Teacher Guide: Comparing Integers
Learn how to compare positive and negative numbers using inequality symbols and the number line.
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Class quiz
10 questions on Negative Numbers. Students join with a name, you see everyone's score.
For Teachers
- Compare two integers using , , and symbols correctly
- Use a number line to determine which integer is greater or smaller
- Order a set of integers from least to greatest and greatest to least
- Apply integer comparison to real-world contexts like temperature and elevation
- • Understanding of positive and negative numbers
- • Ability to locate integers on a number line
- • Familiarity with the concept of zero as neither positive nor negative
- 1. Why is greater than ? How can something that looks smaller be greater?
- 2. If you owe someone 50 dollars and your friend owes 20 dollars, who is in a better financial situation? How does this relate to comparing negative numbers?
- 3. Can you think of a situation where having a 'more negative' number is actually better? (Hint: think about golf scores)
- 4. Why do you think mathematicians chose to put negative numbers to the left of zero on the number line?
Larger digits mean larger numbers, even for negatives (thinking )
Zero is the smallest number
Mixing up and symbols
For Struggling Students:
- • Provide a physical number line manipulative that students can touch
- • Use only single-digit integers initially ( to )
- • Connect every comparison to temperature: 'Which is colder?'
- • Allow students to draw the number line for every problem
For On-Level Students:
- • Compare two-digit integers including numbers like and
- • Order sets of 4-6 integers from least to greatest
- • Solve word problems involving temperature and elevation comparisons
- • Use both and to write the same comparison two ways
For Advanced Students:
- • Compare integers with absolute values: 'Which is further from zero?'
- • Create their own real-world comparison problems
- • Explore comparing negative fractions and decimals
- • Investigate the density property: finding integers between two others
- 6.NS.C.7 (CCSS.MATH.CONTENT.6.NS.C.7)
Understand ordering and absolute value of rational numbers
- 6.NS.C.7.A (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 diagram
- 6.NS.C.7.B (CCSS.MATH.CONTENT.6.NS.C.7.B)
Write, interpret, and explain statements of order for rational numbers in real-world contexts
- visualInteractive Number Line
Students drag and compare integers on a dynamic number line
- activityTemperature Sorting Game
Order cities by temperature from coldest to warmest
- worksheetInequality Practice
Fill in , , or between integer pairs
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
- means greater than (the number on the left is larger)
- means less than (the number on the left is smaller)
- means equal to (both numbers have the same value)
Worked Examples
Compare and . Which is greater?
Visualize on the number line
Place both numbers: is at position , is at position → is further right
Apply the rule
Numbers further right are greater →
Verify with real-world context
is warmer than , so is greater → Confirmed:
Answer: (negative four is greater than negative nine)
Common Mistakes
Thinking because
Why it's wrong: With negative numbers, the absolute value (digit size) works opposite! is further from zero in the negative direction, so it's actually smaller.
Correct: because is closer to zero (further right on the number line).
Confusing and symbols
Why it's wrong: It's easy to mix up which symbol points which way.
Correct: The symbol always 'eats' the bigger number. Think of it as a hungry alligator that always wants the larger meal: and .
Forgetting that zero is greater than all negatives
Why it's wrong: Zero might seem like 'nothing,' but it's actually greater than every negative number.
Correct: . Zero is the boundary between positive and negative.
Why It Matters
- Weather forecasting: Is colder than ? Yes, because
- Elevation: Which is lower: meters (below sea level) or meters?
- Finance: A balance of euros is worse than euros because
- Sports: In golf, (5 under par) is better than (2 under par) because lower is better
Real World Applications
Temperature Comparison
Weather forecasters compare temperatures to determine which days are colder or warmer.
Example:
Moscow recorded and Helsinki recorded . Since , Helsinki was warmer.
Three cities have the following temperatures: City A: , City B: , City C:
Order the cities from coldest to warmest.
Step 1: Write the mathematical expression
Compare: , ,
Elevation Comparison
Geographers use negative numbers for elevations below sea level.
Example:
The Dead Sea is at meters and Death Valley is at meters. Since , the Dead Sea is lower.
A submarine is at meters. A diver is at meters. The ocean floor is at meters.
Order these from deepest to shallowest.
Step 1: Write the mathematical expression
Compare: , ,
Bank Balance Comparison
Banks show negative balances when you owe money (overdraft).
Example:
Account A shows euros. Account B shows euros. Since , Account B is in better standing (owes less).
Three friends check their accounts: Alex has euros, Ben has euros, Carla has euros.
Who has the most money? Who owes the most?
Step 1: Write the mathematical expression
Order: , ,
Key Takeaways
- 1Use (less than) and (greater than) to compare integers
- 2On the number line: RIGHT = GREATER, LEFT = SMALLER
- 3Any positive number is greater than any negative number
- 4Zero is greater than all negative numbers but less than all positive numbers
- 5For negative numbers: closer to zero means greater ()
Frequently Asked Questions
Why is greater than ?
Is zero positive or negative?
How do I remember which way and point?
Why do we say is less than ?
Glossary
- Integer
- A whole number that can be positive, negative, or zero (e.g., , , )
- Greater than ()
- A symbol meaning the number on the left is larger than the number on the right
- Less than ()
- A symbol meaning the number on the left is smaller than the number on the right
- Inequality
- A mathematical statement that compares two values using , , , or
- Number line
- A visual representation of numbers arranged from least to greatest, left to right