Sea Squares and Snap Cubes

Today we continued exploration of growing patterns using snap cubes and the book, Sea Squares. The book uses a rhyming format to investigate square numbers in things you find in or near the ocean. I first read the book to both my boys. Then I showed my 8yo son the beginning of a pattern, designed to go with pages of the book.

On the page with "1 spout, 1 whale and 1 strong tail" I showed him arrangement #1, a single cube.

On "2 white gulls, with 2 eyes each, have 4 bright eyes to watch the beach" I made arrangement #2, shown below in a square of 4 pink cubes.

The next page continues with "3 clowns with frowny faces have 9 stripes in fishy places." I asked my son to build what he thought arrangement #3 in this pattern might look like. At first he made the arrangement shown below, a row of 4 tiles on top of a row of 5 tiles. I asked him to show me where he saw 9. He pointed to all the tiles. I asked him where he saw the 3. He looked at it for a bit, stumped. So we went back a page  (to the gulls and my pink arrangement #2) and I asked him where he saw 4, and then where he saw 2. He could show me that 4 was all the tile and that 2 was both along the sides (vertical) and across the top/bottom (horizontal.)

Then he got an "ah-ha" look on his face and revised his arrangement #3 to make the blue square shown below.

We continued with the 4th arrangement, "4 seals are quite complete with 16 flippery feet" and he built a 4x4 square.

And then on to the 5th arrangement, "Those 5 lilies of the ocean have 25 fronds in motion" in which he built a 5x5 square.

The text continues through a 10x10 square, but he thoroughly understood the pattern before that point, so he just built a couple more arrangements and then described what the next few would look like. "8x8 would have 64 squares," etc...

Tomorrow I'll describe how we continued the discussion of square numbers using snap cubes.