Illustrative Math Alignment: Grade 8 Unit 3

Overview

Overview

Overview

Overview

This collection of math examples focuses on Linear Functions in Slope-Intercept Form, providing a comprehensive set of 13 examples to help students master some simple techniques for graphing these types of functions. The examples cover a range of skills and increase in complexity, allowing students to progressively build their understanding of slope-intercept form.

Overview

This collection of math examples focuses on the Point-Slope Formula, a fundamental concept in algebra that helps students understand linear equations and their graphical representations. The collection comprises 8 Math Examples, each designed to reinforce different aspects of the Point-Slope Formula and its applications.

Overview

This collection of 29 math examples focuses on the fundamental concept of finding the equation of a line given two points, a crucial skill in understanding linear functions. These resources offer a comprehensive exploration of this topic, with examples that progressively increase in complexity.

Overview

This comprehensive collection of 22 math examples focuses on Linear Equations in Standard Form, providing educators with a valuable resource to enhance their lesson plans. The examples are designed to progressively increase in complexity, covering a wide range of skills related to this fundamental algebraic concept. By utilizing visual models, these examples help simplify and clarify the often challenging aspects of linear equations, making them more accessible to students.

Overview

Overview

Overview

Overview

Overview

Overview

This collection of math examples focuses on the topic of Linear Intercepts, offering a wide range of examples that increase in complexity and engage students in key algebraic skills. This collection is ideal for building proficiency in understanding and analyzing linear functions.

Overview

The collection of definitions on the topic of Slope from Media4Math provides a comprehensive resource for students and educators to explore the concept of slope in mathematics. This collection includes key terms such as "slope-intercept form," "rise over run," and "slope formula," which are fundamental in understanding how slope is used to describe the steepness and direction of a line. These definitions are crucial for students as they form the foundation for more advanced topics in algebra and calculus.

Overview

The collection of definitions on the topic of Linear Functions from Media4Math is an invaluable resource for students and educators alike. This comprehensive set includes essential terms such as slope, y-intercept, linear function, and rate of change. Understanding these terms is crucial for mastering the concept of linear functions, which are foundational in algebra and essential for advanced mathematical studies.

Instructional Videos on the Slope Formula.

Overview

Test your understanding of using the Slope Formula with this selection of quizzes in worksheet format.

Review the following basic information on the slope formula.

This is a collection of instructional resources that use the Desmos graphing calculator. These are Google Slide Shows. Subscribers can download these as PPT presentation.

Video Tutorial: Linear Functions: Negative Slope, Negative y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a negative slope and a negative y-intercept.

Video Tutorial: Linear Functions: Negative Slope, Positive y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a negative slope and a positive y-intercept.

Video Tutorial: Linear Functions: Negative Slope, Zero y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a negative slope and a zero y-intercept.

Video Tutorial: Linear Functions: Positive Slope, Negative y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a positive slope and a negative y-intercept.

Video Tutorial: Linear Functions: Positive Slope, Positive y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a positive slope and a positive y-intercept.

Video Tutorial: Linear Functions: Positive Slope, Zero y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a positive slope and a zero y-intercept.

Topic

Slope

Description

The video covers finding a negative slope in Quadrant I using the slope formula. It defines rise over run and demonstrates calculations using points (7, 3) and (5, 7), resulting in a slope of -2. Important terms include numerator, denominator, and coordinates.

Topic

Slope

Description

Explains finding a negative slope in Quadrant II using the slope formula. Demonstrates with points (-1, 4) and (-7, 6), resulting in a slope of -1/3. Covers key concepts like rise over run and coordinate differences.

Topic

Slope

Description

The video discusses finding a negative slope in Quadrant III using the slope formula. Points (-2, -7) and (-6, -5) result in a slope of -1/2. Highlights include simplifying coordinate differences and using the formula.

Topic

Slope

Description

Demonstrates calculating a negative slope in Quadrant IV. Example points are (9, -3) and (3, -1), with a slope of -1/3. Discusses coordinate differences and formula application.

Topic

Slope

Description

The video discusses a negative slope with points in Quadrants I and II. Using (4, 2) and (-2, 8), it calculates a slope of -1. Highlights include rise over run and coordinate simplifications.

Topic

Slope

Description

Explains calculating a negative slope for points in Quadrants III and IV. Example points (7, -5) and (-5, -1) yield a slope of -1/3. Key topics include applying the slope formula and simplifying results.

Topic

Slope

Description

This video explains the slope formula and applies it to find the positive slope of a line in Quadrant I. Key concepts include rise over run and calculating differences in coordinates. The example uses points (2, 3) and (6, 7) with the slope calculated as 1. Vocabulary includes rise, run, numerator, and denominator.

Topic

Slope

Description

This tutorial focuses on a positive slope in Quadrant II. Key topics include calculating slope as rise over run and using coordinate differences. It provides an example with points (-5, 4) and (-3, 8) resulting in a slope of 2. Vocabulary includes numerator, denominator, and difference.

Topic

Slope

Description

Shows how to calculate a positive slope in Quadrant III using the slope formula. Example uses points (-3, -8) and (-2, -2), with a slope of 6. Concepts include rise over run and simplifying fractions.

Topic

Slope

Description

Explains finding a positive slope in Quadrant IV. Demonstrates using points (2, -5) and (4, -1) to calculate a slope of 2. Vocabulary includes rise over run, numerator, and denominator.

Topic

Slope

Description

Covers a positive slope with points spanning Quadrants I and II. Example uses (-3, 3) and (3, 6), yielding a slope of 1/2. Discusses rise over run, numerator, and denominator.

Topic

Slope

Description

This video demonstrates finding a positive slope with points in Quadrants III and IV. Using points (-5, -9) and (3, -5), it calculates a slope of 1/2. Concepts covered include rise over run and simplifying coordinate differences.

Topic

Linear Functions

Definition

Direct variation describes a linear relationship between two variables where one variable is a constant multiple of the other, expressed as y = kx, where k is the constant of variation.

Description

Direct variation is a fundamental concept in linear functions, illustrating how one variable changes proportionally with another. The constant of variation, 𝑘 k, represents the rate of change.

In real-world scenarios, direct variation can model relationships such as speed and distance, where distance traveled varies directly with time at a constant speed. Understanding this concept is crucial in fields like physics and engineering.

Topic

Slope

Definition

Delta x is the change in the x-coordinate in a linear relationship.

Description

The term Delta x is fundamental to understanding slope as it represents the horizontal change in a line’s position. In real-world applications, Delta x can represent the distance traveled over time in physics and engineering contexts.

Topic

Slope

Definition

Delta y is the change in the y-coordinate in a linear relationship.

Description

The term Delta y signifies the vertical change, essential for calculating slope used in graphing and data interpretation. In practical scenarios, Delta y can illustrate changes in temperature over time or the rise in elevation in geography.

Topic

Slope

Definition

Grade is a ratio indicating the steepness of a slope.

Description

The term Grade commonly refers to the angle of elevation or slope expressed as a percentage. In engineering, grades are crucial for designing roads and railways, ensuring safety and efficiency.

Topic

Slope

Definition

Gradient represents the rate of change of a quantity.

Description

The Gradient measures how steep a line is, calculated by the ratio of the rise to run. This concept is significant in fields like physics and economics where gradients can represent relationships between variables.

Topic

Slope

Definition

Negative Slope indicates a decrease in value as x increases.

Description

The Negative Slope signifies that as one variable increases, the other decreases, often used in economics to depict inverse relationships. This term finds relevance in real-world scenarios like demand curves which slope downwards.