Illustrative Math Alignment: Grade 6 Unit 1

Topic

Equations

Description

Similar To. When two geometric shapes are similar, corresponding sides are proportional. ΔABC ~ ΔDEF; AB ∝ DE

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

Congruent To signifies that two geometric shapes are congruent, meaning their corresponding sides and angles are equal. For example, triangles ABC and DEF are congruent, so side AB equals side DE. This term introduces geometric equality, tying equations to geometric properties and congruence criteria.

Topic

Equations

Description

Assigning Values to Variables involves assigning a numerical value to a variable for evaluating functions. For instance, let x = 3 in f(x) = 2x + 8 yields f(3) = 14. This term supports understanding how to evaluate equations and functions by substituting values, a key step in problem-solving.

Topic

Equations

Description

A Conditional Equation is true only for specific variable values. Examples include x + 1 = 4 (x = 3), x2 - 25 = 0 (x = ±5), and 2x - 5 = x + 9 (x = 14). This term supports solving equations by emphasizing that solutions depend on satisfying the given conditions.

Topic

Equations

Description

A Constant Term in an algebraic equation is a number without a variable. Examples include 2 in x2 + 3x + 2 = 0, -10 in x3 - 2x2 + 4x - 10 = 0, and 5 in x4 - 2x3 + 4x2 - x + 5 = 0. This term explains the role of constants in equations, crucial for identifying and isolating terms when solving equations.

Topic

Equations

Description

The Division Property of Equality allows division by the same non-zero quantity on both sides of an equation, maintaining equality. For example, if a = b, then a / c = b / c, where c ≠ 0. Solving 5x = 15 yields x = 3 by dividing both sides by 5. This term builds on equality principles, showing another method to isolate variables and solve equations.

Topic

Equations

Description

Equality refers to a mathematical statement where two expressions are equal. Examples include 1 + 2 = 3 and x + 3 = 7, where both sides represent the same value. This term defines the core concept of equations, ensuring all manipulations preserve equality to find solutions.

This is the transcript for the video of same title. Video contents: In this episode of Algebra Applications, two real-world explorations of inequalities are developed: Hybrid Cars. An examination of the equations and inequalities that involve miles per gallon (mpg) for city and highway traffic reveals important information about hybrid cars and those with gasoline-powered engines. Floods in Venice. Venice experiences a great deal of flooding, and with the expected rise of sea levels over the next century, this ancient city is in peril. Through a series of inequalities, students analyze the impact of flooding.

Linear Expressions, Equations, and Functions

This is the transcript for the video of same title. Video contents: An overview of the key topics to be covered in the video.

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This is the transcript for the video of same title. Video contents: 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.

What Are Algebra Tiles?

This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Addition Equations."

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This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Addition Equations 2."

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This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Division Equations."

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This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Multiplication Equations."

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This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Subtraction Equations."

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This is the transcript for the video entitled, " Anatomy of an Equation: One-Step Subtraction Equations 2."

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This is the transcript that goes with the video segment entitled Video Tutorial: One-Step Equations: Addition.

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This is the transcript that goes with the video segment entitled Video: One-Step Equations: Division.

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This is the transcript that goes with the video segment entitled Video Tutorial: One-Step Equations: Multiplication.

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This is the transcript that goes with the video segment entitled Video: One-Step Equations: Subtraction.

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This is the transcript that goes with the video segment entitled Video: Two-Step Equations: Division and Addition.

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This is the transcript that goes with the video segment entitled Video: Two-Step Equations: Division and Subtraction.

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This is the transcript that goes with the video segment entitled Video: Two-Step Equations: Multiplication and Addition.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript that goes with the video segment entitled Video: Two-Step Equations: Multiplication and Subtraction.

To see the complete collection of video transcriptsy, click on this link.

Topic

Expressions and Equations

Description

The video demonstrates modeling equations with algebra tiles, using a vertical bar to represent the equals sign. Examples include linear equations like x + 2 = -2 and quadratic equations like x-squared + x + 2 = 2. Key vocabulary includes equations, quadratic, integers, and variables.

Topic

Equations

Description

This tutorial explains solving one-step equations involving addition. Key math concepts include identifying the addition operation and isolating the variable to find the solution. Vocabulary includes terms like variable, isolate, and addition operation. The math application involves solving equations such as x + 2 = 5 by subtracting 2 from both sides to isolate the variable and find x = 3.

Topic

Equations

Description

This tutorial extends solving one-step equations involving addition with negative numbers. It focuses on isolating the variable and managing negative values. Vocabulary includes terms like variable, isolate, and negative number. The application includes equations like x + 4 = -9, solved by subtracting 4 from both sides to find x = -13.

Topic

Equations

Description

This tutorial explains solving one-step equations involving division. The key focus is on isolating the variable through multiplication. Vocabulary includes terms like variable, isolate, and division operation. For example, solving x / 5 = 4 involves multiplying both sides by 5 to find x = 20.

Topic

Equations

Description

This tutorial demonstrates solving one-step equations involving multiplication. Key concepts include identifying the multiplication operation and isolating the variable. Vocabulary includes terms like variable, isolate, and multiplication operation. The application involves equations like 2x = 10, solved by dividing both sides by 2 to find x = 5.

Topic

Equations

Description

This tutorial explores solving one-step equations involving subtraction. Key concepts include recognizing the subtraction operation and isolating the variable. Vocabulary includes terms like variable, isolate, and subtraction operation. The application demonstrates solving equations such as x - 3 = 5 by adding 3 to both sides to isolate the variable and find x = 8.

Topic

Equations

Description

This tutorial covers solving one-step equations involving subtraction with negative numbers. The focus is on isolating the variable while handling negative values. Vocabulary includes terms like variable, isolate, and negative number. An example involves solving x - 5 = -12 by adding 5 to both sides to find x = -7.

Topic

Solving Equations

Description

This video introduces one-step equations that require one mathematical operation to solve. The focus is on addition equations, indicated by the addition symbol. The solution process involves using subtraction to isolate the variable. Key math concepts include solving equations, inverse operations, and maintaining equation balance. Key vocabulary includes addition, subtraction, equation, and inverse operation. Practical applications involve basic algebraic problem-solving.

Topic

Solving Equations

Description

This video covers one-step division equations, identifiable by the division symbol or fraction notation. Multiplication is applied as the inverse operation to solve for the variable. Key concepts include solving equations, inverse operations, and keeping equations balanced. Vocabulary emphasized includes division, fraction, multiplication, inverse operation, and equation. These equations are practical for solving proportional problems and foundational algebraic expressions.

Topic

Solving Equations

Description

This tutorial demonstrates solving one-step multiplication equations. Such equations are characterized by a coefficient next to the variable. Division is used to isolate the variable. The key math concepts are solving equations, using inverse operations, and maintaining balance. Important vocabulary terms include multiplication, coefficient, variable, division, and inverse operation. Applications include foundational algebra skills for understanding more complex equations.

Topic

Solving Equations

Description

This video explains how to solve one-step subtraction equations. These equations are identified by the subtraction symbol, and solving them involves using addition to isolate the variable. Key concepts discussed are solving equations, inverse operations, and keeping equations balanced. Important vocabulary includes subtraction, addition, inverse operation, and equation. Applications include solving simple algebra problems encountered in everyday contexts.

In this video, learn about the properties of equality that are the core of the equation-solving process. They'll learn about true properties for each of the four operations. Only subscribers to Media4Math Library can download these resources.

Topic

Solving Equations

Description

This video introduces solving two-step equations involving multiplication and addition. Key concepts include using inverse operations like division and subtraction to isolate the variable. Vocabulary includes variable, equation, inverse operations, multiplication, and addition. Applications include basic algebra.

Topic

Solving Equations

Description

The video explains solving two-step equations that involve multiplication and subtraction. It emphasizes the use of inverse operations such as division and addition. Key terms are variable, equation, inverse operations, multiplication, and subtraction. Algebraic applications are highlighted.

Topic

Solving Equations

Description

The tutorial covers solving two-step equations involving division and addition. It focuses on isolating the variable using inverse operations like multiplication and subtraction. Vocabulary includes variable, equation, inverse operations, division, and addition. Applications are centered on algebraic problem-solving.

Topic

Solving Equations

Description

This video addresses solving two-step equations involving division and subtraction. It demonstrates applying inverse operations, specifically multiplication and addition, to isolate the variable. Terms such as variable, equation, inverse operations, division, and subtraction are emphasized. Algebraic uses are discussed.

In this video, students expand their knowledge of properties of equations with a focus on identities. Students will see how to use identities to solve equations, in particular certain quadratic equations.

In this video, students the basics of equations. They'll learn about true equations, false equations, and conditional 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

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.

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

Inequalities

Description

This video introduces inequalities, contrasting them with equations, and discusses their properties and solution methods. Key concepts include graphing solutions, interval notation, and inequality symbols. Applications are contextualized through scenarios like semester grades and fitness ranges. Key terms include inequality, interval notation, and solution set.

Topic

Inequalities

Description

In this Math Lab explore compound inequalities on a number line.

This video highlights key concepts in inequalities, offering practical examples that make abstract math principles more accessible. Through a comprehensive approach, students can connect theoretical knowledge to real-world applications.

Relevance: This video directly supports the topic by illustrating inequalities in a clear and engaging way, making it easier for students to understand complex ideas.

Topic

Inequalities

Description

Building on Part 1, this video explores systems of inequalities and their geometric representations. Applications include business profit modeling using linear inequalities. Key vocabulary includes half-planes, slope-intercept form, and solution regions. Real-world examples, like yoga studio budgeting, highlight practical uses of inequalities.