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| The 20 Attribute Pieces on the covers of the sixth editions of Mathematics for Elementary Teachers: A Conceptual Approach and Mathematics for Elementary Teachers: An Activity Approach are from a set of 24 pieces that differ in size (small, large), color (red, blue, yellow), and shape (square, triangle, circle, hexagon). Each pair of adjacent pieces on the covers differ from each other by two of these three attributes.
Counting from the top of the cover, the thirteenth attribute piece is a small red triangle that only differs from the preceding piece, a small yellow triangle, by the attribute of color. If the small red triangle is replaced by any one of the following attribute pieces, the pattern of two-differences will be consistent: large yellow circle, large yellow square, large yellow hexagon, small blue hexagon, small blue square, or small blue circle.
Counting from the bottom of the cover, the ninth attribute piece is a small yellow triangle that only differs from the preceding piece, a small red triangle, by the attribute of color. If the small yellow triangle is replaced by any one of the following attribute pieces, the pattern of two-differences will be consistent: large blue triangle, large red hexagon, small yellow circle, or small yellow square.
If the Attribute Pieces are identified by three letters designating size, color, and shape, the 20 pieces on the cover from top to bottom are as follows:
SYC, SRT, SBS, SYT, SRC, SYH, SBT, LYT, LRC, LBS, SBH, SYT, SRT, LBT, SBC, SRH, LYH, LBC, LYS, LRH
When Attribute Pieces are placed in a row they are sometimes called a train. The pieces on the cover form a two-difference train because adjacent pieces differ by exactly two attributes of the three attributes of size, color, and shape.
Problem A: How can the Attribute Pieces shown on the cover be rearranged to form a
one-difference train with 20 pieces?
Problem B: Is it possible to use the 20 Attribute Pieces from the cover to form a
three-difference train?
The answers to Problems A and B are below. Problem A: One possible answer. SRT, SYT, SYH, LYH, LYS, LYT, SYT, SYC, SRC, SRT, SBT, LBT, LBS, LBC, SBC, SBS, SBH, SRH, LRH, LRC Problem B: In order to have a three-difference train, all adjacent pairs of pieces would have to differ by size. Since the cover shows 12 small pieces and only 8 large pieces, a three-difference train with these pieces is not possible. |