If you’re looking for a rigorous K-12 math curriculum that takes a back to basics approach, with plenty of solid math practice and skill assessment, Saxon Math might be the curriculum to look at.

Although not ideal for every student, and while the many different editions out there can be a bit confusing, its spiral approach and more practical math focus can ultimately give students a stronger foundation and a leg up in math.

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## What is Saxon math?

Developed by John Saxon in 1981, Saxon Math has become one of the most well known and widely used homeschool math programs and many schools.

A spiral method, Saxon Math is based on a method of teaching that combines incremental skill development with ample practice to achieve better practical math results than standard curricula.

## Saxon Math method: How Saxon Math Works

### Saxon Philosophy and Pedagogical Features

The Saxon philosophy is really rooted in what is called the *spiral method *of teaching math, emphasizing the introduction concepts slowly over time and giving kids plenty of practice and repetition.

In Saxon Math’s own words it teaches math through a process of *incremental development *and *continual review.*

**Incremental Development**

Saxon Math makes extensive use of the educational concept of chunking*. *

In other words, Saxon math takes complex concepts and topics and breaks them down into smaller, more manageable pieces

The curriculum introduces these pieces a little at a time and lets math concepts build upon one another. This *incremental development, *as it’s called, is designed to spread skill and knowledge development out over time

It is also based on some pretty well-established and long-standing educational studies.

The overall idea here is that by chunking information, i.e.presenting math concepts as more bite sized pieces over a longer period, learning becomes less of a strain on a student’s working memory, leading to longer term information retention and lessening frustration in the long run.

**Continual Review**

The other feature that tends to characterize Saxon Math, is the importance it places in continual review, practice and assessment.

With Saxon, concepts are reviewed and practiced periodically over time, mixing older concepts into newer lessons and thereby cumulatively giving kids lots of practice and repetition over the year.

The general idea being that, by placing a stronger emphasis on practice, reputation and doing exercises, Saxon Math can help with information retention and in making math skills more automatic (known as procedural fluency), leading to greater math achievement on tests and assessments.

This process of continual review does seem to have some support in educational research, as well.

And because this heavy drill and practice is done over time, it can be less frustrating and stressful for some kids, as well, particularly those that tend to get overwhelmed by math.

## Saxon Math Curriculum

Saxon Math is a complete K-12 math curriculum that has been designed for both schools and home learning.

That means there are essentially two lines, Saxon Math and the Saxon Math Homeschool Edition, the former being designed for traditional schools and teachers and the latter for homeschooling families.

Both are based on the same essential spiral method and both use the same basic teaching method and philosophy.

The main differences are the inclusion (or exclusion) of classroom-oriented activities, specialized teachers manuals, some aesthetic differences, and solutions manuals.

The Saxon Math curriculum can be broken up into three levels –** K-3, 4-7 and 8-12, **with K-3 being quite a bit different than the other grades, something we will discuss below.

Overall, Saxon math tends to encourage more self-directed study and independence on the part of the student as they go along in the program, requiring less parent/teacher direction and introducing more student-focused worksheets and assignments.

K-3 is the least self-directed, obviously, with most of the learning being taught from the “top down,” i.e. from the home study/teachers guide.

As kids move into the more advanced grade levels and books, students can do much more of their work and learning independently.

### K-3

The K-3 curriculum is designed to cover basic math concepts, including arithmetic, patterns, time, temperature and more.

Although at times more rigorous than other curriculum, doing quite well at developing key mathematical thinking and skills at this critical age, its scope and sequence is more in line with common core math standards, so don’t expect a precocious introduction of math concepts.

Overall, the Saxon K-3 curriculum is pretty different from the more traditional Saxon curriculum and methodology that kids experience later on.

Originally written for classroom use, the K-3 homeschool versions had to be redone and reorganized to remove classroom activities and prompts, to adhere to state standards and actually are even written by a different author altogether.

In general, K-3 lessons follow a particular format

**The Meeting**– which involves a discussion and demonstration between parent and student over the topics that will be covered, as well as some practice**The Lessons**– introduces and teaches the concepts being covered, in grades 1+ the student these cover two pages in their workbook over the course of the day**Practice and Assessments**

In terms of teaching, compared to the higher grades at least, there is a great deal more teacher-led instruction.

The K-3 curriculum still follows the Saxon spiral approach to math, it should be noted, but lessons can be quite scripted and mapped out.

Some parents really like this as it makes it really easy to start teaching for first time homeschoolers or those who have never taught Saxon Math before, but it can constrain and annoy more experienced homeschoolers and those who homeschool precisely because they wanted more freedom and exploration in the way they teach.

Interestingly, Saxon K-3 does require the use of manipulatives, which means you’ll have to buy a manipulatives kit to go with it.

On the one hand this gives excellent hands-on learning experience, bringing math from an abstract concept to concrete through the use of well made, colorful plastic clocks, blocks and more, which can reinforce learning, especially with students who are tactile-oriented.

But adding a manipulatives kit can bring up the price significantly, with manipulatives kits costing well over $100 for a complete kit, although parents should keep in mind that they are used for 3 grades worth of lessons and so they can get a lot of use for their price.

**K-3 Curriculum coverage**

Home Study Kit Series | Examples of Topics Covered |

Math K | Counting, time, colors, estimation, pattern recognition, story problems and basic skip counting, time and calendars |

Math 1 | Skip counting (1,2,5 10s), number positions, addition and subtraction facts, measurements, money, understanding pictorial diagrams and basic shapes, and more. |

Math 2 | Geometric shapes, Venn diagrams, reading graphs, basic calculations and computation, multi step problems and introduction to fractions, and more. |

Math 3 | Adding and subtracting multi-digit numbers, ordinal positions, probability, single digit division, adding negative numbers, adding/subtracting fractions, coordinate graphing, shapes and polygons, symmetry, more advanced measurements, and more. |

### Saxon for Grade 3-12: Elementary, Middle School and Onwards

From Intermediate 3/Grade 3 onwards, Saxon Math follows a more standard lesson format that has largely come to characterize the program, with lessons emphasizing far more student involvement and individual practice, especially as students progress in level.

This lesson format is generally as follows:

**Saxon Math Lesson Format (grades 3-12)**

Intermediate Series | |

Power Up | Students begin with a review of math facts, count aloud/jump starts, mental math, and problem solving skills. |

Concept | Introduces a new math concept and provides some practice problems |

Written Practice | 15-30+ fairly rigorous and challenging problems per lesson to practice the new concept as well as review previous concepts. Also can include real world connected problems for “Early Finishers,” which are more challenging, time consuming and fulfil state standards requirements, as well. |

In-lesson activities | Sprinkled throughout there are are in-lesson activities that students must complete |

Investigations | Every tenth lesson also includes an investigation, which are more in-depth explorations of concepts with some unique activities built into them |

Assessments |

Numbered Series | |

Warm up | Students begin with a review of math-facts, mental math problems, and some word problems. The numbered editions were created before saxon included count aloud/jump start exercises, so they do not include these. |

Concept | Introduces a new math concept and provides some exercises and problems |

Mixed Practice | 15-30+ fairly rigorous and challenging problems per lesson to practice new and previous concepts. |

In-lesson activities | Sprinkled throughout there are in-lesson activities that students must complete. There are generally fewer of these than in the Intermediate Series. |

Investigations | Every tenth lesson also includes an investigation, which are more in-depth mini-lesson/explorations of concepts with some unique activities built into them. Similarly, there are fewer activities in the Investigations than in the Intermediate series. |

Assessments |

From this lesson structure, you can really get a good sense of Saxon Math’s methodology.

In addition to teaching new material, each lesson reviews previous concepts and works on fundamental skills that will help students in future practice and exams, like problem solving strategies and mental math, and the lessons also, of course, provide many opportunities to work on math problems and exercises.

Compared to the K-3 Math program, the Saxon Math program for Grades 3-12 slowly starts to build the student’s ability to work and learn independently, with a gradual reduction in the need for oversight and guidance (as you would expect), and in general don’t require a whole lot of prep time for parents, which is nice for busy homeschoolers.

### Understanding Saxon Math Editions

Over the years, Saxon Math has released several different editions that have been developed over the years.

Many are still for sale, and are still quite popular with homeschoolers and teachers alike, which makes understanding what people are talking about extremely confusing and doesn’t really help when it comes time to pick one.

For that reason, we’ve created a rough comparison chart for grade and how they compare to the different editions of Saxon that are commonly sold.

**Elementary and Middle School**

Grade | Saxon Level | Or |

Kindergarten | Math K | |

1 | Math 1 | |

2 | Math 2 | |

3 | Math 3 | Intermediate 3 |

4 | Math 5/4 | Intermediate 4 |

5 | Math 6/5 | Intermediate 5 |

6 | Math 7/6 | |

7 | Math 8/7 | |

8 | Math Algebra 1/2 | Saxon Algebra 1 |

## High School Math

Topic | Or |

Algebra 1, 3rd ed | Algebra 1, 4th ed |

Algebra 2, 3rd ed | Algebra 2, 4th ed |

Geometry | Geometry |

Advanced Math | Advanced Math |

Calculus | Calculus |

### So, what are those numbers, anyway?

Saxon math books are leveled with a fractional number, which makes things even more confusing for people, with names like 5/4, 6/5, 8/7 etc.

The **first number is the average grade level for which the book is intended **and the **second is the grade level recommended for advanced students. **So 8/7, for example, is recommended for average 8th grade students or advanced 7th graders.

### What’s the difference between Intermediate and the numbered editions?

Saxon Math’s numbered editions, like 5/4 and 6/5, and its Intermediate Series are broadly similar in the scope and sequence and use the same method of teaching math.

They do have some important differences, however, that parents should be aware of.

The intermediate series:

- are
*hardcover* - do not have teachers manuals, so require a little more parental involvement in day to day lessons
- Use far more graphics to demonstrate math concepts, making them more visual and helping kids connect abstract concepts to concrete ideas
- Have more of a focus on problem solving than the numbered editions, with a defined method of approaching word problems that it teaches (Understand-Plan-Solve-Check)
- Have more activities overall than the numbered series
- Includes a “Power Up” section with its own workbook (as opposed to Warm Ups), which is a section dedicated to working on math facts, count aloud, problem solving and mental math

The biggest difference, however, that parents may want to know is that** the Intermediate series are Common Core state standards aligned, while the numbered editions are not.**

### So, why is there both an Intermediate 3 and a Math 3?

It’s a little confusing, to be sure.

Essentially, because K-3 follows a different structure and format than the other edition (manipulatives, more teacher-intensive), there was a need to help kids transition into the regular series, particularly Math 5/4.

At grade 3, parents therefore have a choice.

Parents who have begun teaching Saxon in Kindergarten can continue with a familiar format until grade 3, minimizing any frustration and distress that changing methodology may create in young children, or introduce them earlier to the traditional Saxon math teaching method.

While both will do the job just fine, we believe that parents jumping into Saxon at the third grade should probably begin with Intermediate 3, rather than Math 3.

We believe that since intermediate 3 is written by the same author and follows the same format as subsequent Saxon curricula (Intermediate and numbered), it will lead to less confusion and difficulties in subsequent years.

### Saxon Math Curriculum Coverage for Grades 3-12

**Saxon Math for Grades 3-5**

**Covers**: Math 5/4, Math 6/5 **or*** **Intermediate 3, Intermediate 4 and Intermediate 5*

Home Study Kit Series | Examples of Topics Covered |

Intermediate 3 | Covers the same topics, broadly speaking, as Math 3 |

Math 5/4 and Intermediate 4 | Word problems, number lines, elapsed time, inverse operations, square roots and powers, add/subtract/multiplying/dividing multi-digit numbers, mixed and improper fractions, fractions, decimals, percents, geometry and measurement, estimating perimeter, area and volume, probability and more. |

Math 6/5 | Word problems, adding/subtracting/multiplying/dividing multi digit whole numbers, reciprocals, decimals, fractions and mixed numbers, divisibility tests, equivalent fractions, converting fractions, decimals, and percents, estimation, variables, expressions and equations, powers and exponents, geometry and measurement, probability |

**Saxon Math for Grades 6-8**

**Covers**: Math 7/6, Math 8/7, Math Algebra 1/2

Home Study Kit Series | Examples of Topics Covered |

Math 7/6 | Introduction to functions, integers, coordinate graphing, exponential expressions, prime factorization, order of operations, inverse operations, number lines, place value, manipulating percentages, estimation of roots, unit multipliers, complex fractions, geometry and geometric solids, angle bisection, triangular patterns and story problem patterns and more. |

Math 8/7 | Measurements, geometry, pre-algebra, ratios, palindromes, more advanced probability and statistics, complex and equivalent fractions, graphing transformations, working with the metric system, point symmetry, manipulation of repeating decimals, scientific notation and concepts in math, graphing inequalities, manipulating algebraic terms, Pythagorean Theorem, slope-intercept form of linear equations, and more . |

Algebra 1/2 | Prime and composite numbers, order of operations and inverses, graphing transformations, pre-algebra, manipulating algebraic terms, coordinates, exponents, square roots, ratios, algebraic phrases, probability, the Pythagorean Theorem and more |

**Saxon High School Series**

**Covers**: Algebra 1, Algebra 2, Geometry, Advanced Math, Calculus

**Requires**: Graphing calculator

Home Study Kit Series | Examples of Topics Covered |

Algebra 1 (3 & 4th edition) | Signed numbers, exponents, and roots, variables, equations and inequalities, absolute value, scientific notation, unit conversions, polynomials and polynomial expressions, graphs, factoring, the; quadratic equation; direct and inverse variations, exponents and growth, statistics, and probability, and more. |

Algebra 2 (3 & 4th edition) | Angles, perimeters, proportional segments, negative exponents, quadratic equations, metric conversions, logarithms, advanced factoring, some precalculus and more. |

Geometry | Triangle congruence, surface area and volume, two-column proofs, vector addition, postulates, proofs and theorems, coordinates, slopes, intercepts and equations of lines and more. |

Advanced Mathematics | Upper level geometry, trigonometry, logarithms, analytic geometry, some advanced algebraic manipulations and problems, some pre-calculus and more. |

Calculus | Limits, functions, differentiation and integration, trigonometry and analytic geometry, |

## How Saxon Math Compares to Other Math Curricula

### Saxon Math’s Spiral Method vs Mastery Methods

Saxon Math’s **spiral based approach** to teaching math can be **a little different than some other math curricula out there, particularly those that use a mastery method.**

With a mastery-based curriculum, such as with Singapore Math or CTCMath, instead of introducing math concepts in bite sized pieces spread out over the school year, students explore topics deeply and more completely until a certain skill proficiency, or *mastery*, is reached.

Afterwards they move on to new topics and concepts, being offered far less repetition and review, as once proficiency is reached as the curricula don’t really come back to them as frequently.

As a result, while students may not get as bored by repetition, gaps in learning can be amplified over time if they are not identified and remediated ASAP.

### Program Rigor

While not the most difficult or advanced math program out there, Saxon Math can be quite a rigorous math program compared to those taught in schools.

With a lot of practice, challenging in-lesson activities and assessments built into the lesson structure, kids get a lot more practice at a wider variety of math question types.

And because Saxon math revisits previous topics, mixing them into exercises and problem banks, it tends to keep kids on their toes while reinforcing essential knowledge and skill.

### Conceptual vs Computational Math Learning

Broadly speaking, Saxon Math takes a more back-to-basics approach to teaching math than many other math programs out there.

In other words, Saxon Math tends to emphasize the memorization of math facts, learning rules and techniques and overall focusing on “doing math” rather than trying to explore math topics conceptually or theoretically.

While Saxon’s often challenging problems sets offer a rigorous curriculum that will certainly develop math thinking skills, compared to some other programs out there, it isn’t **as **focused on gaining a deep understanding of math theory or critical reasoning and creative approaches such as you might find in the Singapore Math method or in those designed for gifted students, such as Beast Academy or Art of Problem Solving.

### How does Saxon Math compare to a Typical Public School Math Program?

Although schools can differ immensely between districts, and even between schools, in how they approach math, broadly speaking there are quite a few similarities between Saxon and what might be found in traditional math programs in schools.

Saxon Math is a secular/non-aligned curriculum that uses a spiral approach and uses a good deal of chunking, which is in line with many best practices in schools today.

Compared to most programs in the public system, however, Saxon Math uses a much more back to basics approach to teaching math, emphasizing math facts and strategies, as well as lots of individual practice and drill, as opposed to group work and creative or unconventional problem solving methods that are taught in many reform math based programs.

The problems and exercises found in Saxon Math tend to be more challenging and varied than those found in standard school textbooks, making it a far more rigorous program overall.

Finally, it also tends to include more hands on learning, in the form of manipulatives and other activities, which makes it a more multisensory learning experience.

Perhaps as a result, students using Saxon tend to have higher scores on standardized tests and increased enrollments in enriched and higher math and STEM classes.

## Is Saxon Math common core aligned?

Saxon math can be common core aligned, depending on which edition you use. **Intermediate and newer editions are common core state standards aligned, while older editions (numbered editions especially – 5/4, 6/5 etc) are not.**

That said, it’s important to note that while Saxon math editions may be common core aligned in curriculum, largely meaning that they include more word problems, problem solving strategies and shift the sequence of topics around a bit, they still follow the same spiral based teaching methodology.

## Saxon Math Cost

*Please note: All prices are in USD and are correct as of writing. They are designed to give users an idea of price and are subject to change and availability. *

To properly teach Saxon Math, especially for homeschoolers, there are a few items parents will need to buy.

### K-3

Kindergarten | Grade 1+2 | |

Meeting Book | ✅ | ✅ |

Home Study Teachers Ed | ✅ | ✅ |

Student Work Kit/cards | ✅ | |

Manipulatives Kit | ✅ | ✅ |

### Grades 3-8

Numbered Editions | Intermediate Editions | |

Textbook | ✅ | ✅ |

Tests and Worksheet | ✅ | ✅ |

Solutions Manual | ✅ | ✅ |

Powerup Workbook | ✅ |

### Grades 9-12

Textbook | ✅ |

Test Book | ✅ |

Solutions Manual or Answer Keys | ✅ |

Homeschool Testing Book | ✅ |

Because these books are designed to work together, **buying each Saxon Math book individually can get pretty expensive. **The teachers manual, for example, can cost over $90 on its own (depending on where you shop).

That’s why **we recommend that parents purchase all-inclusive homeschool kits.** Generally these tend to cost around $100-120 per grade, which can provide some savings and also spare parents the headache of buying books piecemeal (a process that becomes more painful if certain books suddenly get sold out).

Keep in mind, **for K-3 you’ll also have to purchase manipulative kits** as well, which can run about $100.

### Is Saxon Math worth the price?

Saxon Math’s **prices are more or less in line with other book based complete math curriculums** like Horizons, Rightstart and Singapore.

It’s not the least expensive option out there but its** rigorous approach to mathematics, ease of teaching, and its strong focus on practice and computation can and have helped many students **achieve better results in mathematics.

While they do have manipulatives that you need to purchase, these tend to be well made and durable, meaning they will last well beyond the three years they are intended to be used for, meaning they’ll survive to be passed on and well-used by siblings with no issue.

The q**uality of the books is typically very good**, with lots of diagrams (especially in the newer editions) and few printing errors that we could see.

One issue some parents have is that** some editions, the homeschool editions in particular, are softcover**. This means that they can be less durable, especially where younger kids are concerned.

While the Intermediate series does use hardcover texts, some homeschoolers may not want to use those editions and will need to be more careful.

## Saxon Math Pros and Cons

Saxon Math is quite a popular program, well-known and widely used both in homeschools and traditional schools alike.

However, like most other things in life and every other math program out there, it’s not a perfect system and has it’s positive and negative qualities that parents need to consider.

### Saxon Math Pros

**Lots of math practice**

Saxon Math is a firm believer in giving kids lots of practice and repetition in order to build and reinforce math skills.

Over time, this can develop strong computational math fluency, i.e.the ease at which kids successfully work through math problems, which can result in greater academic achievement and stronger foundational skills in math.

**Can foster a sense of accomplishment in students**

With plenty of opportunity for assessment in each lesson, kids can more frequently and more precisely get a sense of how they’re skills are developing.

This can be particularly beneficial to students who are uncertain of themselves and their capabilities, as small achievements in unit exercises and assessments can have a cumulative effect of building up their self-esteem and sense of accomplishment in the long run.

**Doesn’t get as boring**

The spiral method that Saxon Math uses, which breaks complex subjects down into smaller spread out pieces, means that the curriculum will frequently introduce new concepts and topics to work on, keeping learning more fresh.

In this way, kids won’t get bogged down or stuck on any one difficult concept, which can lead to boredom, frustration and even poor self-image.

**There are a lot of resources available**

Because Saxon math is an extremely popular and widespread math curriculum, there are a lot of resources available for its use online, including many guides on how to best teach it, ideas on how best to supplement learning and ideas on how to integrate it into homeschooling and alternative learning structures.

**Easier to teach at home than some other programs**

Saxon Math is a structured program with a lot of guides, solutions, prompts and even teaching scripts that can be used by unfamiliar or inexperienced homeschooling parents to help implement the program for their kids.

Unlike other programs, which can often be quite different to how parents learned math themselves, this means that new parents and those switching into Saxon from another curriculum won;t have to spend nearly as much time learning how to teach the material and can spend more time actually doing so.

### Saxon Math Cons

**Some students need or want more time to learn concepts**

One drawback to the spiral method that Saxon favors is that some students simply need more time to stay focused on and explore a concept before they grasp it.

Other students may be more interested in math theory, wanting to go deeper into a single concept than the curriculum allows.

These students can find the constant moving from subject to subject to be frustrating, counterproductive and even unpleasant at times and may benefit from a curriculum based on a mastery approach.

**Math Fluency vs Critical Reasoning**

A common criticism of Saxon math and its pedagogical approach is that it focuses heavily on practice and computation, working on math facts, drill and *how *to do math rather than exploring the *why *of math concepts.

With more of an emphasis on practice exercises and computation, developing fluent recall in math facts and solving problems, sometimes critical reasoning and a deeper understanding of math can end up being ignored.

That’s not to say that there isn’t any conceptual exploration of math topics, Saxon Math does have sections that explore math concepts in more detail, but the overall emphasis with Saxon tends to be placed more on *doing *math.

**Slower Pace**

With lots of practice exercises, assessments and reviews, the Saxon method can take time to work through. Parents often report taking an hour or more to go through some lessons thoroughly, which can affect homeschool schedules and can frustrate both parent and student.

Similarly, in terms of curriculum advancement, Saxon’s incremental approach and the constant review can mean it moves at a slower pace than some other curriculums, although it does cover all required topics in the end.

## Who is Saxon Math For?

The Saxon Math methodology, with its incremental development, rigorous curriculum and focus on drill and frequent practice, can achieve some impressive results with the right learners.

We think that Saxon Math and its approach can be particularly useful for:

- Students and parents looking to develop solid, foundational skills in math, particularly as they apply to standardized tests, entrance exams and school achievement

- Parents looking for a method that encourages independent learning and requires less parental involvement

- Students who learn best by drilling math and who don’t mind a lot of practice and review

- Parents looking for a more rigorous, back to basics approach to math than can be found in most public schools

- Students who can get overwhelmed or frustrated by focusing on a single topic for a long period and who like moving on and then coming back to concepts

## Who is it not ideal for?

That said, Saxon Math’s approach is not for every student and every homeschool family.

In particular, it may not be the best option out there for:

- Students who have a strong interest in math concepts and want to delve deeply into the theory and logic behind the math. They may be better served by mastery based methods that have less of a computational focus
- Students with strong math skills or talent who learn quickly and may become frustrated or bored by the repetition and review

- Those interested in competition level math preparation or heading to math-heavy college programs. They may benefit from a more conceptual understanding of math than Saxon offers, such as from Beast Academy or Art of Problem Solving

- Students who become anxious or frustrated with constant practice and assessments

## Bottom Line

If you’re looking for a rigorous K-12 math curriculum that takes a back to basics approach, with plenty of solid math practice and skill assessment, Saxon Math might be the curriculum to look at.

Although not ideal for every student, and while the numerous editions out there can be a bit confusing, its spiral approach and more practical math focus can ultimately give students a stronger foundation and a leg up in math.

## FAQ

**About the Author**

David Belenky is a freelance writer, former science and math tutor and a tech enthusiast. When he’s not writing about educational tech, he likes to chill out with his family and dog at home.