Operation Trek Worksheet
Grade 6–8 Mathematics • Rational Numbers & Integers
Operation Trek Worksheet
Multi-Step Real-World Addition & Subtraction
Name:
Date:
Period:
Score: / 25
Mission Briefing: Read each scenario carefully. Define positive and negative values, write multi-step arithmetic expressions, and show all work.
1
The Submersible Expedition (Elevation Shifts)
8 Points
Research submersible Nautilus II begins at sea level (\(0.0\text{ m}\)). Over a six-hour dive, it performs four consecutive maneuvers:
Descends \(2,485.5\text{ m}\) to Ridge Alpha
Ascends \(612.8\text{ m}\) to inspect thermal vent
Dives \(1,840.2\text{ m}\) into trench floor
Rises \(1,295.4\text{ m}\) to seabed beacon
Part A: Submersible's final position relative to sea level?
Part B: Lift distance to reach hoist at \(+14.5\text{ m}\) above sea level?
Show Your Work:
Part A: Part B:
2
The Community Food Truck (Financial Ledger)
8 Points
"The Rolling Whisk" starts festival weekend with a seed balance of \(\$1,450.00\). Over three days, the ledger logs:
Expenses (Debits)
- • Permit fee: \(\$285.50\)
- • Ingredient order: \(\$618.25\)
- • Crew wages: \(\$320.00\)
- • Generator repair: \(\$145.75\)
- • City sanitation: \(\$115.50\)
Revenues & Credits
- • Friday dinner rush: \(\$1,142.80\)
- • Saturday festival sales: \(\$2,384.60\)
- • Farm bulk rebate: \(\$85.00\)
- • Sunday afternoon sales: \(\$890.40\)
Part A: Final ending cash balance on Sunday evening?
Part B: Net financial gain or loss compared to seed balance?
Show Your Work:
Part A Balance: Part B Net Gain/Loss:
Operation Trek • Multi-Step Math Worksheet Turn over for Problem 3 • Page 1 of 2
Operation Trek | Page 2 Continued
Student Name:
3
Arctic Meteorological Station (Extreme Temperature Swings)
8 Points
At Alert Weather Outpost in Nunavut, baseline temperature at 06:00 is \(-18.4^\circ\text{C}\). Over the next 22 hours:
06:00–12:00: Solar radiation raises temp by \(7.9^\circ\text{C}\)
12:00–17:00: Polar storm causes drop of \(14.8^\circ\text{C}\)
17:00–23:00: Arctic winds cause drop of \(9.3^\circ\text{C}\)
23:00–04:00: Inversion layer warms air by \(4.6^\circ\text{C}\)
Part A: Thermometer reading at 04:00 after inversion?
Part B: Difference between warmest peak & coldest low?
Show Your Work:
Part A (04:00 Temp): Part B (Temp Range):
Challenge • Error Analysis Detective
1 Point Bonus
The Scenario: A mountaineer begins at Base Camp (\(1,820\text{ m}\)). She climbs \(435\text{ m}\) up a ridge, rappels down \(182\text{ m}\), and finally descends another \(315\text{ m}\) to River Camp.
Julian's Calculation: \(1,820 + 435 - 182 + 315 = 2,388\text{ m}\)
Explain Julian's error, write the corrected expression, and calculate the true final elevation:
Corrected Expression: Correct Elevation:
Problem 1: Submersible (/8)
Problem 2: Food Truck (/8)
Problem 3: Arctic Weather (/8)
Bonus: Error Check (/1)
Standards: CCSS.MATH.CONTENT.7.NS.A.1, 7.NS.A.2, 6.NS.B.3 Operation Trek Worksheet • Page 2 of 2
Operation Trek Answer Key
Teacher Master Key • Complete Worked Solutions
Operation Trek Answer Key
Multi-Step Addition & Subtraction with Integers and Decimals
Total Points: 25
CCSS.7.NS.A.1 • CCSS.6.NS.B.3
1
Problem 1 Solutions • Submersible Expedition
8 Points (4 pts each)
Signed Modeling: Descend = Negative (\(-\)), Ascend = Positive (\(+\))
Expression: \(0.0 - 2,485.5 + 612.8 - 1,840.2 + 1,295.4\)
Step-by-Step Trajectory:
- Ridge Alpha: \(0 - 2,485.5 = -2,485.5\text{ m}\)
- Thermal Vent: \(-2,485.5 + 612.8 = -1,872.7\text{ m}\)
- Trench Floor: \(-1,872.7 - 1,840.2 = -3,712.9\text{ m}\)
- Seabed Beacon: \(-3,712.9 + 1,295.4 = \mathbf{-2,417.5\text{ m}}\)
Part B Lift Calculation:
Hoist is at \(+14.5\text{ m}\) above sea level.
\(\Delta\text{h} = 14.5 - (-2,417.5)\)
\(\Delta\text{h} = 14.5 + 2,417.5 = \mathbf{2,432.0\text{ m}}\)
Part A Final Answer: \(-2,417.5\text{ m}\) (or \(2,417.5\text{ m}\) below sea level)
Part B Final Answer: \(2,432.0\text{ m}\) total lift
Common Misconception: Students often calculate \(2,417.5 - 14.5 = 2,403.0\text{ m}\), forgetting that lifting from below sea level to above sea level spans across \(0\text{ m}\) (subtracting a negative adds the distance).
2
Problem 2 Solutions • Community Food Truck
8 Points (4 pts each)
Sum of Expenses (Debits):
\(285.50 + 618.25 + 320.00 + 145.75 + 115.50\)
\(= \mathbf{\$1,485.00}\text{ total expenses}\)
Sum of Incomes & Credits:
\(1,142.80 + 2,384.60 + 85.00 + 890.40\)
\(= \mathbf{\$4,502.80}\text{ total revenue}\)
Full Ledger Model: \(\text{Ending} = \text{Seed} + \text{Revenues} - \text{Expenses}\)
\(\text{Ending} = 1,450.00 + 4,502.80 - 1,485.00 = 5,952.80 - 1,485.00 = \mathbf{\$4,467.80}\)
Net Change: \(4,502.80 - 1,485.00 = \mathbf{+\$3,017.80}\) (or \(4,467.80 - 1,450.00 = +\$3,017.80\))
Part A Final Balance: \(\$4,467.80\)
Part B Net Gain/Loss: Net Gain of \(\$3,017.80\)
Common Misconception: Students often omit the initial \(\$1,450.00\) seed balance when reporting the final ending bank balance (giving \(\$3,017.80\) for Part A instead of Part B). Remind them that bank accounts carry forward their opening balance.
Operation Trek • Teacher Solutions Guide Turn over for Problem 3 & Extension Solutions • Page 1 of 2
Operation Trek Solutions | Page 2 Continued
Grading Standards: Accurate Decimal Alignment & Sign Rules
3
Problem 3 Solutions • Arctic Weather Station
8 Points (4 pts each)
Expression: \(-18.4 + 7.9 - 14.8 - 9.3 + 4.6\)
Sequential Temperature Log:
- 06:00 Start: \(-18.4^\circ\text{C}\)
- 12:00 Solar Warmth: \(-18.4 + 7.9 = \mathbf{-10.5^\circ\text{C}}\) (Warmest)
- 17:00 Polar Storm: \(-10.5 - 14.8 = -25.3^\circ\text{C}\)
- 23:00 Gale Winds: \(-25.3 - 9.3 = \mathbf{-34.6^\circ\text{C}}\) (Coldest)
- 04:00 Inversion: \(-34.6 + 4.6 = \mathbf{-30.0^\circ\text{C}}\)
Part B Range Calculation:
Difference between peak high and extreme low:
\(\text{Range} = T_{\text{high}} - T_{\text{low}}\)
\(\text{Range} = -10.5 - (-34.6)\)
\(\text{Range} = -10.5 + 34.6 = \mathbf{24.1^\circ\text{C}}\)
Part A Final Reading: \(-30.0^\circ\text{C}\)
Part B Final Range: \(24.1^\circ\text{C}\)
Common Misconception: When calculating temperature range, students frequently calculate \(-10.5 - 34.6 = -45.1^\circ\text{C}\) or take the absolute values and subtract \(34.6 - 10.5 = 24.1\) without properly understanding the signed subtraction \(-10.5 - (-34.6)\).
Challenge Solution • Error Analysis Detective
1 Bonus Point
Julian's Error: Julian treated the final descent of \(315\text{ m}\) as an addition (\(+315\)) instead of subtraction. Descending reduces elevation, so it must be subtracted.
Correct Expression: \(1,820 + 435 - 182 - 315\)
Computation: \(2,255 - 182 - 315 = 2,073 - 315 = \mathbf{1,758\text{ m}}\)
True Final Elevation: \(1,758\text{ m}\) above sea level
Instructional Coaching & Scaffolding Tips
Support for Developing Learners:
- Have students draw a vertical number line for elevation and temperature problems to visualize crossing \(0\).
- Encourage grouping positive and negative terms (T-chart method) before executing final multi-digit addition/subtraction.
Extension for Advanced Learners:
- Ask students to calculate the average hourly rate of temperature change between 06:00 and 23:00.
- Have students write their own multi-step ledger problem involving a percentage sales tax or discount rebate.
Operation Trek Answer Key • Middle School Mathematics Page 2 of 2
