In module 3, students develop an understanding of rational numbers and use rational numbers to describe real-world quantities. Students plot rational numbers and their opposites on a number line, calculate absolute values, order and compare rational numbers, and apply the concept of magnitude to describe and compare real-world quantities. Students explore the structure of the four quadrants of the coordinate plane. They plot and locate points with rational number coordinates, reflect points across one or both axes, calculate the lengths of lines segments, graph geometric figures, and use the coordinate plane to solve problems.
In topic A, students use positive and negative numbers and 0 to describe real-world quantities such as elevation and temperature. They plot whole numbers and opposites of whole numbers on horizontal and vertical number lines and discover that these numbers are called integers. Then students extend their understanding of integers to locate positive and negative rational numbers on the number line, and they represent opposite quantities in real-world situations by using rational numbers. They choose appropriate scales for a number line to plot a set of rational numbers.
Students apply their understanding of rational numbers on the number line to compare and order sets of rational numbers in topic B. They observe that a number and its opposite are the same distance from 0 and use this understanding to calculate absolute value. Students use rational numbers to describe and compare real-world quantities. They apply the concept of magnitude to describe the distance between two rational numbers.
In topic C, students apply their understanding of rational numbers to discover the four quadrants of the coordinate plane. Students plot and locate points with rational number coordinates in all four quadrants. Students explore the structure of the coordinate plane by reflecting points across one or both axes, noticing patterns in the coordinates of those points. They choose appropriate scales for the x- and y-axes for a given set of points. In a modeling task, students create a time graph by using real-world data about an underwater vehicle’s descent to the bottom of the Mariana Trench.
Students use all four quadrants of the coordinate plane to graph figures and solve problems in topic D. They calculate the lengths of horizontal and vertical line segments in the coordinate plane, both by counting units and by applying their understanding of absolute value. Students graph geometric figures and apply their understanding of distance and symmetry to solve problems such as finding unknown vertices of rectangles or calculating perimeter and area. Lastly, they encounter real-world problems related to the coordinate plane, such as street maps on a grid and the geographic coordinate system.