Various Word Problems

An unknown in a situation is set as a box, written into an expression, and recovered by working backward. Both addition and subtraction and multiplication and division are covered, along with problems that find two quantities from a multiple and a difference or a multiple and a sum, and surplus-and-shortage problems that recover a number of people from what is left over and what falls short.

Solving □ + 7 = 20 as 20 + 7, reversing the direction of the inverse operation, is the standard error. With a multiple and a difference, children divide the difference by the multiplier rather than by the multiplier minus 1. In surplus-and-shortage problems, the surplus and the shortage get subtracted where they should be added.

The way of solving a multi-scene problem, built up in Various Word Problems in grade 4, is applied here to a new form for finding an unknown: an expression with a box, or a surplus-and-shortage problem. This feeds into Various Word Problems in grade 6, which uses elimination to find two unknown numbers at once.