About Martian Mathematics

Martian Mathematics is a complete introduction to the patterns, methods, and practical application of mathematics for children ages four and up. It develops number sense and strengthens logic and reasoning in struggling students. It exposes the subtle patterns that are key to fast mental calculations in gifted students. And it improves working memory and focus in all students. It will transform your students into mathemagicians.


Martian Mathematics strives to avoid the uninspiring arithmetic still popular in American public schools today. We also avoid the silly long-way-around techniques associated with common core math. Our system starts with skip counting, but not like you see in a standard first and second grade curriculum. For example, when we skip count in fives, we don’t only cover the usual sequence:  0, 5, 10, 15, 20, etc. Instead, we use something called the five’s conjugate. If you count to six on your fingers and then close your left hand into a fist, then six becomes one. The five’s conjugate of six is one.

We can then skip count by fives starting at one or six:
1, 6, 11, 16, 21, 26, etc. Similarly, if you count to seven on your fingers and close your left hand into a fist again, then seven becomes two. The five’s conjugate of seven is two. Skip counting in fives starting at two or seven simply repeats these conjugate pairs: 2, 7, 12, 17, 22, 27, etc. You only have to continue this two more times up to nine, and you can skip count by fives from any number, which means you can also add or subtract five to any number. For example, 1876 + 5 = 1881. Knowing the five’s conjugate of just four numbers allows you to add five to any number. This is one of our signature techniques that you won’t find anywhere else.

But that’s not all we have to offer. There is also the telephone sequence, which allows students to easily add or subtract three and seven from any number, and much more. By the end of Level 1, your students will be able to add and subtract any single-digit number to any number, including four- and five-digit numbers, in their head. Unlike other math courses, we don’t postpone multiplication and division. We start with those in lesson 8, and the skip counting approach lends itself naturally to understanding the rules of divisibility—a topic usually addressed in fourth through sixth grade. By the end of Level 5, students will be ready for algebra and Euclidean geometry. The mathematical skills your students learn here are applicable in all technical fields from physics and engineering to computer science as well as the social sciences and business school.