Various Word Problems

Word problems solved by spotting a rule are collected here. Patterns giving the color or the weekday at a given position, the growth of savings, work-rate problems with two people cooperating, problems about Cranes and Turtles, elimination problems that cancel one unknown across two expressions, and age problems each come with their own way of setting up an expression and drawing a diagram.

With patterns, the remainder after dividing by the cycle length gets misread, and a remainder of 0 is answered with the first color. In Cranes and Turtles, the difference produced by assuming everything is a crane is divided by the total count instead of by the difference in legs per animal. In age problems, children cannot make use of the fact that the gap between two ages never changes.

Comparing two people's motion at once, the organizing principle of Traveler Problems, is applied here across a much wider range of settings, from work-rate problems to age problems. Representing an unknown with a box, the method used in Various Word Problems in grade 5, widens into elimination, solving by weighing two expressions against each other. Reasoning that carries on into junior high school and beyond is folded into this unit as well.