Teacher Guide: Introduction to Negative Numbers
Learn what negative numbers are, where they appear in real life, and how to place them on a 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
- Define negative numbers as values less than zero
- Locate and plot negative numbers on a number line
- Compare and order integers including negative numbers
- Identify real-world situations involving negative numbers
- Find the opposite of any integer
- • Understanding of counting numbers (1, 2, 3, ...)
- • Familiarity with number lines
- • Basic understanding of zero as a quantity
- 1. If you had to explain negative numbers to someone who had never heard of them, what would you say?
- 2. Can you think of situations where negative numbers would not make sense? (Hint: Can you have negative apples?)
- 3. Why do you think it took mathematicians so long to accept negative numbers as real numbers?
- 4. How would our world be different if negative numbers did not exist?
- 5. Where have you seen negative numbers in your daily life?
Larger digit means larger number (thinking )
Negative numbers work the same as positive numbers
Zero is a negative number
For Struggling Students:
- • Provide a physical number line students can touch and move along
- • Use two-color counters (red for negative, yellow for positive)
- • Focus only on single-digit negative numbers initially
- • Connect every example to temperature, which is intuitive
For On-Level Students:
- • Practice comparing negative numbers using number line visuals
- • Work with real-world contexts like elevation and bank balances
- • Introduce the concept of opposites
For Advanced Students:
- • Explore negative decimals and fractions
- • Research the history of negative numbers across cultures
- • Create word problems involving negative numbers for classmates
- 6.NS.C.5 (CCSS.MATH.CONTENT.6.NS.C.5)
Understand that positive and negative numbers describe quantities having opposite directions or values
- 6.NS.C.6 (CCSS.MATH.CONTENT.6.NS.C.6)
Understand a rational number as a point on the number line
- 6.NS.C.7 (CCSS.MATH.CONTENT.6.NS.C.7)
Understand ordering and absolute value of rational numbers
- visualInteractive Number Line
Drag and drop numbers onto the correct positions on a number line from to
- activityTemperature Investigation
Students research and compare winter temperatures in different cities around the world
- gameInteger Card Game
Students play a card game where the greater integer wins, including negative numbers
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
Worked Examples
A thermometer shows degrees Celsius. What does this mean?
Identify the sign
The minus sign () tells us this is a negative number → Negative
Understand the meaning
Negative temperature means below zero → is 8 degrees below zero
Answer: The temperature is 8 degrees below the freezing point (0°C). This is very cold - water would be frozen!
Common Mistakes
Thinking is greater than because 7 is bigger than 3
Why it's wrong: With negative numbers, the number closer to zero is actually greater. Think of temperature: is warmer (greater) than .
Correct: because is closer to zero and further right on the number line.
Forgetting that zero is neither positive nor negative
Why it's wrong: Zero is the dividing point between positive and negative numbers. It has no sign.
Correct: Zero is neutral - neither positive nor negative. It separates the two types of numbers.
Confusing the minus sign with subtraction
Why it's wrong: The minus sign in front of a number (like ) means negative, not subtract. Context matters!
Correct: In , the minus means negative five. In , the minus means subtract.
Placing negative numbers to the right of zero on a number line
Why it's wrong: Negative numbers are less than zero, so they belong on the left side of the number line.
Correct: Negative numbers go LEFT of zero, positive numbers go RIGHT of zero.
Why It Matters
Real World Applications
Weather and Temperature
Meteorologists use negative numbers every day when reporting temperatures, especially in winter months. Understanding negative temperatures helps us prepare for cold weather and stay safe.
Example:
If today's high is and tonight's low will be , the temperature will drop degrees.
The weather forecast says the morning temperature is and it will rise by 10 degrees by afternoon.
What will the afternoon temperature be?
Step 1: Write the mathematical expression
Start at and add 10 degrees:
Bank Accounts and Debt
Banks use negative numbers to show when you owe money (debt). A negative balance means you have spent more than you had and need to deposit money to get back to zero or positive.
Example:
If your account shows euros, you owe the bank 25 euros. You need to deposit at least 25 euros to have a balance of zero.
Your bank account balance is euros. You deposit 50 euros.
What is your new balance?
Step 1: Write the mathematical expression
Start with your debt and add the deposit:
Elevation and Geography
Geographers measure elevation relative to sea level, which is defined as zero. Mountains have positive elevations, while valleys and underwater locations have negative elevations.
Example:
Mount Everest is about meters above sea level. The Mariana Trench is about meters (below sea level).
A submarine is at meters (200 meters below sea level). It rises 75 meters.
What is the submarine's new depth?
Step 1: Write the mathematical expression
Start at current depth and add the rise:
Key Takeaways
- 1Negative numbers are less than zero and written with a minus sign (e.g., )
- 2On a number line, negative numbers are to the LEFT of zero
- 3Zero is neither positive nor negative - it separates them
- 4The further left on the number line, the smaller the number
- 5Comparing negatives: because is closer to zero
- 6Every number has an opposite: the opposite of is
- 7Integers include all positive numbers, negative numbers, and zero
Frequently Asked Questions
What is the difference between a negative number and subtraction?
Why is greater than ?
Is zero a positive or negative number?
Where do negative numbers come from? Who invented them?
What are integers?
Glossary
- Negative number
- A number less than zero, written with a minus sign in front (e.g., , )
- Positive number
- A number greater than zero (e.g., , )
- Integer
- Any whole number, including positive numbers, negative numbers, and zero
- Number line
- A line showing numbers in order, with negative numbers on the left, zero in the middle, and positive numbers on the right
- Opposite
- Two numbers that are the same distance from zero but on different sides. The opposite of is
- Zero
- The number that separates positive from negative; neither positive nor negative
- Absolute value
- The distance a number is from zero, always positive. The absolute value of both and is