Introduction
Understanding Positive and Negative Numbers is an important Grade 6 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with understanding positive and negative numbers.
What Is Understanding Positive and Negative Numbers?
Understanding Positive and Negative Numbers means using place value, operations, and equations to reason accurately with numbers.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Understanding Positive and Negative Numbers
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: Which number line correctly shows the position of \(-5\)? What is the correct location of \(-5\) on the number line above?
- A. Between \(-6\) and \(-4\), closer to \(-4\)
- B. At the fifth tick mark to the right of zero
- C. At the fifth tick mark to the left of zero
- D. Exactly at zero
Why it works: On a number line, negative numbers are to the left of zero. \(-5\) is located five units to the left of zero.
Answer: At the fifth tick mark to the left of zero
Visual Model 2
Question: A company's quarterly profit or loss can be shown in a table. If profit is positive and loss is negative, which quarter shows a loss?
| Quarter | Profit/Loss (\textdollar) |
|---|---|
| Q1 | \(+2000\) |
| Q2 | \(-500\) |
| Q3 | \(+1500\) |
| Q4 | \(+3000\) |
- A. Q1
- B. Q4
- C. Q3
- D. Q2
Why it works: A negative value represents a loss. In the table, Q2 has \(-500\), which is the only negative value and thus represents a loss.
Answer: Q2
Worked Examples
Example 1
Question: Which number line correctly shows three points: \(-3\), \(0\), and \(2\)? Based on the number line, which statement is true?
- A. \(-3 > 2\)
- B. \(0 < -3\)
- C. \(-3 < 0 < 2\)
- D. \(2 < 0\)
- Reading the number line from left to right shows the order: \(-3\) is the smallest, then \(0\), then \(2\) is the largest.
- So \(-3 < 0 < 2\).
Answer: \(-3 < 0 < 2\)
Example 2
Question: On a number line, which two integers are exactly \(8\) units apart?
- A. \(-4\) and \(0\)
- B. \(-2\) and \(2\)
- C. \(0\) and \(4\)
- D. \(-4\) and \(4\)
- The distance between \(-4\) and \(4\) is \(4 - (-4) = 4 + 4 = 8\) units.
- These two numbers are \(8\) units apart on a number line.
Answer: \(-4\) and \(4\)
Example 3
Question: A thermometer shows the temperature is 3°C. Which temperature is 7°C colder?
- A. 10°C
- B. -2°C
- C. 0°C
- D. -4°C
- 7°C colder means we subtract \(7\) from the starting temperature: \(3 - 7 = -4°\)C.
Answer: -4°C
Real-World Word Problems
Problem 1
Question: A mountain peak is at an elevation of \(3500\) feet above sea level. A valley floor is at an elevation of \(-800\) feet. What is the difference in elevation?
- A. \(2700\) feet
- B. \(4300\) feet
- C. \(3500\) feet
- D. \(800\) feet
Why it works: The difference in elevation is found by subtracting: \(3500 - (-800) = 3500 + 800 = 4300\) feet.
Answer: \(4300\) feet
Problem 2
Question: A city's elevation is \(150\) feet. A nearby underground parking garage is at an elevation of \(-45\) feet. What is the total distance between them vertically?
- A. \(105\) feet
- B. \(150\) feet
- C. \(195\) feet
- D. \(45\) feet
Why it works: The vertical distance is the difference: \(150 - (-45) = 150 + 45 = 195\) feet.
Answer: \(195\) feet
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
Which situation is best represented by the integer \(-8\)?
- A. A temperature rise of 8°F
- B. A bank deposit of \($8\)
- C. A debt of \($8\)
- D. An elevation \(8\) feet above sea level
Question 2
A thermometer shows the temperature is -12°C. Which sentence best describes this situation?
- A. The temperature is 12°C above zero
- B. The temperature is exactly zero
- C. The temperature rose by 12°C
- D. The temperature is 12°C below zero
Question 3
A scuba diver descends \(25\) meters below sea level. Which integer represents this situation?
- A. \(25\)
- B. \(-25\)
- C. \(-50\)
- D. \(50\)
Question 4
The opposite of \(7\) is \(-7\). Which pair of integers are opposites?
- A. \(3\) and \(-3\)
- B. \(-5\) and \(-5\)
- C. \(2\) and \(-8\)
- D. \(0\) and \(1\)
Question 5
A football team loses \(15\) yards on a play. How should this be represented as an integer?
- A. \(15\)
- B. \(-15\)
- C. \(\frac{15}{2}\)
- D. \(0\)
Question 6
Which statement correctly compares the two integers \(-6\) and \(-3\)?
- A. \(-6 > -3\)
- B. \(-6 = -3\)
- C. \(-6 < -3\)
- D. \(-6\) and \(-3\) are opposites
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: A debt of \($8\)
Negative integers represent values less than zero. A debt of \($8\) means owing money, which is represented by \(-8\).
Question 2
Answer: The temperature is 12°C below zero
A negative number means the value is below zero. Since the temperature is -12°C, it is \(12\) degrees below zero.
Question 3
Answer: \(-25\)
Below sea level is represented by a negative integer. A depth of \(25\) meters below sea level is \(-25\) meters.
Question 4
Answer: \(3\) and \(-3\)
Opposites are two numbers that are the same distance from zero but on opposite sides of zero. \(3\) is \(3\) units right of zero, and \(-3\) is \(3\) units left of zero.
Question 5
Answer: \(-15\)
A loss is a negative change. Losing \(15\) yards means the team moved \(15\) yards backward, represented by the integer \(-15\).
Question 6
Answer: \(-6 < -3\)
On a number line, \(-6\) is to the left of \(-3\), so \(-6\) is less than \(-3\). The farther left a number is, the smaller it is.
Connection to Standards
This lesson supports Grade 6 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Understanding Positive and Negative Numbers becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
