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The following example shows that a unified approach to problem solving based on basic mathematical concepts is valuable across the curriculum. Implementing a unified approach to problem solving in early grades serves to lay the ground work for more efficient learning in all subjects which use mathematical methods in problem solving.

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The example shows again that the structure of the solution of the Mary's Apples puzzle is present in a large number of problem solutions. This results from the fact that the Mary's Apple structure reflects the underlying grammar of problem solving. It is then expected to be present in the solution of all problems. In complex problems it occurs recursively, often in nested structures.

The basic element of a problem solution is Request-Response-Result. This structure is shown below. It is from this that problem solutions are generated. The linear nature of problem solutions assures that recursive use of Request-Response-Result in the transformation process will lead from the initial premise to the answer to the specific question asked.

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The problem solution was developed using SureMath.
Copyright 1995 Howard C. McAllister
The problem was adapted from Algebra 2, John H. Saxon, Jr.
Saxon Publishers, Inc. p312