In this lesson, students will learn that math is important in navigation and engineering. Ancient land and sea navigators started with the most basic of navigation equations (Speed x Time = Distance). Today, navigational satellites use equations that take into account the relative effects of space and time. However, even these high-tech wonders cannot be built without pure and simple math concepts basic geometry and trigonometry that have been used for thousands of years. In this lesson, these basic concepts are discussed and illustrated in the associated activities.

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.

Open Source Calculus and Analysis - A comprehensive textbook introducing the main concepts from calculus and analysis

Features
- Comprehensiveness: all from calculus and analysis that is needed in first year mathematics-oriented programmes
- Mathematical rigour: formal definitions, extended theorems and proofs
- Includes differential equations
- Applicability: integrated symbolic (Mathematica or SymPy) and numerical computation (Python), review exercises, and so on
- Accessibility: final solution to all exercises, QR codes to accompanying videos,…
- Flexibility: using dedicated if-loops in the underlying Latex-code you can compile the version that suits your needs (Mathematica or Sympy, Calculus only or analysis as well, with or without differential equations,…)

PowerPoint Slides to accompany Chapter 10 (Sections 10.1, 10.2 and 10.3) of OpenStax Algebra and Trigonometry textbook. Prepared by River Parishes Community College (Jared Eusea, Assistant Professor of Mathematics, and Ginny Bradley, Instructor of Mathematics) for OpenStax Algebra and Trigonometry textbook under a Creative Commons Attribution-ShareAlike 4.0 International License. Date provided: July 2019.

PowerPoint Slides to accompany Chapter 10 (Section 10.5) of OpenStax Algebra and Trigonometry textbook. Prepared by River Parishes Community College (Jared Eusea, Assistant Professor of Mathematics, and Ginny Bradley, Instructor of Mathematics) for OpenStax Algebra and Trigonometry textbook under a Creative Commons Attribution-ShareAlike 4.0 International License. Date provided: July 2019.

PowerPoint Slides to accompany Chapter 10 (Section 10.8) of OpenStax Algebra and Trigonometry textbook. Prepared by River Parishes Community College (Jared Eusea, Assistant Professor of Mathematics, and Ginny Bradley, Instructor of Mathematics) for OpenStax Algebra and Trigonometry textbook under a Creative Commons Attribution-ShareAlike 4.0 International License. Date provided: July 2019.

PowerPoint Slides to accompany Chapter 7 of OpenStax Algebra and Trigonometry textbook. Prepared by River Parishes Community College (Jared Eusea, Assistant Professor of Mathematics, and Ginny Bradley, Instructor of Mathematics) for OpenStax Algebra and Trigonometry textbook under a Creative Commons Attribution-ShareAlike 4.0 International License. Date provided: July 2019.

PowerPoint Slides to accompany Chapter 8 of OpenStax Algebra and Trigonometry textbook. Prepared by River Parishes Community College (Jared Eusea, Assistant Professor of Mathematics, and Ginny Bradley, Instructor of Mathematics) for OpenStax Algebra and Trigonometry textbook under a Creative Commons Attribution-ShareAlike 4.0 International License. Date provided: July 2019.

PowerPoint Slides to accompany Chapter 9 of OpenStax Algebra and Trigonometry textbook. Prepared by River Parishes Community College (Jared Eusea, Assistant Professor of Mathematics, and Ginny Bradley, Instructor of Mathematics) for OpenStax Algebra and Trigonometry textbook under a Creative Commons Attribution-ShareAlike 4.0 International License. Date provided: July 2019.

Open Textbooks for Rural Arizona participants are invited to remix this template to share their courses, textbooks, and other OER material on our Hub.

This OER course using a new textbook is based a section of MAT103 Pre-Calculus. It is a preparatory course for Calculus. It builds upon the intermediate level of Algebra and makes intensive use of technology to conceptualize functions and methods of function manipulation with emphasis on quantitative change. All course content written by Fahmil Shah. Added to OER Commons by Victoria Vidal.

Word Count: 5097

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)

Students analyze a cartoon of a Rube Goldberg machine and a Python programming language script to practice engineering analysis. In both cases, they study the examples to determine how the different systems operate and the function of each component. This exercise in juxtaposition enables students to see the parallels between a more traditional mechanical engineering design and computer programming. Students also gain practice in analyzing two very different systems to fully understand how they work, similar to how engineers analyze systems and determine how they function and how changes to the system might affect the system.

Working in small groups, students complete and run functioning Python codes. They begin by determining the missing commands in a sample piece of Python code that doubles all the elements of a given input and sums the resulting values. Then students modify more advanced Python code, which numerically computes the slope of a tangent line by finding the slopes of progressively closer secant lines; to this code they add explanatory comments to describe the function of each line of code. This requires students to understand the logic employed in the Python code. Finally, students make modifications to the code in order to find the slopes of tangents to a variety of functions.

 The Quadratics module is divided into 4 parts, including (1) solving by factoringm, (2) solving using the square root property and completing the square, (3) solving using the quadratic formula, and (4) solving by graphing. The goal is for students to recognize the strategies for solving quadratics, and even higher degree functions that can employ the same strategies. For each strategy there is a video page and then a practice homework page. The video pages include printable word documents that are the notes. Each video page is followed by a practice homework page in Derivita.This work, by Cheryl Meilbeck, is licensed under a Creative Commons Attribution 4.0 International License.Links to an external site.CC-BY

RocketModeler was developed at the NASA Glenn Research Center in an effort to foster hands-on, inquiry-based learning in science and math. RocketModeler is a simulator that models the design and flight of a model rocket. The program works in two modes: Design Mode or Flight Mode. In the Design Mode, you can change design variables including the size of the rocket body, the fins, and the nose cone. You can also select different materials for each component. You can select from a variety of standard solid rocket engines. The program computes the center of gravity and pressure for your rocket and determines the stability. When you have a design that you like, you can switch to the Flight Mode (shown below), where you can launch your rocket and observe its flight trajectory. You can pause at any time to record data and then continue the flight through parachute deploy and recovery. This program has recently (Oct 8, 2004) been upgraded to support stomp rockets, bottle rockets, and ballistic shells in addition to solid model rockets. It also supports both English and metric units.

This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles (G-C.5), using trigonometric ratios to solve right triangles (G-SRT.8), and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found (MP.7).

This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?

This is a foundational geometry task designed to provide a route for students to develop some fundamental geometric properties that may seem rather obvious at first glance. In this case, the fundamental property in question is that the shortest path from a point to a line meets the line at a right angle, which is crucial for many further developments in the subject.

Exploration assignments of transformations with both Algebra 2 parent functions and Trigonometric Functions.