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Teacher Guide: Ordering Integers

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

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Printable worksheet

All practice problems on paper, with a separate answer key.

Worksheet Answer key

Class quiz

10 questions on Negative Numbers. Students join with a name, you see everyone's score.

For Teachers

Learning Objectives
  • Define ascending and descending order
  • Order a set of integers from least to greatest
  • Order a set of integers from greatest to least
  • Apply integer ordering to real-world contexts like temperature and elevation
Prerequisites
  • • Understanding of positive and negative numbers
  • • Ability to compare two integers using inequality symbols
  • • Familiarity with the number line
Discussion Starters
  • 1. If you had to explain ascending order to a younger sibling, what would you say?
  • 2. Why do you think golfers prefer negative scores? How does this relate to ordering?
  • 3. Can you think of a situation where you would need to order numbers from greatest to least?
  • 4. What strategy do you use to quickly find the smallest integer in a set?
Common Misconceptions

Larger digits mean larger negative numbers (thinking −15>−3-15 > -3)

Remediation: Use temperature: 'Is −15°C-15°C or −3°C-3°C warmer?' Show on number line that −3-3 is to the right of −15-15, so −3>−15-3 > -15.

Mixing up ascending and descending order

Remediation: Create a mnemonic: 'Ascending = Adding up' (going higher), 'Descending = Down' (going lower). Practice with stairs visual.

Differentiation Ideas

For Struggling Students:

  • • Start with only positive integers, then add one negative at a time
  • • Provide a physical number line for reference
  • • Use temperature contexts exclusively (most relatable)

For On-Level Students:

  • • Order sets of 5-7 integers including negatives
  • • Work with both ascending and descending order
  • • Apply to word problems with context

For Advanced Students:

  • • Order integers with larger values (−100-100, −250-250, etc.)
  • • Extend to ordering negative decimals and fractions (rational numbers)
  • • Create their own real-world ordering problems
Standards Alignment
  • 6.NS.C.7 (CCSS.MATH.CONTENT.6.NS.C.7)

    Understand ordering and absolute value of rational numbers

  • 6.NS.C.7a (CCSS.MATH.CONTENT.6.NS.C.7.A)

    Interpret statements of inequality as statements about the relative position of two numbers on a number line

Lesson Resources
  • visualInteractive Number Line

    Students drag numbers to correct positions on the number line

  • activityTemperature Ranking Game

    Order cities by temperature from coldest to warmest

  • worksheetInteger Sorting Practice

    Practice ordering sets of integers in both directions

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

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

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.

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

How do I remember which way is ascending vs descending?

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.

Why is −2-2 greater than −10-10?

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.

Where does zero go when ordering?

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

More in This Topic

Introduction to Negative Numbers

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Adding and Subtracting Integers

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Comparing Integers

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Multiplying and Dividing Integers

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