Consider a 9 × 9 chessboard, and you wish to cover as much of it as possible using figures shaped like the one to the right, where each of the four squares is the same size as the squares on a chessboard. The pieces can be rotated or flipped over. What is the maximum number of non-overlapping pieces that you can fit? Here are nine problems exploring coloring, or covering, grids and other shapes. This collection of problems can be used in a single problem solving session, or as individual teaser questions.

Geometry
Problem Solving / General

Problem Posing
Problem Sets
Try a Smaller Problem

MP1 - Make sense of problems and persevere in solving them.
MP4 - Model with mathematics.
MP7 - Look for and make use of structure.
MP8 - Look for and express regularity in repeated reasoning.