The Curriculum of the Steiner School - Class 8

Notes and Lesson Plans

Number Bases
updated November 1, 2022

Recorded here is my own personal collection of articles, resources, favorite links, teaching ideas, and lesson plans. It encompasses many years, from the very beginning of my experience studying and learning about Waldorf to the present time. People from all around the world visit my site and recommend it to others. Welcome!

This site records my journey. I hope my honesty is encouraging and helps break down some barriers that may prevent people from trying Waldorf methods. Because this is an ongoing site documenting my curriculum planning and ideas, some materials are more Waldorf-y than others. Please feel free to take what you like and leave the rest.

This page has helpful links and LOADS of free resources to help you plan your eighth grade year. Enjoy!

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Number Bases
for Class 8


Number Bases is the first topic in the 8th grade student workbook in Jamie York's curriculum Making Math Meaningful.

My children have absolutely loved it!

If you are only homeschooling one child, just get the teacher's edition of the workbook. You do not also need the separate student edition. The teacher's edition contains ALL of the pages of the student edition (FULL size BLANK worksheets) and the only difference is that it has the answer key in the back. Here are some extra thoughts on resources for this topic:

I like to introduce number bases by reading Weslandia by Paul Fleischman (octal).

The Multi-Base Bead Frame
Base 2 Through Base 16

I HIGHLY recommend the Montessori Multi-Base Bead Frame as a hands-on manipulative for this topic. It's extraordinary! And it converts to be used for binary (base 2) up to hexadecimal (base 16).

The Montessori Multi-Base Bead frame

I definitely recommend reviewing exponents first, because of the way the board is labeled.

video 4 - Montessori Multi-Base Bead Frame Multiplication: One Digit

video 5 - Montessori Multi-Base Bead Frame Multiplication: 3 Digit Multiplier

video 6 - Montessori Multi-Base Bead Frame: Bases Greater Than 10

Base 2 - Binary

Base 5 - Quinary

video 1 - Introduction to Alternative Bases: Counting in Base 5

Base 6

video 2 - Addition in Base 6 Using the Montessori Cubing Material

video 3 - Addition in Base 6 Using the Multi-Base Bead Frame

Base 8 - Octal

Base 16 - Hexadecimal

a visual introduction to base 16

these are the natural wooden strips from the Subtraction Strip Board

The Not-Golden Mat
Base 2 Through Base 9

Today while working with a student on addition and subtraction with the Montessori Golden Mat, it struck me that the Golden Mat is golden because it is for the base 10 system (the decimal system) and gold is the color of the 10 bar in Montessori! So you could also make a mat for one of these other bases and you would simply use the color of felt that goes with that bead bar.

The quantity of Colored Bead Bars that you would have available to you would also be reduced.

    base 2 - green felt mat; only 1s available

    base 3 - pink felt mat; only 1s, 2s available

    base 4 - yellow felt mat; only 1s, 2s, 3s available


Some people do use the ten bars with the Golden Mat to help children remember that a ten gets traded for a one (in the place to the left) and a one gets traded for a ten (in the place to the right).

It would be a useful exercise for students to make these mats or, at the very least, to calculate what the value of each place would be across the top of the mat. Again, this goes back to the Multi-Base Bead Frame and presenting the value of each column in terms of n and its exponents. Here are a few:


    n0 = 1
    n1 = 2
    n2 = 4
    n3 = 8
    n4 = 16
    n5 = 32
    n6 = 64


    n0 = 1
    n1 = 8
    n2 = 64
    n3 = 512
    n4 = 4,096
    n5 = 32,768
    n6 = 262,144

Last, but not least, here is a cool binary teeshirt!

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