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3.3 Inverse Functions
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This section explores the process for finding inverses of functions, and then proving the function and its inverse algebraically. Additionally, it explores how the graphs of functions and their inverses compare to each other, and it investigates how to use the horizontal and vertical line tests to determine if the inverse is itself a function or not.

A free CK-12 account is required to view all materials.

Subject:
Mathematics
Material Type:
Lesson
Provider:
CK-12 Foundation
Date Added:
10/02/2022
3.4 Graphs of Logs as the Inverse of Exponential Functions
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This lesson explores the statement that the log functions are identified as the inverse of exponential functions. These functions will be compared visually through the graphs of both the logarithmic and exponential functions.

A free CK-12 account is required to view all materials.

Subject:
Mathematics
Material Type:
Lesson
Provider:
CK-12 Foundation
Date Added:
10/02/2022
3D Design Final Project (Lesson 2 of 6): Empathize and Define
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In this lesson, students will learn more about their user and complete the first two steps in the Design Thinking process: Empathize and Define. Note: Students should only work on the content that corresponds to their project choice. For example: if a student chose Project 3A, they would only work on the Project 3A content.

Estimated time required: 1-2 class periods.

Technology required for this lesson: 3D Modeling Software, Digital Fabrication Tools, Laptop/Desktop, Tablet.

Subject:
21st Century Skills
Arts
Creativity and Innovation
Engineering
Interdisciplinary, Project-based, and Real-World Learning
Mathematics
Science
Technology
Material Type:
Lesson Plan
Provider:
Verizon
Provider Set:
Verizon Innovative Learning HQ - Lessons and Apps
Author:
J. Orin Edson Entrepreneurship + Innovation Institute at Arizona State University
Date Added:
09/20/2023
3D Design Final Project (Lesson 3 of 6): Ideate
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In this lesson, students will brainstorm and list ideas for their project (this is called ideation!). Next, students will sketch their three favorite ideas for the project, then draw a prototype plan.

Estimated time required: 1-2 class periods.

Technology required for this lesson: 3D Modeling Software, Digital Fabrication Tools, Laptop/Desktop, Tablet.

Subject:
21st Century Skills
Arts
Creativity and Innovation
Engineering
Interdisciplinary, Project-based, and Real-World Learning
Mathematics
Science
Technology
Material Type:
Lesson Plan
Provider:
Verizon
Provider Set:
Verizon Innovative Learning HQ - Lessons and Apps
Author:
J. Orin Edson Entrepreneurship + Innovation Institute at Arizona State University
Date Added:
09/20/2023
3D Design Final Project (Lesson 4 of 6): Prototype
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In this lesson, students will create a physical prototype and a 3D model in OnShape for their project. Note: Students should only work on the content that corresponds to their project choice. For example: if a student chose Project 3A, they would only work on the Project 3A content.

Estimated time required: 3-4 class periods.

Technology required for this lesson: 3D Modeling Software, Digital Fabrication Tools, Laptop/Desktop, Tablet.

Subject:
21st Century Skills
Arts
Creativity and Innovation
Engineering
Interdisciplinary, Project-based, and Real-World Learning
Mathematics
Science
Technology
Material Type:
Lesson Plan
Provider:
Verizon
Provider Set:
Verizon Innovative Learning HQ - Lessons and Apps
Author:
J. Orin Edson Entrepreneurship + Innovation Institute at Arizona State University
Date Added:
09/20/2023
3D Design Final Project (Lesson 5 of 6): User Feedback
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In this lesson, students will share their up-cycled prototype and 3D model with their end user, receive and record feedback, then make adjustments based on that feedback. Note: the lessons for 3A, 3B, and 3C are almost identical in this section. This is a great chance for students to share their project with a real user and improve the design.

Estimated time required: 1-2 class periods.

Technology required for this lesson: 3D Modeling Software, Digital Fabrication Tools, Laptop/Desktop, Tablet.

Subject:
21st Century Skills
Arts
Creativity and Innovation
Engineering
Interdisciplinary, Project-based, and Real-World Learning
Mathematics
Science
Technology
Material Type:
Lesson Plan
Provider:
Verizon
Provider Set:
Verizon Innovative Learning HQ - Lessons and Apps
Author:
J. Orin Edson Entrepreneurship + Innovation Institute at Arizona State University
Date Added:
09/20/2023
3D Design Final Project (Lesson 6 of 6): Test, Share, and Submit
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In this lesson, students will 3D print their project (if possible), create a pitch video for their project, share their project with their peers, give/receive feedback on each other’s projects, export and submit their designs, and answer a series of reflection questions.

Estimated time required: 3-4 class periods.

Technology required for this lesson: 3D Modeling Software, Digital Fabrication Tools, Laptop/Desktop, Tablet, Video Editing Software.

Subject:
21st Century Skills
Arts
Creativity and Innovation
Engineering
Interdisciplinary, Project-based, and Real-World Learning
Mathematics
Science
Technology
Material Type:
Lesson Plan
Provider:
Verizon
Provider Set:
Verizon Innovative Learning HQ - Lessons and Apps
Author:
J. Orin Edson Entrepreneurship + Innovation Institute at Arizona State University
Date Added:
09/20/2023
3D Design and Printing
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Students will use critical thinking, creativity, collaboration and communication skills to create 3D models of bubble wands using Tinkercad CAD software. The Tinkercad software used in this activity is a tool to help students develop a STEM mindset. It is important to allow students to work through the process as independently as possible with the facilitator acting only as a guide.

Estimated time required: 1 class period.

Technology required for this lesson: 3D Modeling Software, Laptop/Desktop, Tinkercad CAD software.

Subject:
21st Century Skills
Creativity and Innovation
Engineering
Interdisciplinary, Project-based, and Real-World Learning
Mathematics
Science
Technology
Material Type:
Lesson Plan
Provider:
Verizon
Provider Set:
Verizon Innovative Learning HQ - Lessons and Apps
Author:
Project Lead The Way
Date Added:
09/20/2023
3D Modeling Project (Lesson 1 of 5): Project Overview
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This is an applied project where your students will choose from three different project options, each with three different users, then use Design Thinking, entrepreneurship, and 3D modeling to create an innovative product for a real user in Ancient Greece! In Lesson 1, each student will read all three project overviews. Then, they will choose the project they want to work on for the remaining lessons in the project!

Estimated time required: 1-2 class periods.

Technology required for this lesson: 3D Modeling Software, Digital Fabrication Tools, Laptop/Desktop, Tablet.

Subject:
21st Century Skills
Arts
Creativity and Innovation
Engineering
History
Interdisciplinary, Project-based, and Real-World Learning
Mathematics
Science
Social Studies
Technology
Material Type:
Lesson Plan
Provider:
Verizon
Provider Set:
Verizon Innovative Learning HQ - Lessons and Apps
Author:
J. Orin Edson Entrepreneurship + Innovation Institute at Arizona State University
Date Added:
09/20/2023
3D Modeling Project (Lesson 2 of 5): Empathize and Define
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Educational Use
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In this lesson, students will learn more about their user and complete the first two steps in the Design Thinking process: Empathize and Define. They will complete an empathy map and create a well-crafted problem statement.

Estimated time required: 1-2 class periods.

Technology required for this lesson: 3D Modeling Software, Digital Fabrication Tools, Laptop/Desktop, Tablet.

Subject:
21st Century Skills
Arts
Creativity and Innovation
Engineering
English Language Arts
History
Interdisciplinary, Project-based, and Real-World Learning
Mathematics
Science
Social Studies
Technology
Material Type:
Lesson Plan
Provider:
Verizon
Provider Set:
Verizon Innovative Learning HQ - Lessons and Apps
Author:
J. Orin Edson Entrepreneurship + Innovation Institute at Arizona State University
Date Added:
09/20/2023
3D Modeling Project (Lesson 3 of 5): Ideate
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In this lesson, students will ideate and sketch designs for their project.

Estimated time required: 1-2 class periods.

Technology required for this lesson: 3D Modeling Software, Digital Fabrication Tools, Laptop/Desktop, Tablet.

Subject:
21st Century Skills
Arts
Creativity and Innovation
Engineering
History
Interdisciplinary, Project-based, and Real-World Learning
Mathematics
Science
Social Studies
Technology
Material Type:
Lesson Plan
Provider:
Verizon
Provider Set:
Verizon Innovative Learning HQ - Lessons and Apps
Author:
J. Orin Edson Entrepreneurship + Innovation Institute at Arizona State University
Date Added:
09/20/2023
3D Modeling Project (Lesson 4 of 5): Prototype
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In this lesson, students will create a physical prototype and a 3D model in TinkerCAD for their project.

Estimated time required: 2-3 class periods.

Technology required for this lesson: 3D Modeling Software, Digital Fabrication Tools, Laptop/Desktop, Tablet.

Subject:
Mathematics
Technology
Material Type:
Lesson Plan
Provider:
Verizon
Provider Set:
Verizon Innovative Learning HQ - Lessons and Apps
Author:
J. Orin Edson Entrepreneurship + Innovation Institute at Arizona State University
Date Added:
09/20/2023
3D Modeling Project (Lesson 5 of 5): Test, Share, and Submit
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Educational Use
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In this lesson, students will 3D print their project, share their project with their peers, give/receive feedback on each other’s projects, export and submit their designs, and answer a series of reflection questions.

Estimated time required: 1-2 class periods.

Technology required for this lesson: 3D Modeling Software, Digital Fabrication Tools, Laptop/Desktop, Tablet.

Subject:
21st Century Skills
Arts
Creativity and Innovation
Engineering
History
Interdisciplinary, Project-based, and Real-World Learning
Mathematics
Science
Social Studies
Technology
Material Type:
Lesson Plan
Provider:
Verizon
Provider Set:
Verizon Innovative Learning HQ - Lessons and Apps
Author:
J. Orin Edson Entrepreneurship + Innovation Institute at Arizona State University
Date Added:
09/20/2023
3D Modeling with TinkerCAD (Lesson 1 of 4): Intro to 3D Modeling
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Educational Use
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In this series of Ancient-Greece themed lessons, students will learn how to create 3D models and 3D prints using an online software called TinkerCAD. In lesson 1’s activity, students will use TinkerCAD to create digital 3D models of coins.

Estimated time required: 1-2 class periods.

Technology required for this lesson: 3D Modeling Software, Laptop/Desktop.

Subject:
21st Century Skills
Arts
Creativity and Innovation
Engineering
History
Interdisciplinary, Project-based, and Real-World Learning
Mathematics
Science
Social Studies
Technology
Material Type:
Lesson Plan
Provider:
Verizon
Provider Set:
Verizon Innovative Learning HQ - Lessons and Apps
Author:
J. Orin Edson Entrepreneurship + Innovation Institute at Arizona State University
Date Added:
09/20/2023
3D Modeling with TinkerCAD (Lesson 2 of 4): Intro to 3D Printing
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In lesson 2’s activity, students will learn how to 3D model and 3D print a custom designed Ring Project using TinkerCAD and a 3D Printer. The teacher will preview each project in a "Slicing" application before printing the designs.

Estimated time required: 1-2 class periods.

Technology required for this lesson: 3D Modeling Software, Digital Fabrication Tools, Laptop/Desktop.

Subject:
21st Century Skills
Arts
Creativity and Innovation
Engineering
History
Interdisciplinary, Project-based, and Real-World Learning
Mathematics
Science
Social Studies
Technology
Material Type:
Lesson Plan
Provider:
Verizon
Provider Set:
Verizon Innovative Learning HQ - Lessons and Apps
Author:
J. Orin Edson Entrepreneurship + Innovation Institute at Arizona State University
Date Added:
09/20/2023
3D Modeling with TinkerCAD (Lesson 3 of 4): 3D Modeling Ancient Structures
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In lesson 3’s activity, students will learn about architecture and scale, and then they will 3D model and 3D print the Parthenon at 1:200 Scale using TinkerCAD and a 3D printer.

Estimated time required: 1-2 class periods.

Technology required for this lesson: 3D Modeling Software, Digital Fabrication Tools, Laptop/Desktop.

Subject:
21st Century Skills
Arts
Creativity and Innovation
Engineering
History
Interdisciplinary, Project-based, and Real-World Learning
Mathematics
Science
Social Studies
Technology
Material Type:
Lesson Plan
Provider:
Verizon
Provider Set:
Verizon Innovative Learning HQ - Lessons and Apps
Author:
J. Orin Edson Entrepreneurship + Innovation Institute at Arizona State University
Date Added:
09/20/2023
3D Modeling with TinkerCAD (Lesson 4 of 4): 3D Modeling Organic Shapes
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In lesson 4’s activity, students will use TinkerCAD to design an ergonomic pencil grip for Homer (author of The Odyssey and The Iliad) that allows him to write with both hands!

Estimated time required: 2-3 class periods.

Technology required for this lesson: 3D Modeling Software, Digital Fabrication Tools, Laptop/Desktop.

Subject:
21st Century Skills
Arts
Creativity and Innovation
Engineering
English Language Arts
History
Interdisciplinary, Project-based, and Real-World Learning
Mathematics
Science
Social Studies
Technology
Material Type:
Lesson Plan
Provider:
Verizon
Provider Set:
Verizon Innovative Learning HQ - Lessons and Apps
Author:
J. Orin Edson Entrepreneurship + Innovation Institute at Arizona State University
Date Added:
09/20/2023
3D Printing, Computer Aided Design (CAD) and G-Code Basics
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Students learn how 3D printing, also known as additive manufacturing, is revolutionizing the manufacturing process. First, students learn what considerations to make in the engineering design process to print an object with quality and to scale. Students learn the basic principles of how a computer-aided design (CAD) model is converted to a series of data points then turned into a program that operates the 3D printer. The activity takes students through a step-by-step process on how a computer can control a manufacturing process through defined data points. Within this activity, students also learn how to program using basic G-code to create a wireframe 3D shapes that can be read by a 3D printer or computer numerical control (CNC) machine.

Subject:
Computer Science
Engineering
Geometry
Mathematics
Measurement and Data
Science
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
Activities
Author:
Matthew Jourden
Date Added:
05/04/2019
3.MD, 3.G, 3.NF Halves, thirds, and sixths
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CC BY
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This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: A small square is a square unit. What is the area of this rectangle? Explain. What fraction of the area of each rectangle is shaded blue? Name the frac...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/16/2013
3.MD Finding the Area of Polygons
Unrestricted Use
CC BY
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This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Find the area of each colored figure. Each grid square is 1 inch long....

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/27/2013