Introduction
Subtracting Integers is an important Grade 7 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 subtracting integers.
What Is Subtracting Integers?
Subtracting Integers 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 Subtracting Integers
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 subtraction problem is shown by the red arrow (moving right 4 units from \(-7\))?
- A. \(-7-(-4)\)
- B. \(-7-4\)
- C. \(-7+(-4)\)
- D. \(4-(-7)\)
Why it works: Moving right \(4\) units from \(-7\) means adding \(4\), which is the same as subtracting \(-4\): \(-7-(-4)=-7+4=-3\).
Answer: \(-7-(-4)=-3\)
Visual Model 2
Question: A scuba diver starts at \(-50\) meters (below sea level). She descends to \(125\) meters below sea level. What is the net change in her elevation (in meters)?
- A. \(175\) meters
- B. \(75\) meters
- C. \(-75\) meters
- D. \(-175\) meters
Why it works: The change is: final \(-\) initial \(= -125-(-50)=-125+50=-75\) meters. The negative sign indicates she descended 75 meters deeper.
Answer: \(-75\) meters
Worked Examples
Example 1
Question: A football team loses 8 yards on one play and then loses 5 more yards on the next play. Using subtraction with negative numbers, which expression represents the total change in position?
- A. \(0-8-5\)
- B. \(8+5\)
- C. \(0-8+5\)
- D. \(0+8-5\)
- Starting at position 0, losing 8 yards is \(0-8=-8\).
- Then losing 5 more is \(-8-5=-13\).
- This can be written as \(0-8-5=-13\).
Answer: \(-13\) yards
Example 2
Question: If \(a=2\) and \(b=8\), the distance formula \(|a-b|\) gives \(|2-8|=6\). What would the distance be if \(a=-4\) and \(b=5\)?
- A. \(-9\)
- B. \(1\)
- C. \(9\)
- D. \(-1\)
- Distance: \(|-4-5|=|-9|=9\).
- Distance is always positive (non-negative).
Answer: \(9\) units
Example 3
Question: According to the diagram, moving right 6 units from \(-2\) lands at \(4\). Which subtraction expression is this?
- A. \(-2-6\)
- B. \(-2-(-6)\)
- C. \(4-(-2)\)
- D. \(2+6\)
- Moving right (positive direction) from \(-2\) is the same as subtracting a negative. \(-2-(-6)=-2+6=4\).
Answer: \(-2-(-6)=4\)
Real-World Word Problems
Problem 1
Question: A student evaluates \(-4-(-6)\) and claims the answer is \(-10\). What is the student's mistake?
- A. Computing \(-4+6=2\) when the answer should be \(-10\)
- B. Adding the numbers instead of converting to addition: \(-4+(-6)=-10\)
- C. Adding instead of subtracting the opposite value
- D. Correctly applying the rule but making a computation error
Why it works: The error is choice B. The student forgot to flip the sign of \(-6\) to \(+6\). The correct process: \(-4-(-6)=-4+6=2\). The student mistakenly added \(-4+(-6)=-10\) instead.
Answer: \(-4-(-6)=2\)
Problem 2
Question: A scuba diver is at a depth of \(-45\) feet (below sea level). She ascends 15 feet. What is her new depth?
- A. \(-60\) feet
- B. \(-30\) feet
- C. \(30\) feet
- D. \(60\) feet
Why it works: Ascending (moving up) is the opposite of depth change. New depth: \(-45-(-15)=-45+15=-30\) feet.
Answer: \(-30\) 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
What is \(4-(-7)\)?
- A. \(-11\)
- B. \(-3\)
- C. \(3\)
- D. \(11\)
Question 2
Simplify: \(-5-3\)
- A. \(-8\)
- B. \(-2\)
- C. \(2\)
- D. \(8\)
Question 3
What is \(-2-(-6)\)?
- A. \(4\)
- B. \(-8\)
- C. \(-4\)
- D. \(8\)
Question 4
Evaluate: \(10-(-5)\)
- A. \(5\)
- B. \(-15\)
- C. \(-5\)
- D. \(15\)
Question 5
Which expression equals \(-3\)?
- A. \(5-(-2)\)
- B. \(-6-3\)
- C. \(-1-4\)
- D. \(2-5\)
Question 6
What is \(-8-(-2)\)?
- A. \(-10\) (if you add both numbers without flipping the sign)
- B. \(6\) (if you ignore the leading negative)
- C. \(-4\) (if you forget to apply the rule)
- D. \(-6\) (correct: \(-8+2\))
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(11\)
Subtracting a negative is the same as adding its opposite: \(4-(-7)=4+7=11\).
Question 2
Answer: \(-8\)
When subtracting from a negative number, move further left on the number line: \(-5-3=-8\).
Question 3
Answer: \(4\)
Subtracting a negative becomes addition: \(-2-(-6)=-2+6=4\).
Question 4
Answer: \(15\)
\(10-(-5)=10+5=15\). Always convert subtraction of a negative to addition.
Question 5
Answer: \(-3\)
\(2-5=2+(-5)=-3\). Check: A \(=7\), B \(=-3\), C \(=-5\), D \(=-9\).
Question 6
Answer: \(-6\)
\(-8-(-2)=-8+2=-6\). Subtracting the negative shifts right by 2 on the number line.
Connection to Standards
This lesson supports Grade 7 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
Subtracting Integers 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.
