Illustrative Math Alignment: Grade 7 Unit 2

In this Slide Show, apply concepts of linear functions to the context of converting Celsius and Fahrenheit temperatures.

Note: The download is a PPT file.

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In this Slide Show, use the Desmos graphing calculator to explore absolute value functions. To see the complete collection of Desmos Resources click on this link.

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In this Slide Show, use the Desmos graphing calculator to explore linear functions. To see the complete collection of Desmos Resources click on this link.

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In this Slide Show, learn about graphs of linear functions.

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In this Slide Show, learn about linear function models.

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In this Slide Show, absolute value functions are graphed, including graphs centered at the origin, graphs displaced along the x-axis, and graphs displaced along the y-axis. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, the Graph Window is used to graph linear inequalities. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, the Graph Window is used to graph linear inequalities. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, the Graph Window is used to graph inequalities using sliders. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, the Graph Window is used to graph inequalities using sliders. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, linear functions are graphed. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this TI-Nspire Activity, use the Geometry and Graphing Tools to explore the ratio of Circumference to Radius as a linear function. 

Note: The Preview is a Google Slide Show and the download is a PPT. Subscribers to Media4Math can download resources.

In this TI-Nspire Activity, use the Geometry and Graphing Tools to explore the ratio of Circumference to Radius as a linear function. 

Note: The Preview is a Google Slide Show and the download is a PPT. Subscribers to Media4Math can download resources.

In this TI-Nspire Activity, use the Geometry and Graphing Tools to explore the ratio of Circumference to Radius as a linear function. 

Note: The Preview is a Google Slide Show and the download is a PPT. Subscribers to Media4Math can download resources.

The Introduction to Linear Functions lesson by Media4Math is designed for high school students to grasp the fundamentals of linear functions, their properties, and real-world applications. Aligned with Common Core Standards F.IF.4 and F.LE.1, this lesson emphasizes understanding linear functions through equations and graphical representations.

Lesson Summary

In this lesson, students will explore different methods for graphing linear functions, strengthening their understanding of how algebraic equations relate to their graphical representations. The lesson covers:

By the end of this lesson, students will be proficient in graphing linear functions and interpreting their meaning in real-world applications.

This comprehensive lesson plan delves into the concept of slope as a measure of the rate of change in linear functions. Students will engage with various representations—graphs, tables, and real-world scenarios—to calculate and interpret slope effectively. The lesson emphasizes contextual understanding, enabling learners to connect mathematical concepts to everyday situations.

Key components of the lesson include:

This comprehensive lesson plan delves into the concept of slope as a measure of the rate of change in linear functions. Students will engage with various representations—graphs, tables, and real-world scenarios—to calculate and interpret slope effectively. The lesson emphasizes contextual understanding, enabling learners to connect mathematical concepts to everyday situations.

Key components of the lesson include:

This comprehensive lesson plan delves into the concept of slope as a measure of the rate of change in linear functions. Students will engage with various representations—graphs, tables, and real-world scenarios—to calculate and interpret slope effectively. The lesson emphasizes contextual understanding, enabling learners to connect mathematical concepts to everyday situations.

Key components of the lesson include:

In this comprehensive lesson plan, high school students delve into the practical applications of linear functions, bridging the gap between mathematical concepts and real-world scenarios. The lesson focuses on identifying situations that can be modeled with linear equations, formulating these equations, and interpreting their components within various contexts.

Key components of the lesson include:

In this comprehensive lesson plan, high school students delve into the practical applications of linear functions, bridging the gap between mathematical concepts and real-world scenarios. The lesson focuses on identifying situations that can be modeled with linear equations, formulating these equations, and interpreting their components within various contexts.

Key components of the lesson include:

In this comprehensive lesson plan, high school students delve into the practical applications of linear functions, bridging the gap between mathematical concepts and real-world scenarios. The lesson focuses on identifying situations that can be modeled with linear equations, formulating these equations, and interpreting their components within various contexts.

Key components of the lesson include:

This lesson focuses on the application of linear functions in real-world contexts, helping students develop mathematical models to analyze and interpret relationships between variables. Students will explore various linear models, including business growth, water levels, budgeting, and physical laws such as Hooke’s Law and Boyle’s Law.

Key components of this lesson include:

Lesson Plan: Linear Functions and Applications

This is the fifth and final lesson in a five-part series on linear equations and inequalities designed for middle school students. In this lesson, students explore linear functions in-depth, learning how to represent them using equations, tables, and graphs. They will analyze key function properties, including slope, y-intercept, domain, and range, to develop a complete understanding of how linear functions behave.

The lesson focuses on real-world applications, demonstrating how linear functions are used in various fields such as finance, physics, and business. Students will solve problems involving rates of change, cost analysis, and motion, reinforcing the practical significance of linear functions. Through guided practice and hands-on activities, they will interpret linear relationships and predict outcomes using function models.

In this lesson, students will deepen their understanding of equivalent ratios and their role in proportional reasoning. By exploring real-world applications, students will develop the skills to recognize, create, and use equivalent ratios in practical situations. The lesson introduces multiple strategies for working with equivalent ratios, including ratio tables, scaling up and down, and solving problems using proportional reasoning.

Key components of this lesson include:

This lesson introduces sixth-grade students to ratios and rates, emphasizing their applications in real-world problem-solving. Through hands-on activities, students will learn how to calculate unit rates, interpret proportional relationships, and analyze data using tables and graphs.

This lesson plan is designed to provide sixth-grade students with a comprehensive understanding of ratios, proportions, and percents. Through engaging activities, hands-on explorations, and real-world applications, learners develop essential skills in comparing quantities, scaling figures up or down, and converting between fractions, decimals, and percents. This lesson emphasizes critical thinking and problem-solving strategies that help students apply mathematical reasoning to everyday situations, such as adjusting recipes, budgeting, and analyzing data.

Key topics covered in this lesson include:

This lesson introduces seventh-grade students to unit rates and complex fractions, helping them develop a deeper understanding of proportional relationships and fraction operations. Students will learn to compute unit rates with fractional quantities, simplify complex fractions, and apply these skills to real-world situations such as speed calculations, recipe adjustments, and measurement conversions.

In this lesson, students will develop their problem-solving skills by tackling multi-step ratio and proportion problems. They will learn how to analyze complex ratio scenarios, apply proportional reasoning, and use unit conversions to solve real-world problems. This lesson builds on students' understanding of ratios and proportions, reinforcing their ability to work through multi-step calculations with confidence.

Key concepts covered in this lesson include:

In this lesson, students will explore how to represent and analyze proportional relationships using graphs, tables, and equations. They will learn that proportional relationships follow the equation $y = kx$, where $k$ is the constant of proportionality, and that these relationships always form a straight line passing through the origin on a coordinate plane.

Key concepts covered in this lesson include:

In this lesson, students will explore how to represent and analyze proportional relationships using graphs, tables, and equations. They will learn that proportional relationships follow the equation $y = kx$, where $k$ is the constant of proportionality, and that these relationships always form a straight line passing through the origin on a coordinate plane.

Key concepts covered in this lesson include:

In this lesson, students will explore direct variation, a special type of proportional relationship where one variable is a constant multiple of another. They will learn how to identify direct variation in tables, graphs, and equations, determine the constant of variation ($k$), and understand how direct variation relates to linear functions.

Key concepts covered in this lesson include:

This collection of clip art images includes images of 3D figures and composite figures.

This collection of clip art images includes images of 3D figures and composite figures.

This collection of clip art images includes images of 3D figures and composite figures.

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

Description

This math clip art image is part of a series illustrating key linear function concepts. It depicts a bicycle alongside a linear graph, demonstrating the concept of constant speed. The graph shows a linear function that crosses the origin and has a positive slope, representing a scenario where at the starting point (t = 0), no distance has been traveled.

Topic

Linear Functions

Description

This math clip art image is part of a series illustrating key linear function concepts. It features a taxi alongside a graph labeled "Situation: Cost of a Taxi". The graph represents a linear function with a positive y-intercept, demonstrating a scenario with a base fee and a rate per mile traveled.

Topic

Linear Functions

Description

This math clip art image is part of a series illustrating key linear function concepts. It depicts a person walking a dog alongside a graph labeled "Situation: Walking Home". The graph shows a linear function with a negative slope, representing a scenario where the distance from home decreases as time increases.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, which are fundamental to understanding how lines behave in mathematics. The specific content of this image features a mountain and a graph titled "Situation: Altitude Change". It demonstrates a linear function with a negative slope, represented by the equation y = -0.01x + 101, showing how air pressure changes with altitude.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, which are essential for understanding how lines behave in mathematics. The specific content of this image features sunflowers and a graph titled "Situation: Plant Growth". It demonstrates a linear function with a positive slope, represented by the equation y = 2x + 20, showing how the height of a sunflower changes over time.

February 2023. In this issue of Math in the News we look at NFL statistics for the number of concussions. The NFL now tracks concussion, and this is an opportunity to analyze this data and draw conclusions.

Note: The download is a PPT file.

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