DW has begun the process of understanding squaring. She has looked at binomials (3+4) = 7 for several years from different angles. She has continued to process into squaring of numbers. Yesterday we looked at the relationship from 1 to 9 then 10 to 90 and 100 to 900 when squared.
Today we began the slow process to understand how to condense large squares into binomials. For example she is laying out the square of 14 in unit beads. To count all these beads will take forever.
She then began to change the unit beads into 10’s and then the 10’s into 100’s.
She then starts with the squares laid out again beginning with the 100’s (in this example the square is 1 – or 1×1) and then began laying the 10’s on either side of the square like arms and finally in between the arms she placed the remaining green unit beads. She had one 10 bead left over that she traded back in for green unit beads to complete the the square of four.
At that point it became easy to count the beads – 1 squared (in the hundreds place) + 2(1 x 4) (in the tens place) + 4 squared (in the units place) = 100 + 80 + 16 = 196 = 14 squared.