As Montessori educators we have some of the most phenomenal teaching materials available to us to introduce abstract concepts in a concrete way. These materials, designed over one hundred years ago by Dr. Montessori, have stood the test of time and are as powerful today as they were back in their conception. These manipulatives incorporate the principles of isolation of difficulty, self correction/control of error, building upon previous knowledge and precision. One such material that embodies all of these are the Golden Beads or Bank Material.
Once children have a mastery of quantity from 0-9 they can be introduced to the Golden Beads and decimal work. Initially this work starts out as a nomenclature exercise with the Introductory Tray. The children are introduced to the material along with the language that represents the hierarchy of numbers: this is a unit, this is a ten bar, this is a 100 square and this is a 1000 cube. Along with this, the children would be introduced to the numeral cards representing numbers from 0-9,999. (see the post on the 45 layout ) Once the language is successfully paired with the concrete representation the child can then move to gathering quantities to create large numbers. A child could be asked to get 9 ten bars and 4 units. Get 3 thousand cubes, 4 hundred squares, 5 ten bars and 6 units. This goes on for some time until the child gains a real comfort level with the nomenclature and place value.
Each value in our work with the hierarchy of numbers has a designated color. While the golden beads are always golden the numerals representing the different values follow this pattern: numbers for units are green, numbers for tens are blue, numbers for hundreds are red and then the pattern repeats itself. Numbers for thousands are green since they represent the units or starting point for the next hierarchy. Ten thousands are blue, hundred thousands are red and when we move to millions we start with green again. This color coding is the standard used from level to level in Montessori schools around the world.
To help reinforce the color-coding aspect of this work the Number Composition Mat was designed. Children use this mat as an underlay for the building of quantities. So in sticking with the example above, they would bring 6 units to the mat and place them on the narrow green strip on the right, 5 ten bars and place them on the blue strip, 4 hundred squares and place them on the red strip and then 3 thousand cubes would be placed on the wider green strip to the left. Numeral cards could then be placed below the mat showing the symbolic representation of the quantity: 3456
Now to introduce an element of independence to this activity and to encourage the needed repetition for mastery, a set of Place Value Dice can be added. These 10-sided dice numbered 0-9, are color coded to correspond to the colors of place value. (They come in several different varieties and sizes, all described on the website.) So a child would roll the set of 4 dice and then place them below the corresponding sections of the number composition mat: the green die below the units section, the blue die below the tens and so on. Next the child would fetch the indicated quantities from the bank and build the number indicated by the dice. By using these dice all numbers between 0-9,999 could potentially be rolled.
Children love rolling the dice to see what quantity they will get and teachers love not having to come with numbers on the spot (and remember them) for the children to compose. What is even more interesting is watching children explore the patterns of numbers with the dice. So when they think you aren’t looking they manually manipulate the dice so that they all “land” on the same number, for instance 5555. Or they really like to explore what happens when zeros show up. This free exploration and engagement in the activity is where the real aha moments occur and connections are made!
I’ll save the discussion on the many other ways in which the Place Value dice can be used for the next post!