Ordering Integers

Learn how to arrange integers from least to greatest and greatest to least.

Elementary20 minLesson
Printable worksheet

Definition

Ordering integers means arranging a set of positive and negative numbers in a specific sequence.
There are two ways to order integers:
  • Ascending order (least to greatest): Start with the smallest and go up
  • Descending order (greatest to least): Start with the largest and go down
Using the Number Line:
Left→Right=Ascending (least to greatest)\text{Left} \rightarrow \text{Right} = \text{Ascending (least to greatest)}
Right→Left=Descending (greatest to least)\text{Right} \rightarrow \text{Left} = \text{Descending (greatest to least)}
For example, ordering −3-3, 55, −7-7, 22 in ascending order:
−7,−3,2,5-7, -3, 2, 5

Try it now

Which list shows the integers in ascending order (least to greatest)?

Worked Examples

Order these integers from least to greatest: 44, −2-2, 00, −6-6, 33
1

Find the most negative number

−6-6 is further left on the number line than −2-2 → −6-6 is the smallest
2

Find the next negative number

−2-2 is the only other negative number → −2-2 comes second
3

Place zero

Zero is between negative and positive numbers → 00 comes third
4

Order the positive numbers

3<43 < 4, so 33 comes before 44 → 33, then 44

Common Mistakes

Ordering −3-3, −9-9, −1-1 as −1,−3,−9-1, -3, -9 (thinking larger digit means larger number)

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

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

Forgetting where to place zero

Why it's wrong: 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.

Confusing ascending and descending

Why it's wrong: 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.

Interactive Visual

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Practice Problems

16 problems
Problem 1 of 16
Easy
Which list shows the integers in ascending order (least to greatest)?

Why It Matters

Ordering integers is essential in many real-life situations:
  • Weather forecasting: Ranking temperatures from coldest to warmest days
  • Sports standings: Ordering golf scores (where negative is better!)
  • Elevations: Ranking locations from lowest to highest altitude
  • Finance: Sorting account balances or comparing debts
Being able to quickly arrange numbers in order helps you make sense of data and identify patterns!

Real World Applications

Weather and Climate

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

Example:

Weekly lows: Mon −5°C-5°C, Tue −2°C-2°C, Wed 3°C3°C, Thu −8°C-8°C, Fri 1°C1°C. Ordered coldest to warmest: −8°C,−5°C,−2°C,1°C,3°C-8°C, -5°C, -2°C, 1°C, 3°C

1Try It Yourself

A weather report shows these temperatures for five mountain peaks: Peak A: −15°C-15°C, Peak B: −3°C-3°C, Peak C: −22°C-22°C, Peak D: −8°C-8°C, Peak E: −1°C-1°C

Order the peaks from coldest to warmest.

Step 1: Choose the right answer

Choose the temperatures from smallest to largest:

Golf Scores

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

Example:

Player scores: Ali −4-4, Ben +2+2, Cara −1-1, Dan 00, Eve −3-3. Best to worst: −4,−3,−1,0,+2-4, -3, -1, 0, +2

2Try It Yourself

Five golfers finished with these scores: Player A: −7-7, Player B: +3+3, Player C: −2-2, Player D: +1+1, Player E: −5-5

Order the players from best (lowest) to worst (highest) score.

Step 1: Choose the right answer

Choose the scores in ascending order:

Key Takeaways

  • 1Ascending order means arranging from least to greatest (smallest first)
  • 2Descending order means arranging from greatest to least (largest first)
  • 3Use the number line: left to right is ascending, right to left is descending
  • 4The further a negative number is from zero, the SMALLER it is: −9<−3-9 < -3
  • 5Zero always falls between negative and positive numbers

Frequently Asked Questions

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.
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.
On the number line, −2-2 is closer to zero and further to the right than −10-10. Think of temperature: −2°C-2°C is warmer (greater) than −10°C-10°C.
Zero is neither positive nor negative. In ascending order, it comes after all negative numbers and before all positive numbers. Example: −5,−1,0,3,7-5, -1, 0, 3, 7

Glossary

Ascending order
Arranging numbers from smallest to largest (least to greatest)
Descending order
Arranging numbers from largest to smallest (greatest to least)
Integer
A whole number that can be positive, negative, or zero
Number line
A line showing numbers in order, with negatives on the left and positives on the right
Today's challengeOne problem, three tries

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Comparing Integers

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Multiplying and Dividing Integers

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