This ten-inch by ten-inch square is cut into one-half, one-fourth, one-eighth, one-sixteenth, up to one one hundred twenty-eighth. These fractions describe the portion of the whole represented by each region.
The puzzle offers opportunities to explore several important mathematical ideas. Certainly the child does not need to articulate these ideas to benefit from interaction with this puzzle. Current research on enactment suggests that the exploration of concrete representations has the potential to accelerate and to deepen understanding of abstract ideas. The adults in the child’s life can ask the questions that are appropriate to the arrangements the child has created.