Comparing Numbers and Distance from Zero
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.
- 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 $a$.
Let’s use absolute value and negative numbers to think about elevation.
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.
- 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.
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