WHMS Blog

When the bead cabinet is introduced in primary classrooms it may only have the short chains and squares available for use. The use is for numeration, counting forward from a value (instead of always starting at one), and ultimately skip counting. As the year progresses long chains may be added to the cabinet as the children’s desire and ability to count and skip count higher numbers increases. The physical space that the long chains occupy is impressive as well, and provides the children who complete the long chains with a deep sense of accomplishment -as well as a concrete sense of what 9³ or 10³ represents in terms of a concrete quantity.

As children transition into Lower Elementary classrooms, they leave behind many of the practical life and sensorial works (including the pink tower) that filled their work cycles. But, many are often relieved to find their good friend, the bead cabinet, holding a place of prominence in the classroom. On the first day of Lower Elementary, the bead cabinet is available for use, complete with short chains, long chains, squares, cubes, and numerical tags. Practice with the materials continues in the same manner as Primary, with an emphasis on skip counting, doing mental math to add to previous sums, and beginning to memorize and internalize multiplication facts. Near the end of Lower Elementary, a complimentary material to the bead cabinet is presented; the decanomial bead box. This material is basically the bead bars of the bead cabinet unchained. The decanomial bead box contains 55 of each numeration (color) of bead bar. The direct aim of the material is to build a Pythagorean Square in several configurations.

This gives the children a geometric sense of the multiplication table (here 4 x 5 has a shape as well as product) and continues (along with other materials) to solidify their math facts.

The first two passages of the decanomial are a horizontal presentation where the beads are laid out in rows (one taken one time, one taken two times, etc..) and a vertical passage where the beads are configured in columns. (Figure 1) In some classrooms, intrepid math minded children make their way through these presentations and a third presentation that is represented in Upper Elementary.

When children transition to Upper Elementary, they find many of the same math materials from their LE classroom still on the shelf next to undiscovered materials (and forgotten favorites). The bead cabinet and decanomial bead box are there to greet them. In Upper Elementary, the decanomial bead box is used as review for math facts, but also to make a connection between materials that they’ve been working with for half their lives. The final passage of the decanomial is referred to as the angular layout. (Figure 2) Here the square of a factor is placed first -diagonally from the previous square, and then the other bead bars are placed horizontally and vertically to the left and above the square respectively (2² is placed first the (2 x 1) is placed to the left of the square and (1 x 2) is place above the square).

This configuration requires borrowing higher value bead bars from a second decanomial box as the children start to discover that 64 eight (brown) bead bars are required to complete the row and column, 81 nine (blue) bead bars are needed to complete the row and column, and 100 ten (gold) bead bars to complete the final row and column. These are precisely the number of bead bars in the respective colored long bead chains of the bead cabinet.  Once the angular layout of the decanomial is complete, a guide demonstrates how alternate groupings of the rows and columns of similarly colored bead bars can be combined to make squares. Surprisingly, there are 10 ten (gold) squares that can be stacked to create  a 1000 cube (10³), 9 nine (blue) squares that can be stacked to make a 729 cube (9³), and so on until we’ve replaced each stack of squares with its corresponding cube from the bead cabinet. For the grand finale, each successively smaller cube is stacked on top of the previous cube to create what is known as the “tower of jewels” which is the same proportionally to our pink tower of years gone by.