Illustrative Math Alignment: Grade 6 Unit 1

Overview

The Equations collection on Media4Math is an invaluable resource for students and educators alike, offering a comprehensive set of definitions related to equations. This collection includes essential terms such as linear equations, quadratic equations, and polynomial equations. Each term is clearly defined, providing students with a solid foundation in understanding the various types of equations they will encounter in their studies.

Overview

Overview

Overview

Topic

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.

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.

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.

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

Video Tutorial: The Distributive Property: a(-x + b), a negative, b negative. In this video use the distributive property with an expression of the form a(-x + b), a negative, b negative.

Video Tutorial: The Distributive Property: a(-x + b), a negative, b positive. In this video use the distributive property with an expression of the form a(-x + b), a negative, b positive.

Video Tutorial: The Distributive Property: a(-x + b), all constants positive. In this video use the distributive property with an expression of the form a(-x + b), all constants positive.

Video Tutorial: The Distributive Property: a(-x - b), a negative, b negative. In this video use the distributive property with an expression of the form a(-x - b), a negative, b negative.

Video Tutorial: The Distributive Property: a(-x - b), a negative, b positive. In this video, we will use the distributive property with an expression of the form a(-x - b), a negative, b positive.

Video Tutorial: The Distributive Property: a(-x - b), all constants positive. In this video use the distributive property with an expression of the form a(-x - b), all constants positive.

Video Tutorial: The Distributive Property: a(bx + c), a negative, b and c positive. In this video, we will use the distributive property with an expression of the form a(bx + c), a negative, b and c positive.

Video Tutorial: The Distributive Property: a(bx + c), all constants negative. In this video use the distributive property with an expression of the form a(bx + c), all negative.

Video Tutorial: The Distributive Property: a(bx + c), all constants positive. In this video use the distributive property with an expression of the form a(bx + c), all constants positive.

Video Tutorial: The Distributive Property: a(bx - c), a negative, b and c positive. In this video use the distributive property with an expression of the form a(bx - c), a negative, b and c positive.

Video Tutorial: The Distributive Property: a(bx - c), all constants negative. In this video, we will use the distributive property with an expression of the form a(bx - c), all negative.

Video Tutorial: The Distributive Property: a(bx - c), all constants positive. In this video use the distributive property with an expression of the form a(bx - c), all constants positive.

Video Tutorial: The Distributive Property: a(x + b), a negative, b negative. In this video use the distributive property with an expression of the form a(x + b), a negative, b negative.

Video Tutorial: The Distributive Property: a(x + b), a negative, b positive. In this video, we will use the distributive property with an expression of the form a(x + b), a negative, b positive.

Video Tutorial: The Distributive Property: a(x + b), all constants positive. In this video, we will use the distributive property with an expression of the form a(x + b), all constants positive.

Video Tutorial: The Distributive Property: a(x - b), a negative, b negative. In this video, we will use the distributive property with an expression of the form a(x - b), a negative, b negative.

Video Tutorial: The Distributive Property: a(x - b), a negative, b positive. In this video use the distributive property with an expression of the form a(x - b), a negative, b positive.

Video Tutorial: The Distributive Property: a(x - b), all constants positive. In this video, we will use the distributive property with an expression of the form a(x - b), all constants positive.

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

Isolating the variable involves manipulating an equation to get the variable alone on one side.

Description

Isolating the variable is a fundamental technique in algebra used to solve equations. It involves performing operations to both sides of an equation to get the variable by itself. For example, solving 

2x + 3 = 7

involves subtracting 3 and then dividing by 2 to isolate x, resulting in x = 2.

Topic

Equations

Definition

The unknown is the variable in an equation that needs to be solved for.

Description

The unknown in an equation represents the value that needs to be determined. For example, in the equation 

x + 3 = 7

x is the unknown. Identifying and solving for the unknown is a core aspect of algebra.

In real-world applications, finding the unknown is crucial for solving problems in various fields such as science, engineering, and finance. Understanding how to identify and solve for the unknown helps students develop problem-solving skills and apply mathematical concepts to real-life situations.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a series of definitions that focus on constants, variables, and coefficients. These definition cards can easily be incorporated into a lesson plan.

The following section provides a brief review of number properties that are helpful in working with numerical and variable expressions.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.

This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties.