Proportion

Reading across the six columns of a table to catch the fixed number tying x to y, and putting it into the form of an expression, is the first business of the lesson. Once the expression is settled, values not shown in the table can be produced as well. The other shape is a two-tier word problem that finds the amount for one first and reaches the amount wanted from there.

Filling in the fixed number, papers appear that look at a single column of the table and write in the difference of y minus x. Multiplying the filled figure by the x of that column and testing whether it returns to the y there is the way of checking, and an answer written as a difference comes out as another figure.

Only the case where the two change in the same direction is handled here. In Inverse Proportion the partner becomes a relation where one grows as the other shrinks, and the shape of the expression changes too.