Ordering Rational Numbers in Mathematical and Real-World Contexts(TEKS.Math.6.2.D)

Coldest means the lowest number. On a number line: -1.3 < -0.5 < 2.5 < 3, so Tuesday (coldest), then Wednesday, Monday, Thursday (warmest). A common mistake is to look at absolute values and think -0.5 is colder than -1.3 because 0.5 < 1.3, but real temperatures get colder as the value becomes more negative.

In golf, lower scores are better. Order the numbers from least to greatest: -3 < -2 < 0 < +1 gives Carlos (best), Alex, Dana, Bella (worst). A trap is to think 0 is automatically best or to compare absolute values; but performance aligns with the actual order on the number line, not closeness to zero.

Lowest balance means most negative. On a number line: -15.50 < -3.25 < 0 < 4.75, so Emma, then Mia, then Noah, then Jayden. A common error is to ignore the signs and order by the size of the digits, or to think 0 is lower than negatives. In real life, owing money (negative) is less than having no money or a positive balance.

Deeper means more negative. Order the values from least to greatest: -3 < -2 < -0.5 < +1/3, so Buoy A, Buoy B, Buoy C, Buoy D. A trap is confusing opposites and reciprocals: -2 and -1/2 are reciprocals, not opposites, and -1/2 is actually greater than -2 (so it is shallower).

Largest loss is the smallest (most negative) number; largest gain is the greatest (most positive). Order: -1.25 < -0.75 < +0.40 < +1.10, so W, Y, Z, X. Reversing the order or mixing a positive gain in between losses ignores how the number line models losses (negative) and gains (positive).