One of the features that often draws people to Montessori is the way she used concrete materials to help young children understand complicated abstract mathematical concepts. The bead material is an essential part of this, but it can be very confusing if you are not familiar with it. In this post I am going to give a brief overview of the Montessori bead material and also discuss a cheaper alternative that can be used for many but not all of the same lessons. I hope it will be useful for anyone considering using Montessori maths materials.

The golden bead material comes in single unit beads, ten bars, hundred squares and thousand cubes. These are used for decimal quantity, formation of numbers, changing, addition, multiplication, subtraction and division (this site is a good place to read about the five groups of exercises).

Wooden base ten sets like this are available for about a third of the price of the equivalent golden bead material and can be used in exactly the same way. We bought our set from Tower High Learning because it contained ten hundred squares and ten ten-bars, whereas other sets I have seen only contain nine of each. It also came with one hundred unit cubes rather than just ten.

Coloured bead bars consists of bars of 1-10 beads with each number represented by a different colour. These are used with ten-bars to teach teen and tens quantity and multiplication tables.

Cuisenaire Rods are the perfect size to be used with a base ten set instead of coloured bead bars. Obviously the colours are different to the traditional Montessori colours, but this would only be a problem if a child was going to be using both. Cuisenaire no longer seem to sell the wooden ones on their website, but they are available via Learning Resources.

The ten different bead bars also come in short chains and squares (which represent the number squared) and long chains and cubes (which represent the number cubed). These are used for linear counting and skip counting.

There isn’t really an easy alternative to the bead chains, squares and cubes. There are enough bars in the base ten set to lay out a short bead “chain” for 10, although they wouldn’t actually be linked together. The Cuisenaire starter set contains enough pieces for short and long chains for 2 and 3 and a short chain for 4, but not enough for the other numbers. However, it would be fairly easy to make homemade number lines for skip counting and the squares and cubes seem to be used less than the other bead material anyway.

A set of golden beads for decimal work and a set of several bead stairs will cost about £100. The equivalent in a base ten set and a set of Cuisenaire rods will cost about £40. Neither of these options contain enough components to do every variation of every lesson and game (for example, in both cases you are limited by having only one thousand cube), but they do cover most of the maths bead activities. To put it into context, purchasing the complete bead material would cost over £1000, which is obviously well out of the budget of most home educators!

The advantage of buying proper Montessori bead material is that you can add to it gradually over time and it will all be compatible. There isn’t really any way to reduce the limitations of the base ten and Cuisenaire rods alternative, other than doubling up on sets, in which case I would probably opt for the bead material anyway. However, the obvious advantage is that they are much cheaper and I personally think that they are an excellent alternative for anyone wanting to use Montessori’s brilliant concrete methods for understanding maths concepts without buying lots of expensive equipment.

sarahelisabeth

That is really helpful. I love the look of the wooden set. I’m afraid we use Duplo as manipulatives more often than anything else but as we approach larger numbers, its limitations will come into play.

Farren Athalia

I love the fact that your blog teaches me more about Montessori! I didn’t know that it was a Montessori idea but I have always felt that maths should be taught using physically representations of the numbers – whenever I helped the nine year old boy I looked after with his homework we would use beads or coins to represent the numbers he was working with. I really like that you use wooden sets, they just seem nicer than plastic.

Angela

Just wondered if Aaron and Tabitha play with these resources in the intended way? I made a 10×10 container by sticking egg boxes together for Iona, as I’d seen it as a suggestion for teaching various counting ideas, and she wanted it out the other day. I started to explain it to her, while trying not to be too directive, but she just wanted to use it as a maze for her small plastic toys, and refused to do anything mathematical or scientific with it!

Sarah

No they use them for imaginative play too. I’m absolutely happy for them to do that, although I don’t think it would be encouraged in Montessori! In my opinion they can learn so much just by handling and playing with the materials. If there is something I really want them to use “properly”, I find that it helps to demonstrate it to them (sometimes silently works better than explaining) before making it available for use.

Angela

That’s a relief! I read some home ed blogs and their little kids seem to do worksheets etc just as they’re told. Iona rarely does, and I find myself hoping that one day she’ll be a bit more accommodating, or she’ll find getting by in life harder. I’m sure she’ll get there in the end, and she certainly seems to be managing to learn in her own way, but it’s good to hear that it doesn’t always go perfectly for others either!!