This unique wood puzzle was developed by a long-time teacher of mathematics. The 12-inch square area is divided into four colorful regions. Each region represents the multiplication of (4 + 1) times (4 + 1). Helps children to explore several important mathematical ideas:
• Multiplication can always be pictured as a rectangle.
• Proportional reasoning: each rectangle is equivalent to four small squares.
Each large square is equal in area to four rectangles.
• Area concepts: (4 + 1) x (4 + 1) = 16 + 2 x 4 + 1.
• Base four numeration: The small square is 4^0; the rectangle is 4^1; and the big square is 4^2.
• Any value from 1 – 100 can be created by selecting the correct pieces.
• Builds place value understanding.
• Understanding place value helps students later understand polynomials.
The child does not need to articulate these ideas to benefit from playing with the 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.