Montessori education uses beads in much of the math curriculum. Beads are first used for counting, and later adding, subtracting, skip counting, multiples, division, place value, and units. The use of beads are a wonderful tool for teaching many mathematical concepts in a concrete- see and touch- way. The other great thing about the use of beads is that the materials can be handmade at home for the cost of just beads and wire. For someone who wants to use Montessori math lessons at home but can't afford all of the math materials, I've found the beads to great resource and substitute.
This is our handmade Short Bead Stair set. As we prepare for my oldest daughter's start of public school kindergarten this fall, we are slowly going through some of the Montessori math and language curriculum so she can get a solid understanding of concepts she will be exposed to during the kindergarten year. It took only a few minutes to put the stair together using small pliers, wire and beads and my daughters enjoyed helping. Traditionally, there are set colors for each amount (check an online Montessori catalog to see) however I chose from what we had, with the exception of the ten bar which is yellow/gold. It makes sense to make it yellow if you intend to continue on with more advanced bead math work.
This lesson was a review for her since I introduced it much earlier (appropriate for age three and up). To introduce the work, the beads are removed from the container and placed randomly on the mat. The adult finds the one bead bar and asks the child to count it, it is then placed towards the top of the mat. Similarly, have the child count each bar to build the triangle. The objective is that the child will be able to independently sequence the beads in quantity and graduating size.
After introducing the short beads stair, a later lesson we've done (although not a traditional lesson) is matching the beads with the numerals. Again, they are placed randomly on the mat and then matched together.
The beads are counted and then the numeral is found. (If you spot the mistake in this picture it is my fault- I quickly put them back out to take a picture when we were done and I wasn't a careful counter!)
The most recent lesson we have been working on is Teaching the Names of Quantities 11-19
The objective of this lesson is for the child to see the amount, hear the name, and count the beads. The purpose is to teach the child the names 11-19 in association with quantities and to enable the child to recognize them as separate numbers. The use of the ten bar is significant as an early introduction to the units: ones and tens.
For this lesson, it is helpful to have made 9 ten bars. The ten bar is placed on the mat and the child is asked "How many is this?" The child answers "10". To the right, the 1 bar is placed and the adult says "Ten and one is eleven." This phrase is repeated a few times and then another ten bar is placed on the mat under 11. The adult then says "Ten and two is twelve" and so on, just introducing 11, 12 and 13 for the first lesson. The adult can then say "Show me 12. Show me 11..." and then isolating one set and asking "What do we call this?" This method, called the 3 period lesson, assesses the child's understanding. On another day more quantities are introduced until 11-19 have all been introduced. Following this lesson is when quantities and numerals are introduced - more on that later!