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.
6.NS.1: Understand that positive and negative numbers are used to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge). Use positive and negative numbers to represent and compare quantities in real-world contexts, explaining the meaning of 0 in each situation.
6.NS.2: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself (e.g., –(–3) = 3), and that 0 is its own opposite.
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.
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Represent quantities in real-world situations by using positive and negative numbers.
Plot positive numbers, negative numbers, and 0 on horizontal and vertical number lines.
Lesson at a Glance
In this lesson, students analyze the Celsius temperature scale on thermometers. They use positive and negative numbers to represent the temperatures above and below 0°C and plot positive and negative numbers on vertical and horizontal number lines. Through teacher-led instruction and student-to-student dialogue, students recognize the meaning of 0 as a reference point in situations involving temperature and elevation. They find that positive and negative numbers are useful in describing temperatures above and below freezing and elevations above and below sea level. This lesson introduces the terms negative number and positive number.
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Plot integers and their opposites on horizontal and vertical number lines and identify zero as its own opposite.
Identify the opposite of the opposite of a number.
Lesson at a Glance
In this digital lesson, students use an interactive number line to explore distances between a given midpoint and two points. Students notice that when the midpoint is zero, pairs of numbers such as 4 and -4 are the same distance from zero. Then students explore more examples of opposites and plot points that represent the opposite of a given number on a number line. They use their knowledge of opposites to find the opposite of an opposite and the opposite of zero. This lesson introduces the terms opposites and integer.
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.
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Plot rational numbers on horizontal and vertical number lines.
Identify the locations of rational numbers plotted on horizontal and vertical number lines.
Lesson at a Glance
In this lesson, students first work in pairs to write a decimal, plot it on a class number line, and reason about the location of the opposite of their decimal. Using their knowledge of how to plot opposites of whole numbers on the number line, students plot the opposites of decimals in the same way. They improve their accuracy by marking equal interval lengths on the number line before plotting fractions and their opposites. Students identify rational numbers on both horizontal and vertical number lines. This lesson introduces the term rational number.
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Represent opposite quantities in real-world situations by using rational numbers.
Lesson at a Glance
In this lesson, students explore a situation from a historical context that shows the need to use both positive and negative numbers to represent quantities. Students discuss financial terms used to describe opposite quantities in the real world. Students apply their understanding of rational numbers and reference points to contexts about cardinal directions. Students are then paired through an activity where they match situations that describe opposite quantities represented by positive and negative numbers. After the activity, the pairs write a story about opposite quantities, plot points to represent them on a number line, and create a poster to display.