Algebra 1: Principles of Secondary Mathematics (2024)

Math-U-See’s Algebra 1: Principles of Secondary Mathematics course is completely new rather than a revision of their original Algebra 1 course. The new course is more challenging than the previous course, covering many more topics and aligning with math standards. The layout of the course also differs from the rest of the Math-U-See courses. While Math-U-See’s creator, Steve Demme, wrote and provided video instruction for previous courses, this new course was created by Sara Donovan, and she is the primary instructor through most of the video lessons.

Since there might be gaps in a student’s mastery of the skills needed for this course, Demme Learning provides free, readiness-check and skill lessons for those who have completed any pre-algebra course, even their own. Bridge Materials: Pre-Algebra to Algebra 1: Principles of Secondary Mathematics is available under the Demme Learning Digital Toolbox. To access the Toolbox, you need to create a free Digital Toolbox account if you don’t already have one.

Course Components

The course components for Algebra 1 are a two-volume Instructor Handbook, a two-volume Student Worktext, a Tests book, a laminated Formula Sheet, and access to the Digital Toolbox. You can save a significant amount of money by purchasing the course with a digital Instructor Handbook rather than printed books. Student Worktexts and Tests books are only available in print. (For the rest of this review I will refer to both the Instructor Handbooks and Student Worktexts in the singular.)

The digital resources in the Digital Toolbox include access to instructional videos; password-protected solutions for practice problems, tests, exams, and targeted review problems; digital manipulatives; and other resources such as graph paper and extension lessons. The course lessons are taught through streamed videos accessed through the Digital Toolbox.

In addition, students are encouraged to use the Desmos Scientific Calculator or the Desmos Graphing Calculator that are linked on some of the online lesson pages below the videos, or they can use either a scientific or graphing calculator of their own.

Course Design

The course is organized into five units, with four to eight lessons per unit. Each lesson has Part A and Part B which function as separate lessons with their own instructions, examples, practice problems, Checkpoints (a question or problem to check for comprehension of key ideas), and Mastery Checks. Each lesson (Parts A and B together) concludes with Targeted Review problems and a test. The Instructor Handbook suggests that students take two days to complete each part of a lesson, but the time required will vary from lesson to lesson.

Each part (A and B) of a lesson begins with a list of objectives, a sidebar explaining how students might apply the new concept(s) or a reason why they need to learn this, and a brief warm-up exercise. The warm-up might review previous concepts that are foundational to the upcoming lesson or might introduce a concept that will be part of the new lesson. Students should try to complete these on their own, but their answers should be checked before going on if they aren’t sure about them.

Next, a video walks students through a lesson. Students fill in guided notes in their worktext pages as they watch the video, essentially creating the content of a textbook. The video lessons continue with example problems that are also shown in the worktexts. After watching the video, students work on a brief Checkpoint problem to ensure they have grasped the new concept. Some lessons will add another related video that expands on the concept and has its own example problems and Checkpoint problem.

After the instructional part of the lesson, students tackle the first set of practice problems. If they miss many, they can review the lesson and try to solve the second set of practice problems. If they get the first set correct, they don’t need to complete the second set. Students then complete a few Mastery Check problems, which conclude with “Say What You Know”—students are to explain in their own words what they have learned in the lesson. If students complete only the first practice set and answer those problems correctly, but do poorly on the Mastery Check, they can review and complete the second set of practice problems. Once they pass the Mastery Check, they proceed to Part B of that lesson which follows this same pattern. At the end of Part B, students complete a set of Targeted Review problems. The Instructor Handbook identifies the lessons in which concepts tested by the Targeted Review were taught in case students need to review.

I am impressed with the way this course continually checks student comprehension and provides avenues for review as needed. Students who quickly grasp concepts can move ahead rather than complete extra problems.


The Tests book includes both tests and answer keys. The tests are removed and handed out to students. There are three types of tests. Tests for every lesson cover only that lesson’s content and have a traditional, open-response format where students need to work out problems and write their answers. Unit tests cover several lessons using mostly multiple-choice questions along with a few open-response questions. Midterm and Final exams are cumulative and have a few open-response questions along with multiple-choice questions. Multiple-choice questions include “distractor” answers that reflect the errors students are most likely to make.

Instructor Handbook and Formula Sheet

The Instructor Handbook pages include slightly reduced images of the student pages with overprinted answers. These images are surrounded by answers, teaching notes, and tips for helping students if they get stuck. While students should be able to work independently, a teacher or parent needs to be available to check work, administer tests, help if students get stuck, and listen as students provide their oral answers to Say What You Know in each Mastery Check.

The Instructor Handbook says that students should use calculators to check their work, graph equations, and perform calculations with extremely large or small values. It also says on page viii of Instructor Handbook: Book A, “Students are not required to memorize formulas, properties, or conversions. Students are encouraged and reminded to use the Formula Sheet to help them solve problems.” The Tests book also states that students should use the Formula Sheet when taking tests. This reliance on the Formula Sheet is unusual, and it seems critical for future math study that students have memorized many of the basic properties and formulas, such as the commutative property, the slope formula, and exponent rules. However, students spend so much time solving problems in this course that I expect they will memorize the properties and formulas through frequent use.


While I liked the style of the original course, this new course is much more comprehensive and challenging.

Algebra 1: Principles of Secondary Mathematics (2024)
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