Introduction
Compute with Integers in Context 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 compute with integers in context.
What Is Compute with Integers in Context?
Compute with Integers in Context means choosing a model, naming what each number means, and explaining the strategy.
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 Compute with Integers in Context
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: A number line shows a starting position at \(-8\). A jump of \(+15\) units moves the position forward. Where does it land?
- A. \(-23\)
- B. \(15\)
- C. \(23\)
- D. \(7\)
Why it works: On a number line, jump forward means add: \(-8+15=7\).
Answer: \(7\)
Visual Model 2
Question: A thermometer shows -3° C in the morning. By afternoon it reads 8° C. What is the temperature change?
- A. 5° C
- B. -5° C
- C. 11° C
- D. -11° C
Why it works: Temperature change is final minus initial: \(8-(-3)=8+3=11°\) C (an increase of 11 degrees).
Answer: 11° C
Worked Examples
Example 1
Question: A business account tracks income and expenses. A company has income of $500 and expenses of $120, then more expenses of $180. What is the net profit or loss?
- A. $800 profit
- B. $200 loss
- C. $200 profit
- D. $800 loss
- Net is income minus total expenses: \(500-120-180=500-300=$200\) profit.
Answer: $200 profit
Example 2
Question: An elevator in a building starts at ground level (floor 0), goes up 6 floors, then down 9 floors, then up 4 floors. What floor is it on?
- A. Floor \(-1\)
- B. Floor \(6\)
- C. Floor \(19\)
- D. Floor \(1\)
- Elevator position: \(0+6-9+4=1\) (floor 1).
Answer: Floor \(1\)
Example 3
Question: An athlete's weight tracking: Started at \(180\) lbs, lost \(12\) lbs in month 1, lost \(8\) lbs in month 2, gained \(5\) lbs in month 3. What is the current weight?
- A. \(155\) lbs
- B. \(160\) lbs
- C. \(205\) lbs
- D. \(165\) lbs
- Weight changes: \(180-12-8+5=180-20+5=165\) lbs.
Answer: \(165\) lbs
Real-World Word Problems
Problem 1
Question: A submarine is \(-120\) feet (below sea level). It ascends \(45\) feet. What is its new elevation?
- A. \(-165\) feet
- B. \(-75\) feet
- C. \(75\) feet
- D. \(165\) feet
Why it works: Ascending means the elevation increases: \(-120+45=-75\) feet.
Answer: \(-75\) feet
Problem 2
Question: An aircraft descends \(800\) feet. If it started at an altitude of \(15{,}000\) feet, what is its new altitude?
- A. \(14{,}200\) feet
- B. \(14{,}800\) feet
- C. \(15{,}200\) feet
- D. \(15{,}800\) feet
Why it works: Descending means altitude decreases: \(15{,}000-800=14{,}200\) feet.
Answer: \(14{,}200\) 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
The temperature at 6:00 AM was -8° C. By noon, it had risen 22° C. What was the temperature at noon?
- A. -30° C
- B. -14° C
- C. 14° C
- D. 30° C
Question 2
Marcus has a bank account with a balance of \(-35\) dollars (overdrawn). He deposits \($50\). What is his new balance?
- A. \(-85\) dollars
- B. \(-15\) dollars
- C. \(15\) dollars
- D. \(85\) dollars
Question 3
In a football game, a team gained \(12\) yards on one play and lost \(8\) yards on the next play. What was the net yardage change?
- A. \(4\) yards
- B. \(-4\) yards
- C. \(-20\) yards
- D. \(20\) yards
Question 4
A diver is \(-45\) feet below the surface. She descends another \(20\) feet. What is her new depth?
- A. \(-25\) feet
- B. \(65\) feet
- C. \(25\) feet
- D. \(-65\) feet
Question 5
The price of a stock was $42. Over two days it lost $5 per day. What is the stock's price now?
- A. $32
- B. $37
- C. $47
- D. $52
Question 6
At the end of a game, a player had a score of \(-15\) points. They earned \(25\) points on their next turn. What is their new score?
- A. \(-40\) points
- B. \(-10\) points
- C. \(10\) points
- D. \(40\) points
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: 14° C
Add the temperature change to the initial temperature: \(-8+22=14°\) C.
Question 2
Answer: \(15\) dollars
Adding a deposit to an overdrawn balance: \(-35+50=15\) dollars.
Question 3
Answer: \(4\) yards
Net change is gain plus loss: \(12+(-8)=4\) yards gained.
Question 4
Answer: \(-65\) feet
Descending deeper adds to the negative value: \(-45+(-20)=-65\) feet.
Question 5
Answer: $32
Loss of $5 per day for 2 days means: \(42-5-5=42-10=$32\).
Question 6
Answer: \(10\) points
Adding earned points to negative score: \(-15+25=10\) points.
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
Compute with Integers in Context 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.
