Ideas and representations progress in sophistication, but not depth, from one level to the next. Equivalencies are first noted in grade 6, where decimals are represented by their equivalents on a grid. By the end of grade 6, students are converting fractions to decimals to percents. Appropriate use of different forms is not addressed. By grade 8, there are only a few lessons that address equivalent forms of numbers other than references to equivalencies of fractions expressed as repeating decimals.
Shapes can match exactly or have the same shape in different sizes.
This benchmark receives minimal coverage throughout the material. A great deal of geometry instruction centers around measurement with little focus on the properties of shapes. In grade 6, the material deals with the properties and construction of quadrilaterals but draws no attention to distinguishing among the various figures. In grades 7 and 8, students encounter very similar lessons that examine properties of polygons including classification by shape. There is no reference to triangle rigidity or the boundary and area relation for circles.