Illustrative Math Alignment: Grade 8 Unit 3

Topic

Quadratics

Description

This image includes a table with time (x) and speed (f(x) and g(x)). The graph shows constant and changing speeds, emphasizing the slope. The slope of a Speed-vs-Time graph is called acceleration, which is the rate that speed changes.

The use of math clip art helps students visualize how acceleration is represented graphically, aiding in understanding real-world applications.

Teacher's Script: "Notice the slope of these lines. How does it show acceleration? Let's explore what this means for speed changes."

Topic

Quadratics

Description

This image presents a table with time (x) and speed (g(x)). The graph emphasizes acceleration as the slope, with an equation showing g(x) = 20x. The equation of the linear function is the acceleration (a) times the amount of time.

The use of math clip art clarifies how equations relate to real-world motion, enhancing comprehension.

Teacher's Script: "See how the equation shows acceleration? What does the slope tell us about speed changes?"

Topic

Quadratics

Description

This image features a table with time versus speed data, along with a graph that explains finding distance by calculating the area under a triangular region. To find the distance traveled over a period, calculate the area of the triangular region.

The use of math clip art aids in understanding by connecting theoretical concepts with practical applications.

Teacher's Script: "Notice how we find distance using the triangle area. How does this connect to what we've learned about motion?"

Topic

Quadratics

Description

This image displays a graph with speed versus time, highlighting the equation of the line and the area under it. It emphasizes using these equations when acceleration starts from zero. If you know the acceleration rate of a car that starts from speed zero, use these equations for speed and distance traveled.

The use of math clip art provides visual clarity in understanding how equations model motion from rest.

Teacher's Script: "Notice these equations—how do they help us understand acceleration from rest?"

Topic

Quadratics

Description

This image shows a graph with speed on the y-axis and time on the x-axis. The equations for speed and distance traveled are given as s = a⋅t and d = 1/2at2. The graph illustrates how speed increases linearly, while distance traveled follows a non-linear path.

Math clip art like this helps students understand the difference between linear and quadratic relationships in real-world contexts.

Topic

Quadratics

Description

This image shows a graph similar to the previous image but at t = 2 seconds. The equations are updated to s = 2a and d = 2a, indicating that distance has caught up with speed.

The use of math clip art provides visual clarity in understanding dynamic interactions between speed and distance over time.

Teacher's Script: "At two seconds, notice how distance catches up to speed. What does this mean for our understanding of motion?"

Topic

Quadratics

Description

This image depicts a graph of speed versus time with no initial velocity. The equations shown are s = a⋅t for speed and d = 1/2at2 for distance traveled. At t = 3 seconds, the graph highlights that distance outpaces speed.

The use of math clip art helps students visualize how distance can grow faster than speed under certain conditions.

Teacher's Script: "At three seconds, see how distance outpaces speed? Let's explore why this happens."

Topic

Quadratics

Description

This image shows a graph with a line representing speed as a function of time, with initial velocity. The equations for speed are s = a⋅t+vi ​ and for distance traveled are d= 1/2at2 +vi ​•t. The graph illustrates the area under the line, indicating distance.

The use of math clip art provides students with visual tools to understand how initial velocity affects motion over time.

Teacher's Script: "Notice how initial velocity changes the graph. How does this affect our calculations for distance?"

Topic

Linear Functions

Description

In this series of math clip art demonstrating applications of linear functions, the business model series offers insight into real-world uses of linear equations. This specific image serves as an introduction, presenting the title "Applications of Linear Functions: Building a Business Model."

Topic

Linear Functions

Description

This math clip art is part of a series illustrating applications of linear functions in business modeling. The image focuses on the production cost of t-shirts, highlighting that each t-shirt costs $10 to produce, including materials and labor.

Topic

Linear Functions

Description

This math clip art continues the series on applications of linear functions in business modeling. The image depicts a sewing machine with t-shirts, introducing the concept of fixed monthly costs in a business, set at $2000 for expenses like rent and utilities.

Topic

Linear Functions

Description

This math clip art is a crucial part of the series on applications of linear functions in business modeling. It presents the equation C = 10x + 2000, which encapsulates the business model we've been building. Here, C represents the total monthly costs, x is the number of t-shirts produced, 10 is the cost per shirt, and 2000 represents the fixed monthly costs.

Topic

Linear Functions

Description

This math clip art continues the series on applications of linear functions in business modeling. It presents a graph of the linear function for cost that we've been developing throughout this series. The image prompts students to consider the domain and range of this function within the context of the t-shirt business.

Topic

Linear Functions

Description

This math clip art is part of a series demonstrating applications of linear functions in business modeling. The image shows a graph of the linear model we've developed, emphasizing its predictive power. It challenges students to use the model to predict the cost of producing 500 t-shirts.

Topic

Linear Functions

Description

This math clip art continues the series on applications of linear functions in business modeling. The image presents a graph and poses a question about determining the number of t-shirts produced given a total monthly expenditure of $5000. This scenario demonstrates how linear models can be used to solve for unknown variables.

Topic

Linear Functions

Description

This math clip art is part of a series illustrating applications of linear functions in business modeling. The image depicts t-shirts with a caption that introduces the concept of limitations in linear models. This encourages critical thinking about the applicability and constraints of mathematical models in real-world scenarios.

Topic

Linear Functions

Description

This math clip art concludes the series on applications of linear functions in business modeling. The image reiterates the limitations of linear models and introduces a specific example: the possibility of reduced per-unit costs when producing large quantities of t-shirts. This concept challenges the assumption of constant per-unit costs in our linear model.

Topic

Linear Functions

Topic

Linear Functions

Topic

Linear Functions

Topic

Linear Functions

Topic

Linear Functions

Topic

Linear Functions

Topic

Linear Functions

Description

This math clip art image is the seventh in a series dedicated to illustrating applications of linear functions, specifically focusing on building a linear function model for equipment rental costs. The image builds upon the previous one by introducing the concepts of domain and range in the context of the rental cost function. It continues to feature the construction equipment scenario, emphasizing the practical constraints on the function's input and output values.

Topic

Linear Functions

Description

This math clip art image is the eighth in a series exploring applications of linear functions, focusing on building a linear function model for equipment rental costs. The image emphasizes the relationship between the coefficient of x in the linear equation, the slope of the line in the graph, and the real-world rental rate. It continues to feature the construction equipment scenario, providing a concrete context for understanding these mathematical concepts.

Topic

Linear Functions

Topic

Linear Functions

Topic

Linear Functions

Description

This image introduces the topic Applications of Linear Functions: Cricket Chirps and sets the stage for understanding the relationship between the number of cricket chirps and outside temperature. It serves as a title card for a series of images exploring how linear functions can model real-world scenarios, specifically the connection between cricket chirps and outdoor temperature.

Topic

Linear Functions

Description

This image in the series on applications of linear functions introduces the concept of crickets as nature's thermometers. It visually represents how the frequency of cricket chirps can indicate outside temperature, setting the foundation for exploring the linear relationship between these variables.

Topic

Linear Functions

Description

This image in the series on applications of linear functions illustrates the direct relationship between temperature (T) and the number of cricket chirps (C). It visually represents how these two variables are connected, laying the groundwork for developing a linear function model.

Topic

Linear Functions

Description

This image presents a data table showing different values for cricket chirps (C) and corresponding temperatures (T). It's a crucial step in building a linear function model, as it provides the raw data from which the relationship will be derived.

Topic

Linear Functions

Description

This image in the series on applications of linear functions presents a graph of the chirps-vs-temperature data. It shows discrete points plotted on a coordinate plane, demonstrating the linear relationship between cricket chirps and temperature.

Topic

Linear Functions

Description

This image builds upon the previous one in the series on applications of linear functions. It shows the same data points as before, but now connected by a straight line. This line represents the continuous relationship between cricket chirps and temperature.

Topic

Linear Functions

Description

This image in the series on applications of linear functions highlights a crucial feature of the graph: the y-intercept. It shows where the line intersects the y-axis, indicating the y-intercept value.

Topic

Linear Functions

Description

This image in the series on applications of linear functions focuses on calculating the slope of the line. It highlights two specific points on the graph and shows the slope formula used to determine the slope value.

Topic

Linear Functions

Description

This image in the series on applications of linear functions presents the equation of the linear function. This equation represents the relationship between temperature (T) and the number of cricket chirps (C).

Topic

Linear Functions

Description

This image concludes the series on applications of linear functions, focusing on the domain and range of the cricket chirps-temperature model. It visually represents the statement "The domain is x ≥ 0. The range is y ≥ 40," which provides crucial information about the limitations and applicability of the linear function.

Topic

Linear Functions

Description

This image serves as the title card for a series of math clip art illustrations demonstrating applications of linear functions, specifically focusing on distance versus time scenarios. The series, comprising ten images, is designed to explore linear models for speed calculations using distance-time data. This introductory image sets the stage for students to delve into the practical applications of linear functions in real-world contexts.

Topic

Linear Functions

Description

This math clip art image is part of a series illustrating applications of linear functions, focusing on building a linear function model for distance versus time. The image presents a car and a data table, introducing a scenario where a car travels at a constant speed of 30 feet per second, which is approximately 20 miles per hour. This visual representation helps students connect abstract mathematical concepts to real-world situations.

Topic

Linear Functions

Description

This math clip art image continues the series on applications of linear functions, focusing on the relationship between distance and time. It builds upon the previous image, showing an expanded data table that illustrates how the distance traveled (represented by f(x)) increases for each second (x) that passes. The image emphasizes that for every increase of 1 in x, the values of f(x) increase by 30, corresponding to the car's speed of 30 feet per second.

Topic

Linear Functions

Description

This math clip art image is part of a series demonstrating applications of linear functions, specifically in modeling the relationship between distance and time. The image introduces a graph that visually represents the data from the previous illustrations. It shows a distance-vs-time graph based on the car's movement, clearly depicting a linear function.

Topic

Linear Functions

Description

This math clip art image continues the series on applications of linear functions, focusing on the distance-time relationship. It builds upon the previous graph by connecting the data points with a continuous line. The image emphasizes that because the car moves continuously, the linear function model is represented by this unbroken line, not just discrete points.

Topic

Linear Functions

Description

This math clip art image is part of a series illustrating applications of linear functions, specifically modeling the relationship between distance and time. The image introduces the equation f(x) = 30x, which represents the function that models the car's movement. This equation encapsulates the linear relationship between time (x) and distance (f(x)) that has been explored in previous images.

Topic

Linear Functions

Description

This math clip art image continues the series on applications of linear functions, focusing on the domain and range of the distance-time function. The image emphasizes that the domain of this function is x ≥ 0, and the range is y ≥ 0. This representation helps students understand the practical constraints on the variables in real-world applications of linear functions.

Topic

Linear Functions

Description

This math clip art image continues the series on applications of linear functions, focusing on the relationship between distance and time. It builds upon previous illustrations by emphasizing that the coefficient of x in the equation f(x) = 30x represents both the slope of the line and the speed of the car. This image reinforces the concept that in a linear function, the rate of change remains constant throughout.

Topic

Linear Functions

Description

This math clip art image is part of a series illustrating applications of linear functions, with a focus on the distance-time relationship. It presents a new scenario with a car and an updated data table. The image likely introduces a different speed or starting point, allowing students to compare and contrast with the previous example and explore how changes in initial conditions affect the linear function.

Topic

Linear Functions

Description

This math clip art image concludes the series on applications of linear functions in the context of distance versus time relationships. It presents a linear graph corresponding to the data table introduced in the previous image. This visual representation allows students to see how the new scenario translates into a graphical form, reinforcing the connection between tabular data and its linear graph.

Topic

Linear Functions

Description

This image serves as the title card for a series of illustrations demonstrating applications of linear functions, specifically focusing on Hooke's Law. The series, comprising eight images, explores the relationship between force and displacement in springs, showcasing how linear models can represent real-world phenomena.

Topic

Linear Functions

Description

This image is part of a series illustrating applications of linear functions, focusing on Hooke's Law. It depicts a spring before and after being stretched by a weight, visually representing the fundamental concept of Hooke's Law.

The illustration shows a spring in its original state and then stretched by an object of mass m, extending by a length x. This visual representation helps students understand the relationship between the applied force (weight) and the resulting displacement of the spring, which forms the basis of the linear function in Hooke's Law.

Topic

Linear Functions

Description

This image is a continuation of the series on applications of linear functions, specifically illustrating Hooke's Law. It builds upon the previous image by introducing the mathematical equation F(x) = kx, which is the core of Hooke's Law.

The illustration shows that when a spring is stretched a distance x, a force F(x) is generated that is proportional to x. This visual representation, combined with the equation, helps students understand the linear relationship between force and displacement in springs.