DW has been working with the peg board to solve square root problems. She is still not understanding the relationships among the a squared + 2(a x b) + b squared. The geometrical relationships are feeling right to her, however she often needs to see the math so she can see where she is going, so all the pieces can fit in her mind.
So, today we sat down with the pegs, graph paper, colored pencils, and uninterrupted time.
We began to lay out the beads and form our first square which we translated to the graph paper. We then wrote down the math equation and began to work out the first square in numerical terms as well.
The discussion continued as we subtracted and came up with the beads we could not fit into the first square. It matched with our actual beads left over. We then exchanged and began to layout the rectangles. Discussing that there are two wings, we began to theorize about what (“b”) times the 2 times “a” could be close to our partial remainder. We made our decision and began to lay it out on the peg board and with colored pencils. After the math and the subtraction, we could see whether our “b” theory was correct. It was not. We needed to have one less in the width of 2(ab). We fixed it and then discovered that we could form a square in the remaining space. YEY!
Clear as mud?