Pre-Algebra (Using Saxon 8/7)

Saxon 8/7

Pre-Algebra Course Information

Saxon Math 8/7 is the culmination of Saxon Math Homeschool for Middle Grades, reviewing arithmetic calculation, measurements, basic geometry, and other foundational concepts and skills. At the same time, Math 8/7 includes extensive pre-algebra exercises, preparing the student for upper-level mathematics. 

Why Saxon 8/7 as a Pre-Algebra Course? Dr. Shormann recommends Math 8/7, 3rd edition. Then, skip Saxon Algebra ½ and take Shormann Algebra 1 with Integrated Geometry.  Learn more

Course Materials: Pre-Algebra DIVE videos are provided at no extra cost for Ensign Peak Academy students who are enrolled in any live classes. Pre-Algebra students will need to purchase the Saxon 8/7 with Pre-Algebra, Third Edition Complete Homeschool Kit with Solutions Manual.  (You may be able to find a used copy at a discounted price.)

Table of Contents: Click here to view Table of Contents

Placement Test: Is this the best course for you? Take the Placement Test to find out.

Prerequisite: Memorization* of Multiplication Facts to 9. To successfully complete this course, memorization of multiplication facts to a minimum of 9 is essential to learning the concepts in Saxon Math 8/7. If your student can complete the Multiplication Mastery Test in five minutes or so, they are ready for this course. If  not, please see this article.  *Three seconds or less – no skip counting, using fingers or tricks

How to be successful in this course:

This course is organized into 36 modules, to facilitate completion of the course during the standard Ensign Peak Academy school year. However, this is only a general guide. Dr. Shormann recommends using a timed method.  Instead of requiring the student to complete one lesson per day, the student should work on math a minimum of four to five days per week , for no more than 45 minutes to an hour per day. At the end of that time, regardless of how much of the lesson is completed, the student should stop. The following day, pick up where they left off the next day. This ensures the student has time to go back and re-learn forgotten concepts and master new concepts without overwhelming or frustrating the student.

During the first 25 lessons, and occasionally throughout the course, it may take two or three days to complete one lesson. That’s okay! As mastery, long-term retention, and fluency develop, learning math will become faster and easier. This timed method is critical to student success. 

Learn More: How will my student finish on time?

Can I Skip the Review Lessons or Increase the Pace?  For strong math students, see this article: Skip Review Lessons


Each lesson is made up of four parts: DIVE Lecture, Saxon Facts Practice drills, Saxon Lesson Practice, and Saxon Mixed Practice. The DIVE lecture number corresponds with the assigned Saxon lesson for that day. So, if you are assigned Lesson 4, you will watch DIVE Lecture 4 and complete Saxon Lesson 4 in the Saxon Student Textbook.


Because the lesson in the Saxon textbook is only a summary of the complete lesson, John Saxon recommended an experienced teacher to teach his courses. In the DIVE lectures, Dr. Shormann includes the missing connections between the lessons, creating bite-sized lessons that are easier to understand. Teaching Saxon to homeschoolers for more than 20 years, he knows where students struggle and adds additional instruction for these concepts. Dr. Shormann recommends that students not read the lesson in the Saxon textbook, if they will watch the DIVE video.

During the lecture students should take brief notes and solve example problems. After each example problem is presented, pause the lecture and solve it on your notes. Don’t just copy the example problems. As John Saxon recommended, Dr. Shormann uses different example problems than the Saxon lesson. This provides additional practice on the new concept, if needed.

Occasionally, to provide concrete examples of abstract concepts, a Saxon Activity Sheet is used during the lecture. These sheets are in the Saxon Tests & Worksheets booklet.

STEP 2.  DO THE FACTS TESTS DAILY (in Saxon Tests & Worksheets booklet)

Facts Tests: After the DIVE lecture, open the Saxon Textbook to the assigned lesson. At the top is a small box titled Warm Up. The first line indicates which Facts Test to complete. The Facts Tests are drills used to memorize and develop fluency in the skills that make completing daily homework assignments faster. These drills are essential to preparing students for Algebra 1. Do them every time they are assigned. The goal is to do them accurately in 5 minutes or less. Mental Math & Problem Solving: Do once a week or so. Strong students may skip the Mental Math & Problem Solving. If the student struggles with these, show them how to do the problem and move on. Do not spend more than 5 or 10 minutes on the Mental Math & Problem Solving Section.


The Lesson Practice has 5-10 problems that provide practice on the new concept introduced in the DIVE lecture. Students should review the DIVE lecture, as needed, to solve these problems.


Finally, the Mixed Practice section is completed. It provides more than enough review of previously learned concepts. Saxon’s unique method of continual review (not spiral) means the student is either practicing the concept in the mixed practice or building on it in the new lesson. Practicing a concept daily over a long period of time has been proven to build long-term retention which increases recall speed and raises exam scores.

Students will often forget a concept in this section.  Don’t be concerned about this. The important thing is to quickly re-learn the forgotten concept.  A lesson reference number is in parentheses next to each problem that indicates which lesson that concept was taught in. When “stuck” on a problem, simply click on that DIVE lesson to quickly re-learn that concept. Better than an answer, this gives students the opportunity to apply what was just learned, building long-term retention.

If you follow Dr. Shormann’s system to efficiently re-learn forgotten concepts, the student will eventually develop fluency which makes learning math faster and easier. This system is described in the Lesson Practice Problem items.

How many Mixed Practice problems should the student do?

Each Mixed Practice section has 30 homework problems. Because the DIVE lecture provides expert instruction, students don’t need as much practice. Most students need to do about 20 problems per lesson to build mastery and fluency. The weekly test scores determine the amount of practice needed. This encourages students to study and do their best on the tests.

Odds or Evens + 5 Method: 20 Mixed Practice Problems Per Lesson

This method can be used as long as the weekly test scores are 80+. If the student’s test scores drop below an 80 or 85, increase the number of problems to 25 or 30 for a few weeks. Then, try dropping back to 20.

How the Odds or Evens + 5 Method Works:

  1. On odd numbered lessons, circle all odd numbered questions.
  2. Circle 5 even numbered questions from the most recent lessons. The lesson reference number, in parentheses next to each question, indicates which lesson that concept was taught.
  3. On even numbered lessons, circle all even numbered questions and 5 odd numbered questions.

Strong Math Students: Odds or Evens Only Method

If you have a very strong math student, 15 problems in the Mixed Practice section may be enough practice. Do odd numbered problems on odd numbered lessons, and even numbered problems on even numbered lessons. If the student is following the Student Instructions on page 5, and test scores drop below an 85, try the Odds/Evens + 5 Method.  


After every 10 lessons in the student textbook  there is an Investigation that provides an in-depth study on abstract or harder to grasp concepts. Students watch the corresponding DIVE Investigation lecture and work the problems with Dr.Shormann. It is not necessary to complete the investigations questions in the Saxon text. 

Self Tests (1 hour time limit)

After every 5 lessons or so, a self test is taken.  They are in the back of the Saxon Tests & Worksheets booklet. The tests are cumulative, which means there are concepts from previous lessons. The number in parentheses next to each question indicates which lesson that concept was taught. This provides quick and easy re-learning of missed concepts. Dr. Shormann has a very specific system for studying, taking, and correcting tests that is designed to efficiently fill any gaps before starting the next lesson. 

Concepts are not tested until the student has had time to achieve mastery. This is why the self tests are located several lessons past the lessons for which they test. This provides additional practice, which leads to mastery. 

If test scores drop below an 80 or 85 (with extra credit for corrected problems), increase the number of homework problems in each lesson. When test scores go up, you can try reducing the number of homework problems again.

Proctored Exams

Four proctored exams are required to pass this course. Two attempts are provided for each exam (Exams A and B). Students are only required to make one attempt (Exam A). The second attempt (Exam B) is provided for students who hope to improve upon the score received on the first attempt (Exam A). The highest score of the two attempts becomes the final score.

Exams 1A and 1B test concepts taught in Lessons 1-31

Exam 2A and 2B test concepts taught in Lessons 32-60

Exams 3A and 3B test concepts taught in Lessons 61-90

Exams 4A and 4B test concepts taught in Lessons 91-120

Proctored Exam Policies and Procedures

Ensign Peak Academy courses conclude with a proctored final exam for each semester. Final exams are closed book exams. Locate the final exam by clicking on “Assignments” in the Canvas menu. Please arrange for someone in your community to serve as the proctor for your final exams. Ensign Peak Academy reserves the right to deny proctoring permissions to any applicant. Proctors may NOT be any of the following: relative of student, employer of student, parent of any other student enrolled in an Ensign Peak Academy course, personal tutor of student, church or religious youth group leader, athletic coach, assistant coach, athletic administrator, or athletic academic counselor, or someone with a vested interest in the student’s eligibility to compete in extracurricular activities (e.g. sports, theater, choir, etc.).

Final exams are administered online using a confidential pass code emailed to the proctor by Ensign Peak Academy. Students use their own computer, or a computer of the proctor. Students must remain supervised by the proctor during the entire exam. A chaperone (e.g. parent, friend) may be present so long as the student does not interact with that person during the exam. Interaction during the test with anyone except the proctor is considered dishonest and may be grounds for receiving a failing grade for the course. The student must remain in the room during the examination. The final exams must not be duplicated in any way (including screen-captured, copied/pasted, photographed, printed, etc.). If a proctor is unable to proctor an exam after all, they may not give the exam passcode to another person or the student. In this case, another person needs to apply to serve as a proctor and will receive the code from Ensign Peak Academy. Students must show ID or be personally known to the proctor.

If you have not already provided your proctor’s information, or if you need to arrange for a new proctor, please share this Proctor Application with the person you have asked to serve as your proctor.

IMPORTANT: Please make every effort to have your proctor submit the application at least 2-3 days before you plan to take the exams, so there is sufficient time to send the codes to them. Please contact Diann Jeppson at 801-450-5016 to let her know that the application has been submitted. The application report is checked frequently, but your communication will expedite the delivery of the codes.

Credit for Students Using a Different Math Curriculum

Ensign Peak Academy high school students, who prefer to study math by using another curriculum, may earn credit by 1. Submitting the Independent Math Curriculum Form.pdf, and 2. Completing the four proctored exams in this course.

To prepare to take each of the four proctored exams, be sure that you have learned the concepts taught in the lessons associated with each exam (see above). Compare the math curriculum you are using with this Saxon 8/7 Table of Contents.

Disclaimer: Students may not perform as well on the Shormann Math exams, after using an independent math curriculum, as they may do after using the Shormann Math curriculum.

Solutions for Struggling Students

Struggling in Saxon 8/7? Review this Remediation Plan

If your student is struggling or test scores, after adjusted for partial credit (see Tests), drop below 80%, follow the steps on the remediation plan linked above.  

Did you complete 8/7, but scored less than 80%? (adjusted for partial credit) on the final 5 tests?  Click Here