Illustrative Math Alignment: Grade 7 Unit 7

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

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

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

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

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

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: Division 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: Division and Subtraction.

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 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

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.

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.

This video looks at the algebraic properties of equations of parallel lines. Included is a geometric proof.

This video looks at the algebraic properties of equations of perpendicular lines. Included is a geometric proof.

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.

Topic

Quadratics

Description

This video explains completing the square to solve quadratic equations. Key terms are binomial square, roots, and simplification. It explores the width of a satellite dish, triangle dimensions, and composite figure measurements.

Quadratic functions are foundational to many aspects of mathematics, from graphing parabolas to solving real-world problems involving areas and trajectories. This video is particularly relevant to understanding how these functions operate and provides practical examples to reinforce the theory.