A focused Grade 6 learning session for Compute with Integers in Context using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving compute with integers in context.
Compute with Integers in Context means choosing a model, naming what each number means, and explaining the strategy.
Question: A number line shows a starting position at \(-8\). A jump of \(+15\) units moves the position forward. Where does it land?
Why it works: On a number line, jump forward means add: \(-8+15=7\).
Answer: \(7\)
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?
Answer: $200 profit
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?
Answer: Floor \(1\)
Question: A submarine is \(-120\) feet (below sea level). It ascends \(45\) feet. What is its new elevation?
Why it works: Ascending means the elevation increases: \(-120+45=-75\) feet.
Answer: \(-75\) feet
Compute with Integers in Context becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A submarine is \(-120\) feet (below sea level). It ascends \(45\) feet. What is its new elevation?
Answer B: \(-75\) feet
Ascending means the elevation increases: \(-120+45=-75\) feet.
The temperature at 6:00 AM was -8° C. By noon, it had risen 22° C. What was the temperature at noon?
Answer C: 14° C
Add the temperature change to the initial temperature: \(-8+22=14°\) C.
Marcus has a bank account with a balance of \(-35\) dollars (overdrawn). He deposits \($50\). What is his new balance?
Answer C: \(15\) dollars
Adding a deposit to an overdrawn balance: \(-35+50=15\) dollars.
An aircraft descends \(800\) feet. If it started at an altitude of \(15{,}000\) feet, what is its new altitude?
Answer A: \(14{,}200\) feet
Descending means altitude decreases: \(15{,}000-800=14{,}200\) feet.
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?
Answer A: \(4\) yards
Net change is gain plus loss: \(12+(-8)=4\) yards gained.
A diver is \(-45\) feet below the surface. She descends another \(20\) feet. What is her new depth?
Answer D: \(-65\) feet
Descending deeper adds to the negative value: \(-45+(-20)=-65\) feet.
The price of a stock was $42. Over two days it lost $5 per day. What is the stock's price now?
Answer A: $32
Loss of $5 per day for 2 days means: \(42-5-5=42-10=$32\).
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?
Answer C: \(10\) points
Adding earned points to negative score: \(-15+25=10\) points.
An account shows a balance of $28. A withdrawal of $15 is made. What is the new balance?
Answer C: $13
Subtraction for a withdrawal: \(28-15=$13\).
An elevator starts at floor \(5\). It goes down \(7\) floors. Which floor is it now on?
Answer A: Floor \(-2\)
Moving down from floor 5: \(5-7=-2\), which is floor \(-2\) (basement level).
A town's elevation is \(350\) meters. A nearby valley is \(120\) meters lower. What is the valley's elevation?
Answer B: \(230\) meters
The valley is 120 meters lower: \(350-120=230\) meters.
