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 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.
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.NS.4: Understand that the absolute value of a number is the distance from zero on a number line. Find the absolute value of real numbers and know that the distance between two numbers on the number line is the absolute value of their difference. Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
I can...
Write and interpret statements of comparison about rational numbers.
Compare rational numbers in real-world situations.
Lesson at a Glance
Lesson at a Glance
In this lesson, students play a whole-class game in which they reason about rational numbers to determine an unknown number. Students use number lines to compare rational numbers and represent the relationships between rational numbers with inequality symbols. Students describe the locations of points in relation to each other on horizontal and vertical number lines. Through a partner activity and class discussion, students determine that if a < b, then −a > −b. Students compare real-world quantities such as elevations and temperatures and choose a method for justifying their solutions.
I can...
Order rational numbers.
Write, interpret, and explain statements of order for rational numbers in real-world situations.
Lesson at a Glance
By examining a set of clues, students determine what information they need to order a set of rational numbers. Students interpret number lines in which the scale is not given. By using these number lines, students are challenged to order numbers represented by symbols. In pairs, students use clues to order small sets of rational numbers before transitioning to ordering a large set of rational numbers. Students order numbers in real-world situations when they compare elevations and temperatures. This lesson introduces the term visualize.
I can...
Determine the absolute values of rational numbers.
Lesson at a Glance
In this digital lesson, students play an interactive ring toss game where the goal is to land on zero on a number line. Students are asked what the rules should be for deciding a winner. To decide the winner, students need to find the rings’ distances from zero, or their absolute values. Students find absolute value by placing rings at different locations on the number line and then identifying the distance from zero. Students continue to use rings on an interactive number line to see patterns in the orders of numbers and their absolute values. Students then use their knowledge of opposites and absolute value to determine which statement among three is the lie and justify their choice with a counterexample. This lesson introduces the term absolute value.
Use the digital platform to prepare for and facilitate this lesson. Students 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...
Explain the relationship between the order of rational numbers and the order of their absolute values.
Order and compare the absolute values of rational numbers and the magnitudes of real-world quantities.
Lesson at a Glance
This lesson begins with students examining the locations of golf balls near a cup to analyze a situation in which only distance, and not direction, matters. Students use a set of cards to explore and then explain the relationship between the order of rational numbers and the order of their absolute values. Then students compare and order sets of numbers with absolute values. To summarize their understanding about absolute value and order, students choose from a set of conceptual questions to answer. In pairs, students use magnitude to compare elevations.
I can...
Distinguish between comparisons of absolute value and statements of order in real-world situations.
Determine and interpret distance between rational numbers.
Lesson at a Glance
Through participating in a round of Which One Doesn’t Belong? and watching a video about a fishing boat, students compare positive and negative elevations and distances from sea level. Students represent real-world situations involving temperature and elevation with number lines and then use the number lines to reason about absolute values and statements of order. In a class discussion, students explain how to use absolute value and magnitude to determine the distance between a positive number and a negative number.