Teacher Guide: Ordering Integers
Learn how to arrange integers from least to greatest and greatest to least.
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Class quiz
10 questions on Negative Numbers. Students join with a name, you see everyone's score.
For Teachers
- 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
- • Understanding of positive and negative numbers
- • Ability to compare two integers using inequality symbols
- • Familiarity with the number line
- 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?
Larger digits mean larger negative numbers (thinking )
Mixing up ascending and descending order
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 (, , etc.)
- • Include decimal and fractional integers
- • Create their own real-world ordering problems
- 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
- 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.
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Definition
- Ascending order (least to greatest): Start with the smallest and go up
- Descending order (greatest to least): Start with the largest and go down
Worked Examples
Order these integers from least to greatest: , , , ,
Find the most negative number
Compare and : since is further left on the number line → is the smallest
Find the next negative number
is the only other negative number → comes second
Place zero
Zero is between negative and positive numbers → comes third
Order the positive numbers
Compare and : since → , then
Answer:
Common Mistakes
Ordering , , as (thinking larger digit means larger number)
Why it's wrong: With negative numbers, the larger the digit, the smaller the value. is further from zero in the negative direction.
Correct: Ascending order: (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
- 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
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 , Tue , Wed , Thu , Fri . Ordered coldest to warmest:
A weather report shows these temperatures for five mountain peaks: Peak A: , Peak B: , Peak C: , Peak D: , Peak E:
Order the peaks from coldest to warmest.
Step 1: Write the mathematical expression
Write 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 , Ben , Cara , Dan , Eve . Best to worst:
Five golfers finished with these scores: Player A: , Player B: , Player C: , Player D: , Player E:
Order the players from best (lowest) to worst (highest) score.
Step 1: Write the mathematical expression
Write 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
- 4Negative numbers with larger digits are SMALLER (further from zero)
- 5Zero always falls between negative and positive numbers
Frequently Asked Questions
How do I remember which way is ascending vs descending?
Why is greater than ?
Where does zero go when ordering?
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