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 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.
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.7: Understand that signs of numbers in ordered pairs indicate the quadrant containing the point. Identify rules or patterns in the signs as they relate to the quadrants. Graph points with rational number coordinates on a coordinate plane.
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...
Use ordered pairs to identify the locations of points in the coordinate plane.
Relate the signs of x- and y-coordinates to each of the four quadrants of the coordinate plane.
Lesson at a Glance
In this lesson, students first play a guessing game and must identify a classmate’s point from only a verbal description. By using their recent knowledge that all positive numbers have opposites, students extend the x-axis to the left of the origin and the y-axis below the origin to show the four quadrants of the coordinate plane. Students recognize the importance of the signs and the order of the coordinates of a point. They realize that the signs are useful for identifying the quadrant in which the point is located and that the order allows them to find the exact location of the point. Students revisit the game and recognize the usefulness of a coordinate plane in determining precise locations of points. This lesson introduces the term quadrant.
I can...
Use ordered pairs to plot points in the coordinate plane.
Lesson at a Glance
Using a given set of integers, students create ordered pairs of points in the four quadrants by reasoning about the signs of the coordinates. Students connect what they learned about plotting points on horizontal and vertical number lines to plotting points in the coordinate plane. Students plot points by using the x- and y-coordinates to determine how far to move to the right or left of the origin and then how far to move up or down from there. In pairs, students look for patterns in the coordinates of points that lie between quadrants on the x- or y-axis. When given a star map of the Ursa Major constellation, students identify and plot points with rational coordinates that represent the locations of stars in the constellation.
I can...
Graph points and their reflections in the coordinate plane.
Recognize that when two ordered pairs differ only by the sign of one or both coordinates, the locations of the points are related by reflections across one or both axes.
Lesson at a Glance
In this digital lesson, students use an interactive drawing tool to explore reflections across the x-axis and the y-axis in the coordinate plane. After an introduction to reflection, students observe patterns of reflections across the x-axis or the y-axis by using a point and its reflection to see that these points have coordinates that are opposites. Students use these patterns to plot reflections across one or both axes. Finally, students generalize what they know about reflections to reflect a point (a,b) across one or both axes that results in the following ordered pairs: (-a,b), (a,-b), or (-a,-b)
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...
Draw and label a coordinate plane, choosing a reasonable scale for a given set of points.
Plot points and describe how a graph changes when the scale changes.
Lesson at a Glance
In this lesson, students first consider which graphs have an appropriate scale for different real-world situations. Through a digital interactive, students see how points appear in the coordinate plane when the interval lengths for the x- and y-axes change. In groups, students plot points in coordinate planes with different scales for the axes. Given a graph of the same set of points with an interval length of 1 for both axes, they describe how their graphs compare when the interval length for one axis changes and when the interval lengths for both axes change. Students then choose scales for both the x- and y-axes, construct coordinate planes, and plot sets of points.
I can...
Create time graphs in the coordinate plane.
Solve real-world problems by using time graphs.
Lesson at a Glance
This lesson begins with students using a graph of college tuition data to answer questions about trends in college tuition. Then, students analyze a graph of oil prices from 2020, when the price of crude oil dropped below $0 per barrel. Students explain how a time graph can extend beyond the first quadrant and why time graphs have different shapes. To finish the lesson, students create a graph to model the descent of a vehicle to the bottom of the Mariana Trench and to estimate the time it will take the vehicle to reach the bottom. This lesson introduces the term summarize.