are essential for mathematical competence. The ability to analyze and use logical reasoning are skills that go beyond the math classroom.

In this module, students learn the basics of the equation-solving process. These principles apply to any equation a student is solving and provide a needed foundational reinforcement for students.

In this module students learn how to solve two-step equations. Students are shown how to solve these equations using the Properties of Equality (Addition, Subtraction, Multiplication, and Division).

Specifically, students work with the following equation types:

Just as important as solving these equations, students are shown how to recognize such equations. It's in the recognition of the equation type that students can reason their way to the solution, by deciding which of the Properties of Equality to use.

In this module students learn how to solve two-step equations. Students are shown how to solve these equations using the Properties of Equality (Addition, Subtraction, Multiplication, and Division).

Specifically, students work with the following equation types:

Just as important as solving these equations, students are shown how to recognize such equations. It's in the recognition of the equation type that students can reason their way to the solution, by deciding which of the Properties of Equality to use.

Media4Math Classroom's SAT Math Prep series provide a thorough review of key math topics covered on the SAT. These modules review the key skills that are tested on the SAT with a two-pronged approach:

In this module there is a complete review of the topic of quadratic functions and equations. This module covers four key areas:

Students are given ample opportunities to review and test their understanding of the basics of these areas, before moving on to the more rigorous types of questions they can expect to see on the SAT.

Media4Math Classroom's SAT Math Prep series provide a thorough review of key math topics covered on the SAT. These modules review the key skills that are tested on the SAT with a two-pronged approach:

In this module there is a complete review of the topic of quadratic functions and equations. This module covers four key areas:

Students are given ample opportunities to review and test their understanding of the basics of these areas, before moving on to the more rigorous types of questions they can expect to see on the SAT.

Media4Math Classroom's SAT Math Prep series provide a thorough review of key math topics covered on the SAT. These modules review the key skills that are tested on the SAT with a two-pronged approach:

In this module there is a complete review of the topic of quadratic functions and equations. This module covers four key areas:

Students are given ample opportunities to review and test their understanding of the basics of these areas, before moving on to the more rigorous types of questions they can expect to see on the SAT.

This module reviews systems of equations. In particular, these topics are covered.

Plan on spending at least 30 minutes per topic. This entire module can be completed over a two-hour period, which can be broken up into several sessions.

For each topic students will review key concepts, look at numerous examples, and then look at sample SAT assessment items, with clear explanations to each assessment item.

Media4Math Classroom is developing a series of instructional modules for reviewing SAT math topics in detail. These modules review the key skills that are tested on the SAT with a two-pronged approach:

In this module there is a thorough review of the topic of linear equations. This module covers four key areas:

Students are given ample opportunities to review and test their understanding of the basics of these areas, before moving on to the more rigorous types of questions they can expect to see on the test.

Media4Math Classroom is developing a series of instructional modules for reviewing SAT math topics in detail. These modules review the key skills that are tested on the SAT with a two-pronged approach:

In this module there is a thorough review of the topic of linear equations. This module covers four key areas:

Students are given ample opportunities to review and test their understanding of the basics of these areas, before moving on to the more rigorous types of questions they can expect to see on the test.

This module reviews systems of equations. In particular, these topics are covered.

Plan on spending at least 30 minutes per topic. This entire module can be completed over a two-hour period, which can be broken up into several sessions.

For each topic students will review key concepts, look at numerous examples, and then look at sample SAT assessment items, with clear explanations to each assessment item.

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.

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.

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.

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.

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 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.

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

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.

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.

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.