Someone asked, “If you want to start Montessori math from scratch at age 6, what would you need? What would you skip?”
Would you hate it if I said, “It depends?”
Backing up, children in Montessori programs learn math concepts by working with materials that get progressively more abstract. It mirrors the child’s developmental needs, e.g. a preschooler learning by using manipulative vs an older child who can think more in their head.
So, in training when we asked this question of how to teach an elementary child whose had no Montessori preschool background, our teacher usually says we can start by using the stamp game or even go back to the golden beads, depending on the child’s development.
Over the years, I’ve slowly bought most Montessori material offered at Kid Advance, except maybe the printed items like number cards. The advice my trainer gave me has been proven to be true. “Don’t make something if it’s available to buy.” There are just so many things you can prep and make in Montessori, it’s best to save your prep time for those.
The AMI progression of math is just slightly different from the AMS progression. So it depends on if you started Montessori math in the Primary years or not and which album you want to follow. For this list, let’s assume that the child is entering first grade and has only learned to count.
I’ve listed the material I’ve needed so far, not including geometry, which is a whole other set of items. We havn’t done things like negative numbers or cubing. Each material to buy is linked to where I bought it.
Material to Buy
1. Bead Cabinet – counting, skip counting, multiples, squaring & cubing
The bead cabinet is a huge purchase. I bought my squaring and cubing chains and made my own labels. I also didn’t buy the bead cabinet itself.
Even though it feels like the material doesn’t get too much use, I’ve found it indispensable in teaching squaring and cubing concepts. I don’t think you can teach these concepts with substitute materials.
2. Stamp Game – 4 operations
Instead of Golden Beads, you can start the Elementary child with the Stamp Game. It is used in teaching the 4 operations.
3. Large bead frame – counting, addition, multiplication
The large bead frame is used to teach numeration, namely counting up to 1 million, as well as addition and multiplication operations. For addition, it’s that one last step before abstraction; for multiplication it’s the first step after stamp game. It would be a bit cheating, but with the large bead frame, you wouldn’t need to get the small bead frame.
4. Division Racks and Tubes – division
There’s really only one material for division other than stamp game so this is a must. I found the Kid Advance version a little bit hard to maneuver because the grooves in the boards aren’t deep enough to hold the beads.
My children never really took to these materials, I think it’s partly my fault because I wasn’t methodical about it.
5. Decimal boards & Cubes – decimals
Decimal is one of those where you can teach the kids the “trick”, which is to point out how it mimics normal operations. But, if you want them to have a very concrete grasp of the idea that 1/10 is one tenth of 1, 1/100 is one tenth of 1/10, etc, it’s really nice to have the material on hand for them to see it.
When we used the concrete material, the kids are very often confused, because the place values are switched, thousandsth is to the right of hundredth, whereas thousand is to the left of hundred.
I similarly did not love the Kid Advance version of decimal board because the colors for the decimal cubes weren’t easy to distinguish from the normal digits.
6. Peg Board – multiples, factors, squaring and square roots, ratio
The peg board is used to teach multiples, factors, squaring and square roots, you can’t live without it.
The peg boards from Kid Advance also weren’t the greatest. Each peg was like a little umbrella and it was very hard for the children to hold, especially because the holes in the board are not deep enough.
7. Checkerboard Beads and Decanomial Beads – multiplication, squaring and cubing, algebra
This is the MOST ESSENTIAL thing you need in the classroom. There are actually two kinds, one that has the 10-bar, and one that goes only up to 9. The 9 one is used in checkerboard multiplication, where you don’t want them to have the 10-bar available.
Because you need a lot of beads when you do the decanomial layout, and due to the problem of the 9-bar vs 10-bar, I ended up getting both decanomial beads and checkerboard beads. The beads are great substitute for anything you need. For example, for divisibility, I used the few golden beads I have from the bead cabinet, and whatever I didn’t have I just used the bead bars.
If you had to buy just one item, it would be the bead bars. You use them in primary and elementary, so they’re quite worth the investment. They can be used as substitutes for many activities, like snake game, colored bead stairs, etc.
8. Binomial & trinomial cubes, cubing materials – squaring and cubing
The binomial and trinomial cubes are sensorial materials to learn squaring and cubing. The cubing materials are to learn actual cubing. You can’t live without it and there are no substitute. The cubing materials are quite expensive so it took me a few years to decide I really really need them and I finally splurged on them.
Optional
These items are optional because while it makes life easier to have them, you may be able to find work arounds for them. So if you’re on a limited budget, you can buy these when you feel you absolutely can’t live without it in your classroom.
1. Flat frame – multiplication
The flat frame is the last step before solving on paper because the material has removed all color coding. But both of my children did not spend too much time on this material so you may be able to skip it.
2. Fraction skittles – fractions
Fraction skittles are used in Primary to introduce the concept of fractions. I thought I didn’t need them anymore and stored it somewhere that I can’t find now, only to realize I need it to teach fraction division! Oops. I made by making little skittles out of sculpy and then cut them. But it would have been nice to have the skittles.
3. Fraction circles – fractions
You can make your own paper fraction pieces and bypass the fraction circles. I have them on my TpT Store. But this is a nice material to have because you can use it to trace fractions. It has weight so kids can kind of feel how 1/5 weighs less than 1; all indirect cues on their value.
4. Centesimal Circle – decimal fractions
This was just a super cool material used to illustration decimal fractions and can also be used for angles. I really loved it. But you could maybe make it out of paper?
5. Golden Beads
Even though you don’t need this much past Primary. There are some instances like teaching divisibility, when you do. Or, if your child has a lot of trouble even with the stamp game, you can go backwards and use the golden beads. It’s just been nice having the golden beads around for various activities when I need it. But given its price, it is an investment so you may want to wait till you find you really need the material. Or make paper versions.
Despite my love for this material, neither of my kids have used it much. But I love this version from Montessori Services as it’s cloth and your beads won’t roll around, unlike the wood versions.
I find the material to be just one of several you can offer to the child to teach multiplication, depending on their interest. Each of them have varying degree of abstraction and different ways of presenting multiplication but I found that the kids gravitate toward one kind of thinking about multiplication and find the other ways really hard to grasp.
Material You Can Make
Most of the paper-like products you can make. Some Montessori box curriculum companies also provide them for printout. Below is a non-exhaustive list of items I’ve made. The longer I homeschool the more I just buy with my charter school money. It takes so long and often the kids don’t repeat use it enough to justify the time spent.
- Golden Beads
- Large and small numbers
- Fraction numbers
- Fraction pieces
- Table A, B, C for multiplication
- Finger charts for addition/subtraction/multiplication/division
- operations memorization booklets
- Math Great Stories Poster in Chinese
I don’t have words to express my feelings because awesome! Clarity of pictures, details etc. Thanks 😊