# 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.