The Parent/Teacher Guide has complete instructions on how to teach this math program.  The Student Workbook has worksheets and practice pages. Both are needed for a complete program.

This unique approach to subtraction was developed by Prof. Emeritus Michael Butler at the world renowned UCI Farm Elementary School.

  • Memorizing the recipe for how to borrow does not result in understanding of the basic concepts of regrouping.  The Patterns in Arithmetic series teaches for understanding.  The student constructs understanding through experience not being told "how to do" the problems.
  • The student is guided to find patterns and generalize those patterns in to working knowledge of how procedures work and why they work that way.
  • Circle Math is our unique way to teach beginning subtraction and regrouping.
  • Parents are guided though a series of lessons that give sample dialogues that a teacher might have with a student who is learning.

    Click on covers below to view or order,

    Patterns In Arithmetic:

    Grade 1:  Book 1 - Beginning subtraction with a hands on approach and Circle Math

    Grade 2:  Book 2 - Continues subtraction into the hundreds, no regrouping

    Subtraction:  Booklet 3 - General Principles of Regrouping (borrowing) - Grade 3

        Regrouping:  Introduction and Philosophy

        Review of Circle Math:with Subtraction

        Discovering how to Regroup with Subtraction using manipulatives and Nonstandard    


        Standard Regrouping

        Three Digits Regrouping:  Manipulative and Recording

    Subtraction:  Booklet 4 - Large Numbers and Practice - Grade 4

        Introduction to Nonstandard Regrouping and IOUs 

        Standard Regrouping:  Review 

        Nonstandard Regrouping and IOUs:  Review    

        Standard Three Digit Regrouping

        Standard Three Digit Regrouping with Recording

        Gus the Bus Driver Word Problems

    Chrysalis Charter School:  Base Ten Subtraction (special education students) - Grade 3

        Regrouping:  Teacher Instructions     

        Tens and Ones:  Manipulative, Recording, Expanded Notation


        Covering as a Strategy

        Trading  Tens and Ones

        Standard Regrouping:  Short Way

        Families of Fact 

        Hundreds, Tens, and Ones:  Manipulative

        Standard Regrouping with Hundreds 

        Word Problems