# 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 $$|\text-18| > 4$$. 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 $\text-a$ 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 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.

### 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.