Lesson 7
Comparing Numbers and Distance from Zero
Lesson Narrative
In this lesson, students use precise language to distinguish between order and absolute value of rational numbers (MP6). It is a common mistake for students to mix up “greater” or “less” with absolute value. A confused student might say that 18 is greater than 4 because they see 18 as being the “bigger” number. What this student means to express is \(\text18 > 4\). The absolute value of 18 is greater than 4 because 18 is more than 4 units away from 0. In the “Submarine” activity, students visualize possible elevations of characters with sticky notes on a vertical number line. The freedom to move a sticky note within a specified range anticipates the concept of a solution to an inequality in the next section.
Learning Goals
Teacher Facing
 Critique comparisons (expressed using words or symbols) of rational numbers and their absolute values.
 Generate values that meet given conditions for their relative position and absolute value, and justify the comparisons (using words and symbols).
 Recognize that the value of $\texta$ can be positive or negative, depending on the value of $a$.
Student Facing
Let’s use absolute value and negative numbers to think about elevation.
Required Materials
Required Preparation
For every 4 students, create a set of 5 sticky notes that read Clare, Andre, Han, Lin, and Priya. These are for the launch of the “Submarine” activity.
Learning Targets
Student Facing
 I can explain what absolute value means in situations involving elevation.
 I can use absolute values to describe elevations.
 I can use inequalities to compare rational numbers and the absolute values of rational numbers.
CCSS Standards
Addressing
Glossary Entries

absolute value
The absolute value of a number is its distance from 0 on the number line.
The absolute value of 7 is 7, because it is 7 units away from 0. The absolute value of 5 is 5, because it is 5 units away from 0.

negative number
A negative number is a number that is less than zero. On a horizontal number line, negative numbers are usually shown to the left of 0.

opposite
Two numbers are opposites if they are the same distance from 0 and on different sides of the number line.
For example, 4 is the opposite of 4, and 4 is the opposite of 4. They are both the same distance from 0. One is negative, and the other is positive.

positive number
A positive number is a number that is greater than zero. On a horizontal number line, positive numbers are usually shown to the right of 0.

rational number
A rational number is a fraction or the opposite of a fraction.
For example, 8 and 8 are rational numbers because they can be written as \(\frac81\) and \(\text\frac81\).
Also, 0.75 and 0.75 are rational numbers because they can be written as \(\frac{75}{100}\) and \(\text\frac{75}{100}\).

sign
The sign of any number other than 0 is either positive or negative.
For example, the sign of 6 is positive. The sign of 6 is negative. Zero does not have a sign, because it is not positive or negative.