List of Formulas Anglish Features Types of Story Problems Inveractive Anglish Programing Class III Cutting up Boards

Class II - Relational (More than) Problems

Many story problems are presented in relational form. For example, "Jane has \$5.00 more than Joe." is a statement of the amount of money Jane has in relation to Joe. These problems normally establish a base entity, the unknown, and express the value of the other entities in relation to it. Thus if the amount of money Joe has is unknown, or "u", then Jane has "u+5" dollars. Similarly, "Bill is 5 pounds lighter than Bob," is translated into "p" pounds for Bob and "p-5" pounds for Bill. Finally, "If Pearl has 6 times as many marbles as Paul" and "m" is the number of Paul's marbles, then Pearl has "6Xm" marbles. The story problems in this class use the natural language relational words to relate two or more activities, prices, sizes, numbers, dollars or any other entities.

Relational words may relate terms (things which are added/subtracted) or factors (things which are multiplied or divided). The general form of the relational equation

unknown X factor + term = entity
can be used to relate many different types of items. Not all problems have both a "times" factor and a term component, but the generalized form can be used for all problems if "1" is used as a default "times" factor when none is specified and "0" is used as the default "more than" term.

A table is constructed for problems using this formula by labeling the columns of the table with one of the different forms of the relational equation. A row entry is made for each entity in the problem. For example, the problem "Jane has \$5.00 more than Joe. If Joe has \$2.00, how many does Jane have?" identifies two people, Jane and Joe, so the table will have two entries. The "more than" phrase implies a term value of "5.00" for Jane. No factor component is given for Jane so a default factor of "1" is used. The base entity, Joe in this case, has default values for both the factor and term. In this very simple problem, the "unknown" of \$2.00 is told us. Thus the table is:

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|    |unknownXfactor+term=entity|
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|Jane|  2.00 |  1   |5.00|      |
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|Joe |  2.00 |  1   |  0 |      |
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Another example of relatonal equations are the Cutting up Boards problems like "A twelve foot board is cut such that one piece is three feet shorter than half the length of the other. Determine the length of each piece."
Class III problems combine rate and relational formulas.