The child is introduced to the next area of math after experience with the decimal system. The child is shown the traditional names of the teens and tens from eleven to ninety-nine. These are introduced through the teens and tens beads and boards where we begin with the quantity and then introduce the symbol. The child is introduced to the long and short chains of the bead cabinet in this mathematical area. The hundred and thousand chain are introduced first because it is the most familiar to the child. The child is prepared through linear counting for skip counting as well. The short chains represent the squares of the numbers one to ten. The child sees how the chain can be folded up into a square and then unfolded to be counted. However, we do not teach the children squaring and cubing, rather we offer a sensorial impression. The child continues to take in concepts over time through repeated work, concentration, and exploration.
The next area is memorization. Here the child memorizes the essential combinations for all four operations. These combinations are often thought of as the tables in the operations. The essential equations can be held in our memory and used in daily operating tasks. The materials in this area are less concrete and more symbolic. This area requires more work on paper and little work with quantity. It requires more writing the symbols for operations and less work with manipulative objects. The snake game is introduced here and offers a visual way to see the essential combinations. The child works with the addition strip board and explores impressions of commutative law. The child through work with the essential tables is given the opportunity to works out whole series of tables, fills in the sheets, recites it, and then repeats which builds memorization and intellect. The child activates her auditory and visual memory while reciting essential combinations.