Illustrative Math Alignment: Grade 6 Unit 1

Topic

Solving Equations

Description

This example effectively demonstrates solving a two-step equation using algebra tiles, where the visual model helps students understand how to manipulate the equation. The image shows algebra tiles used to solve the equation 2x - 2 = -4. The tiles are manipulated to find the solution x = -1. In this example, the caption emphasizes the importance of using model tiles to visualize the equation.

Topic

Solving Equations

Description

This example effectively demonstrates solving a two-step equation using algebra tiles, where the visual model helps students understand how to manipulate the equation. The image shows algebra tiles used to solve the equation 2x - (-2) = -4. The tiles are manipulated to find the solution x = -3. In this example, the process involves modeling tiles on both sides of the equals sign, converting subtraction of a negative into addition, and creating zero pairs to isolate the variable.

Topic

Solving Equations

Description

This example effectively demonstrates solving a two-step equation using algebra tiles, where the visual model helps students understand how to manipulate the equation. The image shows algebra tiles used to solve the equation -x + 1 = 4. The tiles are manipulated to find the solution x = -3. In this example, the process involves modeling tiles on both sides of the equals sign, creating zero pairs, and replacing each side with corresponding opposite tiles.

Topic

Solving Equations

Description

This example effectively demonstrates solving a two-step equation using algebra tiles, where the visual model helps students understand how to manipulate the equation. The image shows algebra tiles used to solve the equation -x - 1 = 4. The tiles are manipulated to find the solution x = -5. In this example, the process involves modeling tiles on both sides of the equals sign, converting subtraction into addition of a negative, creating zero pairs, and replacing each side with corresponding opposite tiles.

Topic

Solving Equations

Description

This example effectively demonstrates solving a two-step equation using algebra tiles, where the visual model helps students understand how to manipulate the equation. The image shows a visual representation of solving the equation -2x + 1 = 5 using algebra tiles. The tiles are arranged to show steps: modeling both sides, creating zero pairs, and replacing with opposite tiles to solve for x = -2. This process illustrates the importance of maintaining balance in equations.

This Teacher's Guide provides an overview of the 13 worked-out examples that solve a variety of one-variable equations with fractions.

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What Are Percents?

This Teacher's Guide provides an overview of the 27 worked-out examples that solve a variety of one-variable equations.

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

This set of tutorials provides 10 examples of finding the determinant of a quadratic equation to determine the number of real roots. NOTE: The download is a PPT file.

February 2014. In this issue of Math in the News we look at the dramatic growth in subscribers for Netflix. We calculate the rate of growth. We also explore how companies like Netflix are changing the viewing habits of all Americans.

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

This is part of a collection of math quizzes on the topic of Equations with Fractions.

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ary">click on this link.

This is part of a collection of math quizzes on the topic of Equations with Fractions.

Related Resources

Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of Equations with Fractions.

Related Resources

Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of Equations with Percents.

Related Resources

Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of Equations with Percents.

Related Resources

Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of Equations with Percents.

Related Resources

Quiz Library

ary">click on this link.

Topic

Equations

Description

The Not Equal To Sign (≠) indicates two expressions are not equal, forming an inequation. For example, 2 + 1 ≠ 4 and x + 3 ≠ x are inequations. This term builds on equality concepts by introducing inequalities, critical for exploring a broader range of mathematical statements.

Topic

Equations

Description

An Equation is a mathematical statement that says two expressions are equal to each other. Equations can be true or false, as shown in examples like 1 + 1 = 2 (true) and 1 + 2 = 4 (false). This term introduces the concept of equality and sets the foundation for understanding other types of equations.

Topic

Equations

Description

An Equation in One Variable has an unknown represented by a single variable. Examples include 2 + 3x = 5 and (x + 2)^2 = 25. This term focuses on single-variable equations, forming a basis for solving and understanding algebraic structures.

Topic

Equations

Description

Equations in Two Variables. A two-variable equation shows a relationship between two variables. Examples include y = 3x + 5, x2 + y2 = 25, and xy = 5, highlighting equations that can be graphed in a coordinate system. This builds on the idea of variables in equations and introduces the concept of relationships between variables, applicable in graphing and real-world modeling.

Topic

Equations

Description

Equivalent Equations result from changing an equation while maintaining equality, often by performing the same operation on both sides. For example, x - 3 = 5 becomes x = 8 after adding 3 to both sides. This term demonstrates how equations can be manipulated without altering their solution, a key concept in solving equations.

Topic

Equations

Description

A False Equation is mathematically inaccurate. For example, 2 + 1 = 4 is false, and x + 3 = x has no solution, as no value of x satisfies the equation. This term contrasts true equations and emphasizes the need to verify solutions, highlighting logical consistency in mathematics.

Topic

Equations

Description

An Identity Equation is always true for all variable values. Examples include x = x and (x + 1)2 = x2 + 2x + 1. Identity equations often use the symbol ≡ to indicate their universal truth. This term introduces a special class of equations, linking algebraic manipulation and properties of equivalence.

Topic

Equations

Description

An Inequation is a mathematical statement that shows two expressions are not equal, as in 2 + 1 ≠ 4 or x + 3 ≥ 0, which includes inequalities. This term broadens the discussion to include inequalities, expanding the types of relationships between expressions.

Topic

Equations

Description

Isolating the Variable refers to the process of solving an equation by focusing on and isolating the variable of interest. For example, x + 3 = 5 becomes x = 2 by subtracting 3 from both sides. This term highlights a key step in solving equations, emphasizing strategies for simplifying equations to find solutions.

Topic

Equations

Description

The Left Side of the Equation is the expression on the left of the equals sign. For example, in 2x + 3 = x - 5, the left side is 2x + 3. This term provides clarity in identifying components of equations, aiding in understanding structure and solving strategies.

Topic

Equations

Description

A Linear Equation is an equation where variables have an exponent of 1. Examples include x + 2 = 7, 2x + 3y = 4, and y = -2x + 10. Graphs of two-variable linear equations are straight lines. This term introduces a fundamental class of equations with specific properties, crucial for algebra and graphing.

Topic

Equations

Description

The Addition Property of Equality allows the addition of the same quantity to each side of an equation while maintaining equality. For example, if a = b, then a + c = b + c. This concept ensures equations can be manipulated while preserving their equality, demonstrated by solving x - 2 = 3 as x = 5 after adding 2 to both sides. This term introduces the basic manipulation of equations, forming the foundation for solving linear equations and maintaining equality.

Topic

Equations

Description

A Literal Equation includes more than one variable and often represents formulas, such as A = πr2, V = l*w*h, and SA = 2πr*h + 2πr2. This term connects to real-world applications and highlights the versatility of equations in representing formulas and relationships.

Topic

Equations

Description

A Multi-Step Equation involves more than two mathematical operations to solve. For example, 4x + 2 = 2x + 8 simplifies to x = 3 after subtraction and division steps. This term emphasizes solving more complex equations, showing sequential steps and reinforcing logical progression in algebra.

Topic

Equations

Description

The Multiplication Property of Equality allows multiplication by the same non-zero quantity on both sides of an equation, maintaining equality. For example, if a = b, then a * c = b * c. Solving x/2 = 3 yields x = 6 by multiplying both sides by 2. This term builds on equality principles and demonstrates another method for solving equations by manipulating terms.

Topic

Equations

Description

A Non-Linear Equation includes non-linear terms such as polynomials of degree 2 or higher, exponential, logarithmic, or trigonometric terms. Examples include y = x2 - 4x + 5 and y = sin(x). This term expands understanding beyond linear relationships, introducing diverse mathematical models and their applications.

Topic

Equations

Description

A Numerical Expression consists of numbers and operations without variables. Examples include 2 + 3 = 5 and 2(4 + 3) = 14. This term highlights fundamental operations, foundational for understanding and solving equations.

The topic of this video is closely tied to Equations, providing an essential understanding of its fundamental concepts. This video explores the mathematics behind this topic by delving into how key principles are applied in practical contexts.

Topic

Equations

Description

A One-Step Equation involves a single mathematical operation to solve. For example, x + 2 = 3 simplifies to x = 1 by subtraction. This term introduces the simplest form of equations, essential for beginners to build confidence and understanding in solving.

Topic

Equations

Description

A Polynomial Equation consists of a polynomial expression equal to zero. Examples include x2 + 3x + 2 = 0 and x3 - 2x2 + 4x - 10 = 0. This term defines a key class of equations, critical for algebra and calculus studies.

Topic

Equations

Description

A Quadratic Equation is a polynomial of degree 2. Examples include x2 - 2 = 23 and 2x2 + 3x + 2 = 0. Graphs of such equations are parabolas. This term extends understanding of polynomial equations, connecting algebra to geometry through parabolas.

Topic

Equations

Description

The Reflexive Property of Equality states that any quantity is equal to itself. Examples include 5 = 5 and x + 2 = x + 2. This term reinforces the foundational principle of equality, essential for logical reasoning in mathematics.

Topic

Equations

Description

Right Side of the Equation. The expression to the right side of the equals sign in an equation. 2x + 3 = x - 5 (right side highlighted)

The topic of this video is closely tied to Equations, providing an essential understanding of its fundamental concepts. This video explores the mathematics behind this topic by delving into how key principles are applied in practical contexts.

Topic

Equations

Description

An Algebraic Equation is another term for a polynomial equation, represented as a sum of terms equal to zero. Examples include x2 + 3x + 2 = 0 and x3 - 2x2 + 4x - 10 = 0. It highlights the structure of polynomial equations using constants, variables, and powers. This term connects to the topic by defining the types of equations learners encounter when solving or simplifying expressions.

Topic

Equations

Description

Roots of an Equation. The solution or solutions to an equation. y = -x2 + 7x - 10; solutions: x = 2, x = 5

The topic of this video is closely tied to Equations, providing an essential understanding of its fundamental concepts. This video explores the mathematics behind this topic by delving into how key principles are applied in practical contexts.

Topic

Equations

Description

Solution. A value for the unknown that turns a conditional equation into a true equation. For example, x = 5 is a solution to x + 2 = 7

The topic of this video is closely tied to Equations, providing an essential understanding of its fundamental concepts. This video explores the mathematics behind this topic by delving into how key principles are applied in practical contexts.

Topic

Equations

Description

Solving an Equation. The process of finding the value(s) for a variable that result in a true equation. For example, x + 2 = 3 has a solution of x = 1

The topic of this video is closely tied to Equations, providing an essential understanding of its fundamental concepts. This video explores the mathematics behind this topic by delving into how key principles are applied in practical contexts.

Topic

Equations

Description

Subtraction Property of Equality. The property that allows the subtraction of the same quantity from each side of an equation while maintaining the equality. For example, x + 2 = 3 becomes x = 1

The topic of this video is closely tied to Equations, providing an essential understanding of its fundamental concepts. This video explores the mathematics behind this topic by delving into how key principles are applied in practical contexts.

Topic

Equations

Description

Symmetric Property of Equality. The property that states that an equation can be written two ways, with both sides interchanged. If a = b, then b = a.

The topic of this video is closely tied to Equations, providing an essential understanding of its fundamental concepts. This video explores the mathematics behind this topic by delving into how key principles are applied in practical contexts.

Topic

Equations

Description

The Unknown. In a conditional equation, the variable is also referred to as the unknown. 3x = 12, where x is the unknown

The topic of this video is closely tied to Equations, providing an essential understanding of its fundamental concepts. This video explores the mathematics behind this topic by delving into how key principles are applied in practical contexts.

Topic

Equations

Description

Transitive Property of Equality. The property that states that two quantities equal to a third quantity are equal to each other. If a = b and b = c, then a = c

The topic of this video is closely tied to Equations, providing an essential understanding of its fundamental concepts. This video explores the mathematics behind this topic by delving into how key principles are applied in practical contexts.

Topic

Equations

Description

True Equation. A mathematically accurate equation. If variables are involved, the true equation is for the values of the variable that make the equation true. Examples: 2 + 1 = 3; (2 + 3)2 = 25; x + 3 = 9 for x = 6

The topic of this video is closely tied to Equations, providing an essential understanding of its fundamental concepts. This video explores the mathematics behind this topic by delving into how key principles are applied in practical contexts.

Topic

Equations

Description

Two-Step Equation. A two-step equation is an equation that involves two mathematical operations to solve. The example given is 2x + 2 = 8, where the first operation is subtraction, leading to 2x = 6, followed by division to solve for x = 3. This concept extends the understanding of solving equations by introducing a sequence of operations, crucial for solving more complex equations.

Topic

Equations

Description

Variable Expression. A variable expression is made up of numbers, operations, and variables. Examples include 2x + 3 = 5 (expression on the left), 4 = 3x + 7 (expression on the right), and 4x + 3 = x - 5 (expressions on both sides). This connects variables to equations and highlights their role in forming relationships within mathematical contexts.

Topic

Equations

Description

An Algebraic Expression consists of numbers, operations, and variables. Unlike equations, expressions may not have an equality. Examples include 2x + 3, 4 = 3x + 7, and 4x + 3 = x - 5, demonstrating their versatility in representing mathematical relationships. This term distinguishes between expressions and equations, forming the basis for manipulating algebraic forms before solving equations.