This high-quality, wood puzzle was developed by a long-time teacher of mathematics as tool to encourage exploration of geometry. The 12-inch square is divided 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:
• Fraction equivalents
• Fraction multiplication with a common factor of ½
• Proportional reasoning
• Powers of two
• The limit of the sum of a sequence as the number of pieces goes to infinity
The child does not need to articulate these ideas to benefit from play 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.