Let’s use absolute value and negative numbers to think about elevation.
$a$ is a rational number. Choose a value for $a$ and plot it on the number line.
A submarine is at an elevation of -100 feet (100 feet below sea level). Let’s compare the elevations of these four people to that of the submarine:
| possible elevation |
compare to submarine |
distance from sea level |
|
|---|---|---|---|
| Clare | 150 feet | $150 > \text-100$ | $|150|$ or 150 feet |
| Andre | |||
| Han | |||
| Lin |
Here are some numbers and inequality symbols. Work with your partner to write true comparison statements.
-0.7
$\text{-}\frac {6}{3}$
-4
$\text{-}\frac {3}{5}$
-2.5
0
1
2.5
$\frac72$
4
8
$|3|$
$|\text-8|$
$|0.7|$
$|\text{-}\frac {5}{2}|$
$<$
$=$
$>$
One partner should select two numbers and one comparison symbol and use them to write a true statement using symbols. The other partner should write a sentence in words with the same meaning, using the following phrases:
For example, one partner could write $4 < 8$ and the other would write, “4 is less than 8.” Switch roles until each partner has three true mathematical statements and three sentences written down.
For each question, choose a value for each variable to make the whole statement true. (When the word and is used in math, both parts have to be true for the whole statement to be true.) Can you do it if one variable is negative and one is positive? Can you do it if both values are negative?
We can use elevation to help us compare two rational numbers or two absolute values.
We can use similar descriptions to compare rational numbers and their absolute values outside of the context of elevation.
