Principles of Mathematics – Book 1 – Additional Resources

This is an online webpage designed to go along with Book 1 of Principles of Mathematics.

Found a resource helpful that’s not listed here? Have a question about the curriculum? Send us an email at

Principles of Mathematics eCourseeCourse Supplement

Need more visual input? An optional eCourse component is be available. The eCourse features short videos to go with each lesson. View more.


Helpful Resources

Note: All the links below go to external sights; we have no control over the content, nor is a listing here an endorsement. Feel free to find other online resources instead–these are just listed here as a convenience.

Online Abacus

Online Scientific Calculator

Resources for Extra Worksheets

Below are some sites that offer printable worksheets if your student needs extra practice or drill on a concept.

Fraction problems:

Percent problems:

Graphing problems:

Three-Year Schedule

For students needing longer with each concept, here is a three-year schedule that shows you how to complete both books in 3 years.

Binary and Hexadecimal Notes

Understanding other bases is not a crucial concept; so long as students really grasps place value, you can let them move on.

However, understanding other bases can help solidify the meaning of place value–and it’s pretty cool! Here’s an example of a hands-on idea for teaching the hexadecimal system. You could follow a similar approach for the binary system.

Put 2 bowls on the table. Write “1s” on a piece of paper and put it in front of the bowl on the right. Write “10s” on a piece of paper and put it in front of the bowl to the left.
Write the numbers 0-9 on tiny pieces of paper and put them in each bowl. Point out that we can have 0-9 1s, 0-9 10s, in our normal place value system. We can count up to 9 using 1s, but once we get to 10, we have to move to the next “bowl.” 1 from the 10 bowl represents 1 ten. 1 from the 100s bowl represents 1 hundred. And when we write it on paper, a 1 in the ten’s place represents 1 ten, while a 1 in the one’s place represents 1.
Then change the labels on the bowls to “1s” and “12s.”  And add A, B, and C inside each bowl, explaining that A represents 10, B represents 11, and C represents 12. Now, we could represent up to 12 using our first bowl. And every number or letter in the middle bowl represents a set of 12 rather than a set of 10.
The thing that might be confusing is that our decimal system only has the digits 0-9 and for a base 12 system to work, we’d need 12 different digits, much like the base 16 hexadecimal system on page 34.
The main point is to get the student to think of the digits in a number as representing sets–in 21, the 2 represents 2 sets of ten in our base-10 system. If 21 were written in base 12, though, then the 2 would be representing 2 sets of twelve instead.


Here’s a free preview of the eCourse that explains more about using an abacus. Preview more lessons and check out the course on

Preview more lessons and check out the course on

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1 thought on “Principles of Mathematics – Book 1 – Additional Resources

  1. […] Both my sons have now worked through Book 1 & 2 of Principals of Mathematics, and it has been exactly as I’d hoped. It has transitioned them very well into Algebra 1, with a little bit of overlap that has helped them ease into the Saxon course. I also purchased the e-course which has a video for each of the lessons, which we found very helpful. You will also find a few corrections and additional resources here. […]

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