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.
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.
6.NS.3: Compare and order rational numbers and plot them on a number line. Write, interpret, and explain statements of order for rational numbers in real-world contexts.
6.AF.8: Solve real-world and other mathematical problems by graphing points with rational number coordinates on a coordinate plane. Include the use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
I can...
Find the lengths of horizontal and vertical line segments with rational number coordinates as endpoints in the coordinate plane by counting the number of units between endpoints and by using absolute value.
Lesson at a Glance
In this digital lesson, students use an interactive to move line segments of fixed length around the coordinate plane. Then students notice patterns between the coordinates of the endpoints and the length of the line segment. Students use these patterns to develop strategies to find the length of a line segment between two points. They examine line segments where both endpoints are in the same quadrant and line segments where endpoints are in different quadrants. At the end of the lesson, students apply their strategies to use the coordinates of two points that lie on a horizontal or vertical line segment to determine the distance between the points and find a path through an interactive maze.
Use the digital platform to prepare for and facilitate this lesson. Students will also interact with the lesson content and activities via the digital platform.
If student computers or devices are not available, use the alternate version of this lesson.
I can...
Graph geometric figures in all four quadrants of the coordinate plane.
Use distance and symmetry to solve geometric problems in the coordinate plane.
Lesson at a Glance
This lesson begins with students using their knowledge of reflections and distance in the coordinate plane to complete a drawing of a letter from the alphabet. Students identify the symmetry of line segments and explain how one point can be the endpoint of four different horizontal or vertical line segments with the same length. Students observe patterns before generalizing about the similarities and differences of the x- and y-coordinates of the points that lie on horizontal and vertical line segments. In pairs, students apply their understanding of distance, symmetry, and reflections to solve problems involving perimeter and area of rectangles in the coordinate plane.
I can...
Solve geometric and real-world problems by using the coordinate plane.
Lesson at a Glance
Throughout this lesson, students work collaboratively in small groups to complete tasks involving the coordinate plane. Students begin the lesson by using a map of Portland, Oregon, to determine the distance a person walks. Students discuss how street maps can be both similar to and different from the coordinate plane. Then students create a figure in the coordinate plane given a set of clues about symmetries and distances. Next, students use a set of criteria to design a town. Through gallery walks, students compare their peers’ figures and towns with their own. To complete the lesson, students compare the latitude and longitude grid system to the coordinate plane.