Illustrative Math Alignment: Grade 8 Unit 3

Topic

Equations

Description

This tutorial focuses on solving a quadratic equation in standard form where a and b are negative, and c is positive. Using the quadratic formula with a = -9, b = -12, and c = 4, key vocabulary such as quadratic equation, roots, and standard form are explained. Simplification steps highlight the process of finding two real roots.

Topic

Equations

Description

The video outlines solving quadratic equations where all coefficients a, b, and c are negative. With values a = -5, b = -8, and c = -2, the quadratic formula is applied. Key terms include quadratic formula, roots, and simplification. The process demonstrates obtaining two real roots through detailed algebraic steps.

Topic

Equations

Description

This video explains solving a two-step equation involving addition and multiplication. The key concepts include isolating the variable by undoing operations using inverse operations. For example, subtracting from both sides to handle addition and dividing to simplify the coefficient of the variable. Vocabulary includes variable, coefficient, isolate, and inverse operation. Applications focus on understanding algebraic manipulation to find solutions.

Topic

Equations

Description

This video explains solving equations with addition and division where the divisor is negative. Steps include subtracting the constant and multiplying by the negative reciprocal. Vocabulary includes negative divisor, reciprocal, and isolate. Applications focus on managing division in equations with negative values.

Topic

Equations

Description

This segment explains solving equations with addition and division where both the divisor and the constant are negative. Key steps include subtracting the constant and multiplying by the negative reciprocal. Vocabulary includes negative reciprocal, isolate, and simplify. Applications refine algebraic problem-solving involving multiple negatives.

Topic

Equations

Description

This tutorial focuses on solving equations with subtraction and division. Steps include adding the constant to isolate the variable and multiplying by the reciprocal of the divisor. Vocabulary includes reciprocal, subtraction, and isolate. Applications reinforce division concepts in algebraic equations.

Topic

Equations

Description

This video covers equations with subtraction and division, where the divisor and the constant are negative. Techniques involve adding the constant and multiplying by the negative reciprocal. Vocabulary includes negative reciprocal, subtraction, and isolate. Applications focus on handling division with negative values in equations.

Topic

Equations

Description

This segment covers equations involving addition and multiplication where a negative number appears. It emphasizes isolating the variable by subtracting the constant, simplifying, and dividing by the coefficient. Vocabulary includes isolate, simplify, and negative numbers. Applications extend algebraic problem-solving skills with negative values.

Topic

Equations

Description

This video introduces solving equations with subtraction and multiplication. Steps include adding the constant to isolate the variable and dividing by the coefficient. Vocabulary includes subtraction, isolate, and coefficient. Applications enhance understanding of balancing equations with subtraction operations.

Topic

Equations

Description

This segment focuses on handling subtraction and multiplication when a negative number is involved. Techniques include adding the constant, simplifying, and dividing by a positive coefficient. Vocabulary includes subtraction, negative coefficient, and isolate. Applications involve solving equations with more complex negative value interactions.

Topic

Equations

Description

This tutorial demonstrates equations with addition and negative coefficients. The process involves subtracting the constant, simplifying, and dividing by the negative coefficient. Vocabulary includes negative coefficient, simplify, and inverse operation. Applications refine algebraic methods in equations with negative variable multipliers.

Topic

Equations

Description

This video examines equations with addition, multiplication, negative coefficients, and negative constants. It outlines steps to isolate the variable, simplify, and divide by the negative coefficient. Vocabulary includes negative constants, simplify, and isolate. Applications improve skills in handling equations with layered negative components.

Topic

Equations

Description

This segment focuses on equations with subtraction and negative coefficients. Steps include adding the constant, simplifying, and dividing by the negative coefficient. Vocabulary includes negative coefficient, isolate, and subtraction. Applications highlight algebraic problem-solving with negative coefficients.

Topic

Equations

Description

This video presents subtraction, multiplication, and negative coefficients alongside negative numbers. Solving requires adding the constant, simplifying, and dividing by the negative coefficient. Vocabulary includes subtraction, negative values, and isolate. Applications stress solving equations with multiple negative components.

Topic

Equations

Description

This tutorial covers equations involving addition and division. Key steps are subtracting the constant and multiplying by the reciprocal of the divisor. Vocabulary includes reciprocal, division, and isolate. Applications build on foundational algebraic techniques involving division.

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.

This is part of a collection of video tutorials on solving quadratic equations by completing the square. Each video is a step-by-step tutorial.

Note: The download is a PDF template for use in modeling the examples shown in the videos.

This is part of a collection of video tutorials on solving quadratic equations by completing the square. Each video is a step-by-step tutorial.

Note: The download is a PDF template for use in modeling the examples shown in the videos.

This is part of a collection of video tutorials on solving quadratic equations by completing the square. Each video is a step-by-step tutorial.

Note: The download is a PDF template for use in modeling the examples shown in the videos.

This is part of a collection of video tutorials on solving quadratic equations by completing the square. Each video is a step-by-step tutorial.

Note: The download is a PDF template for use in modeling the examples shown in the videos.

Topic

Mathematical Properties

Description

This video introduces the distributive property using cases with positive constant terms. Examples include finding the area of a rectangle and parallelogram and converting word problems into expressions like x + 5 multiplied by a factor. Vocabulary includes terms like area, expression, and distribute, with applications in geometry and algebra.

Topic

Mathematical Properties

Description

This video addresses positive constants with negative x-coefficients and subtraction. Examples include expressions like -x - 9 multiplied by 7. Vocabulary includes distribute, inequality, and positive area. Applications link inequalities with the distributive property to find positive solutions.

Topic

Mathematical Properties

Description

This video examines scenarios with negative constants and coefficients involving subtraction. Examples include expressions like -x - 8 multiplied by -5. Key vocabulary includes distribute, negative subtraction, and evaluate. Applications demonstrate managing multiple negative terms in expressions.

Topic

Mathematical Properties

Description

This video focuses on negative coefficients and subtraction in expressions. Examples like -x - (-8) multiplied by -4 are explored. Vocabulary includes distribute, negative signs, and subtraction. Applications emphasize handling subtraction with negatives.

Topic

Mathematical Properties

Description

This video introduces expressions with positive constants and coefficients greater than 1. Examples include 5 multiplied by 3x + 7. Vocabulary includes distribute, variable, and addition. Applications highlight multiplying expanded expressions.

Topic

Mathematical Properties

Description

This video examines positive constants with addition and larger coefficients. Examples like 7x + 9 multiplied by -8 are discussed. Vocabulary includes distribute, large coefficients, and evaluate. Applications explore handling addition with negatives in expressions.

Topic

Mathematical Properties

Description

This video covers all-negative constants and coefficients with addition. Examples include -8x + (-5) multiplied by -4. Vocabulary includes distribute, double negatives, and addition. Applications explore handling multiple negatives in algebra.

Topic

Mathematical Properties

Topic

Mathematical Properties

Description

This video focuses on subtraction with large positive coefficients. Examples include 8x - 5 multiplied by -6. Vocabulary includes distribute, subtraction, and coefficients. Applications showcase simplifying complex expressions with subtraction and negatives.

Topic

Mathematical Properties

Description

This video explores all-negative constants, coefficients, and subtraction. Examples include -3x - (-6) multiplied by -8. Vocabulary includes distribute, negative subtraction, and double negatives. Applications emphasize managing subtraction with negatives in expressions.

Topic

Mathematical Properties

Description

This video explores the distributive property where the constant term a is negative. Examples involve converting phrases into expressions such as x + 3 multiplied by -4. Key vocabulary includes distribute, evaluate, and coefficient. Applications focus on translating verbal scenarios into algebraic representations.

Topic

Mathematical Properties

Description

This video focuses on scenarios where both constants a and b are negative. Examples include expressions like x + (-9) multiplied by -3. Vocabulary includes distribute, negative terms, and evaluate. Applications highlight handling negative coefficients in algebraic expressions.

Topic

Mathematical Properties

Description

This video covers cases with positive constants and a negative x-term. Examples include calculating areas and translating word problems such as -x + 25 multiplied by 6. Key terms include distribute, negative coefficient, and variable expression. Applications emphasize solving algebraic problems with mixed signs.

Topic

Mathematical Properties

Description

This video examines cases with negative constants and x-term coefficients. Examples transform verbal descriptions like -x + 5 multiplied by -7 into expressions. Vocabulary includes distribute, product, and expression. Applications demonstrate working with double negatives in algebraic operations.

Topic

Mathematical Properties

Description

This video addresses situations with all negative constants and coefficients. Examples include expressions like -x + (-6) multiplied by -4. Key vocabulary includes distribute, double negatives, and evaluate. Applications focus on understanding interactions of negatives in algebraic expressions.

Topic

Mathematical Properties

Description

This video explores the distributive property with positive constants and subtraction. Examples involve geometry problems, such as calculating areas using x - 8 multiplied by a factor. Vocabulary includes subtract, area, and distribute. Applications center on integrating subtraction into the distributive process.

Topic

Mathematical Properties

Description

This video highlights cases with a negative constant a and subtraction. Examples include expressions like x - 8 multiplied by -9. Vocabulary includes distribute, negative coefficient, and subtraction. Applications stress combining subtraction and negatives in algebraic contexts.

Topic

Mathematical Properties

Description

This video discusses scenarios with negative constants and subtraction. Examples feature expressions like x - (-7) multiplied by -8. Vocabulary includes distribute, negative subtraction, and evaluate. Applications focus on navigating multiple negative signs in algebra.

This video provides a step-by-step tutorial on using the quadratic formula. In this example there are two real roots. Note the download is a PDF that can used to demonstrate the step-by-step calculations.

This video provides a step-by-step tutorial on using the quadratic formula. In this example there are two real roots. Note the download is a PDF that can used to demonstrate the step-by-step calculations.

This video provides a step-by-step tutorial on using the quadratic formula. In this example there are two real roots. Note the download is a PDF that can used to demonstrate the step-by-step calculations.

This video provides a step-by-step tutorial on using the quadratic formula. In this example there is only one real root. Note the download is a PDF that can used to demonstrate the step-by-step calculations.

This video provides a step-by-step tutorial on using the quadratic formula. In this example there are two complex roots. Note the download is a PDF that can used to demonstrate the step-by-step calculations.

What Is a Variable?

A variable is a symbol, usually a letter, that can stand for different things.

What Is a Variable?

A variable is a symbol, usually a letter, that can stand for different things.

What Is a Variable?

A variable is a symbol, usually a letter, that can stand for different things.

Watch the following video on Order of Operations. (The transcript is included.)

Video Transcript

A numerical expression includes numbers and operation symbols, addition, subtraction, multiplication, and division.

Because addition is commutative, adding from left to right, or right to left, gives you the same result.

The expressions 2 + 3 and 3 + 2 give the same result. But this isn't the case with all operations.

Subtraction isn't commutative.