By the end of seventh grade students are adept at manipulating numbers and equations and understand the general principles at work. They understand and use factoring of numerators and denominators and properties of exponents. They know the Pythagorean Theorem and solve problems where they compute the length of an unknown side. Students know how to compute the surface area and volume of basic 3-D objects and understand how they change under a change in scale.
Students convert between different units of measurement.
They increase their facility with ratio and proportion and compute percentages of increase, decrease, and simple compound interest. They graph linear functions and understand the idea of slope and its relation to ratio. Multiply and divide expressions involving exponents with a common base. Simplify and evaluate expressions that include exponents. Fit a line to the plot and understand that the slope of the line equals the quantities.