The Relationship Between Absolute Value and Order
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New York State Common Core Math Module 3, Grade 6, Lesson 12
Lesson 12 Student Outcomes
Students understand that the order of positive numbers is the same as the order of their absolute values.
Students understand that the order of negative numbers is the opposite order of their absolute values.
Students understand that negative numbers are always less than positive numbers.
Lesson 12 Opening Exercise
Record your integer values in order from least to greatest in the space below.
7, -12, 0, -5, -2, 5, -1, -9, 8, 2
Example 1: Comparing Order of Integers to the Order of their Absolute Values
Write an inequality statement relating the ordered integers from the Opening Exercise. Below each integer write its absolute value.
Are the absolute values of your integers in order? Explain.
Circle the absolute values that are in increasing numerical order and their corresponding integers, and then describe the circled values.
Rewrite the integers that are not circled in the space below. How do these integers differ from the ones you circled?
Rewrite the negative integers in ascending order and their absolute values in ascending order below them.
Describe how the order of the absolute values compares to the order of the negative integers.
Example 2: The Order of Negative Integers and their Absolute Values
Draw arrows starting at the dashed line (zero) to represent each of the integers shown on the number line below. The arrows that correspond with and have been modeled for you.
As you approach zero from the left on the number line, the integers increase, but the absolute values of those integers decrease. This means that the order of negative integers is opposite the order of their absolute values.
Exercise 1
Complete the steps below to order the numbers.
a. Separate the set of numbers into positive and negative values and zero in the top cells below.
b. Write the absolute values of the rational numbers (order does not matter) in the bottom cells below.
c. Order each subset of absolute values.
d. Order each subset of rational numbers.
e. Order the whole given set of rational numbers.
Lesson 12 Summary
The absolute values of positive numbers will always have the same order as the positive numbers themselves. Negative numbers, however, have exactly the opposite order as their absolute values. The absolute values of numbers on the number line increase as you move away from zero in either direction.
Lesson 12 Problem Set
- Micah and Joel each have a set of five rational numbers. Although their sets are not the same, their sets of numbers have absolute values that are the same. Show an the sets in order and the absolute values in order.
- For each pair of rational numbers below, place each number in the Venn diagram based on how it compares to the other
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