Optimal, Integral, Likely is a free, open-source textbook intended for UBC’s course MATH 105: Integral Calculus with Applications to Commerce and Social Sciences. It is shared under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Student groups work with manipulatives—pencils and trays—to maximize various quantities of a system. They work through three linear optimization problems, each with different constraints. After arriving at a solution, they construct mathematical arguments for why their solutions are the best ones before attempting to maximize a different quantity. To conclude, students think of real-world and engineering space optimization examples—a frequently encountered situation in which the limitation is the amount of space available. It is suggested that students conduct this activity before the associated lesson, Linear Programming, although either order is acceptable.

This book consists of ten weeks of material given as a course on ordinary differential equations (ODEs) for second year mathematics majors at the University of Bristol. It is the first course devoted solely to differential equations that these students will take.

This lesson allows students to build fluency with shapes by identifying them in in the outdoor classroom.

Students will use their knowledge of parallel and perpendicular lines to compare those that are manmade and others found in nature

STUDENT ACTIVITY - 4th - TXThis is a distance-learning lesson students can complete at home. The student will use their knowledge of parallel and perpendicular lines to compare those that are man-made and others found in nature. This activity was created by Out Teach (out-teach.org), a nonprofit providing outdoor experiential learning to transform Science education for students in under-served communities.

In this lesson the students will use their knowledge of measurement to determine perimeter and find missing lengths when given the total perimeter.

In this lesson the students will use their knowledge of measurement to determine perimeter. Since this is a virtual lesson for at home learning, steps will be included for students to make an 8 inch paper ruler out of notebook paper.

Aperçu : Bienvenue dans les leçons de codage Make Stuff Move. Cette première leçon va vous montrer comment définir la couleur et la luminosité du pixel et l'allumer sur notre bouclier d'animation Make Stuff Move.

In this lesson students will use their knowledge of decimals to solve problems in a real- world setting.

In this lesson, students will explore and record data about different plants that they observe. Students will then create a bar graph to reflect the data that that they collected. For example, a student might find 7 tomato plants, 5 cabbages, and 4 squash plants; their graph would reflect these numbers.

STUDENT ACTIVITY - 4th - NCThis is a distance-learning lesson students can complete at home. The student will explore and record data about different plants that they observe. Then they will create a bar graph to reflect the data that that they collected. This activity was created by Out Teach (out-teach.org), a nonprofit providing outdoor experiential learning to transform Science education for students in under-served communities.

In this lesson, students will explore and record data about different plants that they observe. Students will then create a bar graph to reflect the data that that they collected. For example, a student might find 7 tomato plants, 5 cabbages, and 4 squash plants; their graph would reflect these numbers.

In this lesson, students will explore and record data about different plants that they observe. Students will then create a bar graph to reflect the data that that they collected. For example, a student might find 7 tomato plants, 5 cabbages, and 4 squash plants; their graph would reflect these numbers.

This book was written for students and instructors who want to learn how to use a computer for other than the most common uses, such as web browsing, document creation, or paying bills online. This book is for anyone who wants to perform computational tasks that they design. In other words, if you wish to learn how to program a computer, this book is for you.

Because prealgebra is a subject that practically everyone is supposed to learn in grade school, it provides a platform to introduce basic computer programming concepts. Consequently, this book should also be of interest to students in middle or high school who want to learn how to program, and who are willing to invest the time and effort in learning a programming language that they could continue using throughout their schooling and in their professional life. Similarly, this book could also be of interest to pre-service and in-service mathematics teachers wishing to have at their disposal a complementary tool to assist in fostering understanding, competency, and interest in mathematics among their students. This book can be integrated with the teachers’ curriculum as way to tackle non-traditional math problems using an inexpensive modern computer language. By the end of the book, a reader will have learned enough to be able to write a preliminary, step-by-step one variable equation solver that can be expanded in the future to use with more complex equations. In other words, by the end of the book, you will be able to write code that programs their machines to solve equations. This code is foundational and readers are ecouraged to learn on their own how to build on it to suit their mathematics learning needs.

From the preface, "These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems."

Prior to 1990, the performance of a student in precalculus at the University of Washington was not a predictor of success in calculus. For this reason, the mathematics department set out to create a new course with a specific set of goals in mind:

A review of the essential mathematics needed to succeed in calculus.
An emphasis on problem solving, the idea being to gain both experience and confidence in working with a particular set of mathematical tools.
This text was created to achieve these goals and the 2004-05 academic year marks the eleventh year in which it has been used. Several thousand students have successfully passed through the course.

This book is full of worked out examples. We use the the notation “Soluion.” to indicate where the reasoning for a problem begins; the symbol ?? is used to indicate the end of the solution to a problem. There is a Table of Contents that is useful in helping you find a topic treated earlier in the course. It is also a good rough outline when it comes time to study for the final examination. The book also includes an index at the end. Finally, there is an appendix at the end of the text with ”answers” to most of the problems in the text. It should be emphasized these are ”answers” as opposed to ”solutions”. Any homework problems you may be asked to turn in will require you include all your work; in other words, a detailed solution. Simply writing down the answer from the back of the text would never be sufficient; the answers are intended to be a guide to help insure you are on the right track.

Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus.

This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.