They use letters for numbers in formulas involving geometric shapes and in ratios to represent an unknown part of an expression. They solve one-step linear equations. Students understand and use factoring of numerators and denominators and properties of exponents. They know the Pythagorean theorem and solve problems in which they compute the length of an unknown side. Students know how to compute the surface area and volume of basic three-dimensional objects and understand how area and volume change with a change in scale.
Students make conversions between different units of measurement.
They increase their facility with ratio and proportion, compute percents of increase and decrease, and compute simple and compound interest. They graph linear functions and understand the idea of slope and its relation to ratio. The problems for kindergarten through grade seven are organized by grade level and according to the standards for the five strands in the Mathematics Content Standards. The problems for grades eight through twelve are presented according to the standards for the discipline headings algebra, geometry, and so forth. Teachers may use these problems as a resource to develop students skills in working with the standards.