Expressions Using Letters

The starting point is expressing a relationship between quantities with the unknown written as x. Total Weight, Distance and Time (Line Diagram), Perimeter of an Equilateral Triangle and Perimeter of a Square are put into expressions, and the areas of squares, rectangles, triangles, trapezoids, rhombuses and parallelograms are written with letters too.

Leaving the divide-by-2 out of an area expression for a triangle or a trapezoid stands out. If substituting a number for x gives twice the correct value, this is the pattern. With perimeters, the number of sides gets attached to the wrong figure, as in writing x × 4 for an equilateral triangle.

With Symmetric Figures now behind it, the subject turns to the connection between quantities such as distance and weight, captured in general terms with a symbol. The seed of using a letter, x, standing outside both numbers and figures, is planted in this unit and grows in earnest from junior high school onward.