# Building Blocks

This picture comes from the "Building Blocks" exploration in Advanced Common Core Math Explorations: Factors and Multiples. My classes typically spend about three days solving the puzzle. Afterward, each student keeps a copy of the answer to use throughout the remainder of the school year (for all sorts of interesting mathematical purposes!).

I notice that there are more white blocks than any other color.
I notice that when a square contains white blocks, they are always at the bottom of the diagram.
I notice that white blocks appear only in alternate columns.
I notice that red blocks appear along diagonals.
I notice that all of the orange blocks are in the rightmost column.

I wonder if colors always appear at predictable intervals.
I wonder if this picture is part of a larger pattern.
I wonder if this picture has anything to do with numbers.
I wonder if I can predict any of the colors that belong in squares to the left, right, above, or below the picture.
I wonder if every square will always have a different block picture when I extend the pattern.
I wonder if there is anything important about the squares that have only one block.

The picture contains just a little slice of the puzzle—part of the problem and part of the answer—so it may be a little misleading. In case you want to give it a try yourself, the picture that students actually begin with is here. Keep noticing and wondering... and have fun! Please see the "Building Blocks" activity on the Factors and Multiples page under the ACCME books menu for more information.