Students stack a given number of unit cubes in various ways and find the surface areas of the structures they have built. They sketch their figures and discuss which of the figures has the largest surface area and which has the smallest, and justify their conclusions. Students make models of cubes using blocks or other manipulatives, and investigate how the volume changes if the length, width, and height are all doubled. They discuss how various other changes to the data would affect the mean, the median, the mode, or the range. Understand and describe the general behavior of functions.
Students investigate graphs without numbers.
For example, they may study a graph that shows how far Olivia has walked on a trip from home to the store and back, where time isshown on the horizontal axis and the distance covered is on the vertical axis. Students tell a story about her trip, noting that where the graph is horizontal, she has stopped for some reason. They look at the data that has been collected in tabular form and as a graph on a coordinate grid. For those graphs that are straight lines, the students try to match the graph by entering and graphing a suitable equation. Use patterns, relationships, and linear functions to model situations in mathematics and in other areas.