Ordering from Least to Greatest

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

Find the most negative number: Compare $-2$ and $-6$: since $-6$ is further left on the number line = $-6$ 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: Compare $3$ and $4$: since $3 < 4$ = $3$, 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: Compare $5$ and $2$: since $5 > 2$ = $5$ 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 larger the digit, the smaller the value. $-9$ is further from zero in the negative direction.

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). 'A' for ascending comes before 'D' for descending in the alphabet, just like smaller numbers come before larger ones!

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: $-5, -1, 0, 3, 7$