Illustrative Math Alignment: Grade 7 Unit 7

This is the transcript that goes with the video segment entitled Video Tutorial: Quadratics: Using the Discriminant to Test for Solutions to Quadratic Equations.

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This is the transcript that goes with the video segment entitled Video Tutorial: Quadratics: What is a Quadratic Equation?

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What Are Rational Numbers?

This is the transcript that goes with the video segment entitled Video: Rational Numbers: Comparing and Ordering Rational Numbers.

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This is the transcript that goes with the video segment entitled Video: Rational Numbers: Dividing Rational Numbers.

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This is the transcript that goes with the video segment entitled Video: Rational Numbers: Multiplying Rational Numbers.

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This is the transcript that goes with the video segment entitled Video: Rational Numbers: Numerical Expressions with Rational Numbers.

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This is the transcript that goes with the video segment entitled Video Tutorial: Rational Numbers: Rational Numbers and Absolute Value.

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This is the transcript that goes with the video segment entitled Video Tutorial: Rational Numbers: Rational Numbers and Absolute Value.

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This is the transcript that goes with the video segment entitled Video Tutorial: Rational Numbers: Rational Numbers and Exponents.

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This is the transcript that goes with the video segment entitled Video Tutorial: Rational Numbers: Rational Numbers and Irrational Numbers.

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Distance Measures on a Number Line

Distance Measures on a Number Line

This is the transcript that goes with the video segment entitled Video Tutorial: Rational Numbers: Rational Numbers On the Cartesian Coordinate System.

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This is the transcript that goes with the video segment entitled Video Tutorial: Rational Numbers: Rational Numbers On the Cartesian Coordinate System.

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This is the transcript that goes with the video segment entitled Video Tutorial: Rational Numbers: Subtracting Rational Numbers.

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This is the transcript that goes with the video segment entitled Video Tutorial: Rational Numbers: Subtracting Rational Numbers.

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This is the transcript that goes with the video segment entitled Video Tutorial: Rational Numbers: Variable Expressions with Rational Numbers.

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This is the transcript that goes with the video segment entitled Video Tutorial: Rational Numbers: Variable Expressions with Rational Numbers.

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What Are Rational Numbers?

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Multiplying Rational Expressions.

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This is the transcript for the TI-Nspire Mini-Tutorial entitled, Solving a System of Two Linear Equations.

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This is the transcript for the TI-Nspire Mini-Tutorial entitled, Creating a Template to Find the Roots of a Quadratic Equation.

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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.

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

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Topic

Polynomials

Description

This segment discusses solving polynomial equations by finding roots and applying the quadratic formula. It highlights the use of discriminants to determine the number of real solutions. Applications include solving real-world problems modeled by polynomial equations. Key vocabulary includes quadratic formula, discriminant, roots, and solutions.

Topic

Equations

Description

This video explains converting a linear equation from standard form to slope-intercept form with positive A, B, and C values. Starting with Ax + By = C, key vocabulary includes slope, y-intercept, standard form, and simplification. The tutorial demonstrates isolating y by subtracting the x-term and dividing by the y coefficient, resulting in slope m and y-intercept b.

Topic

Equations

Description

This segment covers transforming a linear equation from standard to slope-intercept form with positive A and B and negative C. The equation Ax + By = C is manipulated to isolate y, using key terms like slope, y-intercept, and simplification. Steps include subtracting the x-term and dividing by the y coefficient to reveal slope m and y-intercept b.

Topic

Equations

Description

This tutorial details converting a linear equation where A and C are positive and B is negative from standard to slope-intercept form. Using Ax – By = C, vocabulary such as slope, intercept, and simplification is explored. By isolating y through subtraction and division, the video derives the slope and y-intercept values.

Topic

Equations

Description

This video explains converting a linear equation from standard form to slope-intercept form when A is positive, B is negative, and C is negative. Key steps include moving the x term to the right side, ensuring y has a coefficient of 1, and simplifying the equation. The coefficient of x becomes the slope, and the constant term is the y-intercept. Concepts covered include slope, y-intercept, and the properties of standard and slope-intercept forms.

Topic

Equations

Description

This video demonstrates converting linear equations with positive B and C and negative A from standard form to slope-intercept form. Starting with Ax + By = C, terms like slope and intercept are discussed. Adding the x-term and dividing by the y coefficient isolates y, leading to the slope-intercept equation.

Topic

Equations

Description

This video describes the process of converting equations when A and C are negative, and B is positive. The tutorial emphasizes balancing the equation by adding the x term to both sides, simplifying, and dividing to isolate y. The x coefficient is identified as the slope, and the constant term is the y-intercept. Key math concepts include coefficients, linear equations, and the transformation between forms.

Topic

Equations

Description

The video focuses on converting equations where A and B are negative, and C is positive. The steps involve isolating the y term by adding the x term to the right side, simplifying, and ensuring the y coefficient is 1. The coefficient of x represents the slope, and the constant is the y-intercept. Vocabulary includes slope, linear equations, and y-intercept.

Topic

Equations

Description

This tutorial demonstrates how to convert equations where all terms A, B, and C are negative. It follows a similar process of isolating y by adding the x term to both sides, simplifying, and dividing. The video clarifies that the x coefficient determines the slope and the constant term indicates the y-intercept. Covered concepts include linear equations, slope, and y-intercept.

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

Equations

Description

This tutorial discusses solving quadratic equations in standard form with positive a, b, and c values. Key concepts include the quadratic formula, substitution, and identifying real roots. Vocabulary includes terms like quadratic formula, roots, and standard form. Applications demonstrate solving equations like 2x2 + 3x + 1 = 0 to find two real roots.

Topic

Equations

Description

This tutorial addresses quadratic equations with positive a and b and negative c values. It emphasizes the quadratic formula, substitution, and finding real roots. Vocabulary includes terms like quadratic formula, roots, and standard form. Applications include solving 5x2 + 6x - 2 = 0 to find two real roots.

Topic

Equations

Description

This video demonstrates solving a quadratic equation in standard form where a and c are positive, and b is negative. The standard form is ax2 + bx + c = 0. The quadratic formula is used, with step-by-step substitution of a = 4, b = -5, and c = 1 into the formula. Key vocabulary includes quadratic equation, quadratic formula, roots, and real numbers. The solution simplifies terms, notes the plus-minus for two roots, and determines the two real roots.

Topic

Equations

Description

The tutorial explores solving a quadratic equation in standard form with negative a and positive b and c values. The equation is ax2 + bx + c = 0. Substituting a = -6, b = 8, and c = 2 into the quadratic formula, the video explains simplification steps leading to two real roots. Key vocabulary includes quadratic equation, quadratic formula, roots, and real numbers. Simplifications in the square root and numerator emphasize the presence of two distinct solutions.

Topic

Equations

Description

This segment discusses solving quadratic equations with positive a and negative b and c. Using a = 7, b = -8, and c = -2, the quadratic formula is applied. Key terms include standard form, quadratic formula, real roots, and simplification. The process reveals two real roots after simplifying the square root and other terms in the formula.

Topic

Equations

Description

This video addresses solving a quadratic equation in standard form with negative a and c, and positive b. Substituting a = -8, b = 10, and c = -3 into the quadratic formula, the tutorial emphasizes key concepts such as standard form, quadratic formula, roots, and real solutions. Detailed steps simplify terms, revealing two distinct real roots.

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.