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!

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

ETC Montessori makes a Multi-Base Math Chart which works well
for this concept. This mat is intended to be used with the Montessori cubing material and the colored rods.

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

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

etc.

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:

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