Acc7.6 Functions and Volume

In this unit, students are introduced to the concept of a function. They learn to understand and use the terms “input,” “output,” and “function”—for example, “temperature is a function of time.” They describe functions as increasing or decreasing between specific numerical inputs, and they consider the inputs of a function to be values of its independent variable and its outputs to be values of its dependent variable. (The terms “independent variable” and “dependent variable” were introduced in grade 6.) They use tables, equations, and graphs to represent functions, and describe information presented in tables, equations, or graphs in terms of functions. In working with linear functions, students coordinate and synthesize their understanding of “constant of proportionality” (which was introduced in an earlier course), “rate of change” and “slope” (which were introduced earlier in this course), and increasing and decreasing. Students then turn to focus on features of 3 dimensional shapes and consider volume formulas as examples of functions. They analyze and describe cross-sections of prisms, pyramids, and polyhedra. They understand and use the formula for the volume of a right rectangular prism, and solve problems involving area, surface area, and volume. Students perceive similarities in structure between pairs of volume formulas: for a rectangular prism and a cylinder; and for a cylinder and a cone. Students rearrange these formulas to show functional relationships and use them to reason about how the volume of a figure changes as another measurement changes—for example, the height of a cylinder is proportional to its volume; if the radius of a cylinder triples, its volume becomes nine times larger.