A fifth-grade class was given a problem involving hexominos as an individual problem-solving assessment. The class had investigated hexominos earlier in the year and had worked all year to improve their writing about mathematics. The teacher wanted to see what connections students could independently make to prior learning, to other problems and situations, among the Process Standards, and across mathematical strands. Some students made surprisingly sophisticated observations. This is the Sorting Hexominos problem they were given:

While sorting their complete set of hexominos, a group of students made categories according to the longest straight line of squares in a hexomino. For example, they called this first shape a "3-line," while the second shape is a "6-line": How many different hexominos are in the "4-line" category? Explain how you are sure. Think of other similar problems or experiences to help you solve the problem.

Before you look at how the students approached this problem, you may want to explore it yourself. You may use grid paper to sketch hexominos, or use six squares that you can rearrange. Think about how you would explain that you are sure that you have found all possible 4-line hexominos.

  Consider examples of student work