Math Without Borders Review

I am so excited to be sharing my Math Without Borders Review with you today. If you don’t already know, Math Without Borders provides downloadable math curricula and resources for high school and advanced middle school students.  Their curriculum is designed to be comprehensive and cover topics from Algebra through Calculus, plus Physics.  David Chandler is the founder and the educator behind Math Without Borders. Mr. Chandler has over 35 years of experience teaching math and physics at the high school and Jr. college levels.  Many of his students have gone on to attend top universities including Harvard, Stanford, and M.I.T.  Mr. Chandler is passionate about helping students gain a deep understanding of math.  His motto is, “Math is not made easier by watering it down; it is made easier by explaining it clearly.”  To that end he has chosen the strongest textbooks available and he makes them “homeschool friendly” by supporting them with lessons that offer clear, well illustrated explanations.  It is the depth and clarity of the lessons that sets Math Without Borders apart.

Math is a fundamental subject in high school that opens doors to many other disciplines. Strong mathematical skills are required in science, engineering, economics, architecture, design, computer science, and many other fields. Furthermore, math teaches students critical thinking, problem-solving, and analytical skills that are valuable in all areas of life. 

The Math Without Borders Home Study Companion series teaches high school math to students through video courses taught by David Chandler, a seasoned educator with experience teaching math courses at all levels. The videos are available as instant downloads and can be used in conjunction with textbooks by Paul A. Foerster for Algebra 1, Algebra 2/Trigonometry, Precalculus, and Calculus. The Geometry course is paired with a different text, Geometry: A Guided Inquiry by Chakerian, Crabill, and Stein.

To access the course, students must download the files onto their own computers. The lessons are in standard video files that can be played on the media player of any computer.  For all of these courses, students will need a scientific handheld calculator or a scientific calculator app that can be downloaded to their phone. Some of the courses benefit from additional free software tools such as GeoGebra, which is great for graphing and geometric constructions, and a spreadsheet program (like Libre Office Calc).

The textbooks chosen for these courses are widely regarded as some of the most comprehensive (but also some of the most well written) high school math textbooks available.  These are not watered down in any way.  Chandler uses a whiteboard to teach every concept and work through examples following the text. He occasionally teaches topics in a different way than the text, for additional clarity and sometimes to give a different perspective.  Once he has taught a concept, Chandler works through many examples before leaving students to solve problems on their own. The course includes a second video with each lesson, in which he works out in detail the solutions to all of the recommended problems. Additionally, the original publisher’s solution manual (for the Algebra 1 and Algebra 2/Trig courses) is available, inexpensively, in pdf format which has full solutions for all of the problems in the text.

The Geometry course has a different structure than the other courses. It follows the text in continuous workbook format rather than as separate daily lessons.  There is an introductory video for each chapter and videos that follow the progress of the work. Each chapter presents the students with a “Central Problem” which is intriguing, but which they will almost certainly not be able to solve immediately.  As the chapter progresses a collection of topics are presented that will shed light on the Central Problem.  By the end of the Central Section the students will be able to solve the Central Problem, and they will have learned a lot of other things along the way, each in the context of immediately applying what they have learned. Following this are a review section, a self-quiz, a review self-test, and an extensive Projects Section. (The first seven chapters also have stand-alone algebra review sections.) Pdf files included with the Home Study Companion contain answers and commentary for all of the problems in the Central and Project sections, and a video solution guide is provided for all of the Review Section problems. The course also has supplementary sections to cover certain topics beyond the textbook to meet specific mathematical standards required by some states.

So, what is covered in each course and why is it so important to find a math program that is robust and comprehensive? Read on to hear my view on each of the courses.

Math Without Borders Review – Algebra IThe Algebra 1 course offered by Math Without Borders is a comprehensive, self-paced online course designed for high school and advanced middle school students. The course covers topics such as expressions, equations, functions, graphing, and problem-solving. It includes interactive video lessons, practice problems, and quizzes. Math Without Borders’ Algebra 1 course aims to help students develop a strong foundation in algebraic concepts and prepare them for higher-level math courses.

Math Without Borders Review - Algebra I Math Without Borders Review - Algebra I Math Without Borders Review - Algebra I Math Without Borders Review - Algebra I

Algebra I is a crucial course in high school that provides a foundation for higher-level math courses, as well as many other fields that require problem-solving skills. Here are a few reasons why it is important to understand Algebra I in high school:

  1. It is a prerequisite for many other courses: Understanding the concepts taught in Algebra I is necessary for success in higher-level math courses such as Algebra II, Geometry, and Calculus, which are essential for pursuing careers in STEM and other fields.
  2. It develops critical-thinking skills: Algebra I teaches students how to solve complex problems by breaking them down into smaller, more manageable parts. This skill is essential not just for math courses, but for many other academic and professional pursuits.
  3. It assists in preparation for standardized testing: Many college entrance exams, such as the SAT and ACT, include algebraic concepts. A strong understanding of Algebra I can help students earn better scores and improve their chances of acceptance into competitive colleges and universities.
  4. It is useful in many careers: Algebra I provides a foundation for careers in various fields, including finance, engineering, data analysis, and computer programming. Individuals who master algebraic concepts in high school will be better prepared to succeed in these fields.

In summary, understanding Algebra I is important because it is a prerequisite for many other courses, it develops critical-thinking skills, it assists in preparation for standardized testing, and it is useful in many careers. Students who take the time to fully understand Algebra I will have more opportunities for success both in school and beyond. Remember, Math builds on itself, so it is imperative to understand each concept before moving onto the next!

Math Without Borders Review – Geometry – The Geometry course offered by Math Without Borders is a comprehensive, self-paced online course for high school and advanced middle school students. The course covers topics such as angles, triangles, quadrilaterals, circles, and three-dimensional figures. It includes interactive video lessons, practice problems, and quizzes. Math Without Borders’ Geometry course aims to help students develop problem-solving skills, critical thinking, and an understanding of geometric concepts. Being a problem solving oriented Geometry course, it integrates better with the rest of the high school math curriculum than a traditional Geometry course.  The course prepares students for higher-level math courses and can also be used as a review for standardized tests, such as the SAT and ACT.

Geometry is an important course in high school that teaches students how to use logic and deduction to solve problems. It is essential to understand geometry for several reasons:

  1. It develops spatial reasoning skills: Geometry teaches students how to visualize and manipulate two- and three-dimensional objects, which is crucial for understanding how objects interact in our world. It helps develop spatial reasoning skills, which are relevant to everyday tasks such as reading a map or understanding how furniture fits into a room.
  2. It helps with problem-solving: Geometry requires students to use logical reasoning and critical thinking to solve problems. These skills are transferable to many other areas and are essential for success in higher education and in the workforce.
  3. It is relevant to everyday life: Geometry is relevant to many areas of everyday life, such as architecture, engineering, design, and art. Understanding geometry helps people communicate ideas more effectively across different fields.
  4. It is important for college admissions: Many college admissions processes require students to have taken Geometry, and a strong understanding of the subject can help improve chances of being accepted into top colleges.

In summary, understanding geometry is important because it develops spatial reasoning skills, helps with problem-solving, is relevant to everyday life, and is important for college admissions. A strong foundation in geometry is beneficial for success in higher education, and the lessons learned from geometry can be applied in many other areas of life.

Math Without Borders Review – Algebra II/Trigonometry – Math Without Borders offers a comprehensive Algebra 2 & Trigonometry course which is an online self-paced course that targets advanced high school students or middle school students who have previously completed Algebra 1 and Geometry courses. This course covers Algebra 2 topics like polynomials, functions, logarithms, and matrices. It also offers Trigonometry lessons covering topics like the unit circle, trigonometric functions, and identities. The course includes interactive video lessons, practice problems, and quizzes. The aim is to help students develop a deeper understanding of algebraic and trigonometric concepts, and to prepare them for higher-level math courses.


Algebra II and Trigonometry are essential courses in high school because they are major stepping stones towards college-level mathematics courses. Here are some reasons why it’s important to learn Algebra II and Trigonometry in high school:

  1. They build a foundation for advanced math: Algebra II and Trigonometry lay the groundwork for college-level math courses, such as Calculus and Linear Algebra. They build the conceptual framework and problem-solving skills needed to tackle more advanced mathematical concepts.
  2. They are important for STEM careers: Algebra II and Trigonometry are fundamental to science, technology, engineering, and mathematics (STEM) careers. These courses help students develop the problem-solving skills, logical reasoning, and critical thinking needed in STEM fields.
  3. They are important for standardized tests: Many college admissions exams, including the SAT and ACT, have math sections that cover Algebra II and Trigonometry. Students who master these topics have an advantage in these exams, which can help them gain admission to their preferred colleges.
  4. They are important for practical applications: Algebra II and Trigonometry are used in many everyday applications, such as engineering, architecture, and financial analysis. Students who understand these topics will be better equipped to handle practical problems and make informed decisions.

In summary, Algebra II and Trigonometry are foundational courses that prepare students for more advanced math courses, STEM fields, standardized tests, and practical applications. Students who master these courses will have a strong foundation for succeeding in college and beyond.

Math Without Borders Review – Pre-calculus – Math Without Borders offers an online self-paced course called Precalculus, which is designed for advanced high school and college students. Precalculus course covers topics such as functions, logarithms, trigonometry, matrices, and vectors. The course extends the topics introduced in Algebra 2 and helps the student gain fluency with those concepts. The course aims to prepare students for college-level math courses and standardized tests like the SAT and ACT. It includes interactive video lessons, practice problems, and quizzes. The goal of the course is to help students master complex mathematical concepts and mathematical problem-solving skills.


Pre-Calculus is an essential course for students who are interested in pursuing college degrees in STEM fields such as engineering, physics, computer science, mathematics and many others. Here are some reasons why learning Pre-Calculus in high school is important:

  1. It develops analytical skills: Pre-Calculus teaches students to analyze and solve complex mathematical problems through logical reasoning and calculations. These analytical skills are crucial in STEM fields where complex problems require innovative solutions.
  2. It prepares students for Calculus: Pre-Calculus serves as a foundation for Calculus, which is a required course for many STEM majors. Developing a strong understanding of Pre-Calculus will help students excel in Calculus and, by extension, their future coursework.
  3. It provides a challenge: Pre-Calculus is a challenging course that requires dedication, focus, and hard work. It teaches students valuable lessons about persistence and the importance of overcoming obstacles, which will serve them well in their future academic and professional careers.
  4. It promotes problem-solving skills: Pre-Calculus emphasizes problem-solving skills, which are crucial for success in STEM fields. Students learn to use various methodologies, including algebraic, graphical, and numerical methods, to solve complex problems.

Overall, Pre-Calculus is an important course that provides students with the necessary skills and foundation to succeed in higher education and future careers in STEM fields.

Math Without Borders Review – Calculus – Math Without Borders offers an online self-paced course called Calculus, which is intended for high school and college students who completed Precalculus. This course covers calculus topics such as limits and continuity, derivatives, integrals, and applications of calculus. The course aims to prepare students for college-level calculus courses and the AP Calculus exam (both A and B levels). It includes interactive video lessons, practice problems, and quizzes. The goal of the course is to help students develop a deep understanding of calculus concepts and the ability to solve complex real-world problems using calculus.

Learning Calculus in high school is important for various reasons:

  1. It’s essential for higher education: Calculus is a prerequisite for many college-level courses in STEM fields. Students who plan to pursue careers in science, technology, engineering or mathematics must have a solid understanding of Calculus.
  2. It helps in problem-solving skills: Calculus enhances problem-solving skills and fosters a deeper understanding of mathematical concepts. This skill set is essential for overall success in academic and career pursuits.
  3. It’s used in various fields: Calculus is used in diverse fields such as physics, engineering, economics, computer science, and statistics. Students who study Calculus in high school are better equipped to succeed in these fields once they enter college.
  4. It helps in college admissions: A strong foundation in Calculus enhances the likelihood of admission to top-tier universities and colleges. Calculus is a challenging subject, and demonstrating proficiency in it can impress college admission committees.

Overall, learning Calculus in high school is essential for higher education and success in a variety of fields. A strong foundation in Math can set a student up for academic and career success, and Calculus is a fundamental step towards achieving that goal.

Math Without Borders Review – Physics – Math Without Borders offers an online self-paced course called Physics, which is designed for advanced high school and college-level students. This course covers topics such as kinematics, energy, momentum, waves, and electricity. The course aims to prepare students for college-level physics and engineering courses. It includes interactive video lessons, lots of lab activities that can be done at home, practice problems, and quizzes. The goal of the course is to help students master Newtonian physics concepts and to see the world through new eyes!

Learning physics in high school is important for several reasons:

  1. It promotes problem-solving skills: Physics involves a lot of problem-solving, critical thinking, and logical reasoning. Learning physics in high school prepares students with the skills they need to make rational decisions and solve problems in their personal and professional lives.
  2. It develops analytical skills: Studying physics trains students to analyze data, make predictions based on evidence, and think critically about scientific ideas. These skills are essential for pursuing a career in science, technology, engineering, or mathematics.
  3. It gives a deeper understanding of the natural world: Studying physics enables students to have a better understanding of the natural world around them, from the behavior of subatomic particles to the behavior of stars and galaxies.
  4. It prepares for college and careers: Many college programs and careers require a strong foundation in physics. A solid understanding of physics is essential for students who want to study engineering, medicine, or science-related fields.

Overall, learning physics in high school is an important step towards developing a strong foundation in STEM fields and setting oneself up for academic and career success.

Overall, the Home Study Companion series, which covers Algebra 1, Geometry, Algebra 2/Trigonometry, Precalculus, Calculus, and Physics, is an excellent way for your student to learn high school math. The videos and textbooks are inexpensive but offer challenging material. The courses are tech-savvy and cover advanced mathematical concepts, and the Home Study Companion courses have plenty of support and guidance for students.

You can download their Free HSC Sampler Pack with the complete first chapter of each course, which means you can judge the style and quality of instruction for yourself before committing to buy. Are you wondering if your student is ready for Algebra?  Work through their revised Arithmetic Skills Checklist!

I hope that you enjoyed reading this Math Without Borders Review! If you’re looking for more curriculum reviews, you can find them here:


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