Ordering from Least to Greatest

Order these integers from least to greatest: $4$, $-2$, $0$, $-6$, $3$

Find the most negative number: $-6$ is further left on the number line than $-2$ = $-6$ is the smallest

Find the next negative number: $-2$ is the only other negative number = $-2$ comes second

Place zero: Zero is between negative and positive numbers = $0$ comes third

Order the positive numbers: $3 < 4$, so $3$ comes before $4$ = $3$, then $4$

Answer: $-6, -2, 0, 3, 4$

Ordering from Greatest to Least

Order these integers from greatest to least: $-1$, $-8$, $5$, $2$, $-4$

Find the largest positive number: $5 > 2$, so $5$ comes first = $5$ is the largest

Find the next positive number: $2$ is the remaining positive number = $2$ comes second

Order the negative numbers from greatest to least: Compare $-1$, $-4$, $-8$: closer to zero is greater = $-1 > -4 > -8$

Answer: $5, 2, -1, -4, -8$

Temperature Rankings

Five cities recorded these morning temperatures: Paris $-3°C$, Moscow $-12°C$, London $2°C$, Oslo $-7°C$, Madrid $8°C$. Order them from coldest to warmest.

Identify the coldest (most negative): Compare all negative temperatures: $-12 < -7 < -3$ = Moscow ($-12°C$) is coldest

Order remaining negatives: $-7°C$ (Oslo) comes next, then $-3°C$ (Paris) = Oslo, then Paris

Order positive temperatures: $2°C$ (London) then $8°C$ (Madrid) = London, then Madrid

Answer: Moscow ($-12°C$), Oslo ($-7°C$), Paris ($-3°C$), London ($2°C$), Madrid ($8°C$)

Mistake: Ordering $-3$, $-9$, $-1$ as $-1, -3, -9$ (thinking larger digit means larger number)

Why: With negative numbers, the further a number is from zero, the smaller it is. $-9$ is further from zero than $-3$ and $-1$, so it is the smallest.

Correct: Ascending order: $-9, -3, -1$ (furthest left to furthest right on the number line)

Mistake: Forgetting where to place zero

Why: Zero is the boundary between positive and negative numbers.

Correct: Zero always comes after all negative numbers and before all positive numbers in ascending order.

Mistake: Confusing ascending and descending

Why: The terms can be mixed up, especially when nervous.

Correct: Ascending = going UP (like climbing stairs): smallest to largest. Descending = going DOWN: largest to smallest.

Weather and Climate

Meteorologists order temperatures to find the coldest and warmest days of the week or to track temperature trends.

Weekly lows: Mon $-5°C$, Tue $-2°C$, Wed $3°C$, Thu $-8°C$, Fri $1°C$. Ordered coldest to warmest: $-8°C, -5°C, -2°C, 1°C, 3°C$

Golf Scores

In golf, scores below par are negative (good!) and above par are positive. Ordering scores shows the rankings.

Player scores: Ali $-4$, Ben $+2$, Cara $-1$, Dan $0$, Eve $-3$. Best to worst: $-4, -3, -1, 0, +2$

Q: How do I remember which way is ascending vs descending?

A: Think of stairs: ascending means climbing UP (numbers get bigger), descending means going DOWN (numbers get smaller). So ascending order starts with the smallest number and ends with the largest.

Q: Why is $-2$ greater than $-10$?

A: On the number line, $-2$ is closer to zero and further to the right than $-10$. Think of temperature: $-2°C$ is warmer (greater) than $-10°C$.

Q: Where does zero go when ordering?

A: Zero is neither positive nor negative. In ascending order, it comes after all negative numbers and before all positive numbers. Example: $-5, -1, 0, 3, 7$