A comprehensive unit on negative and positive numbers. Students master addition, subtraction, multiplication, and division of integers through realistic ledger keeping, temperature logs, physical elevation models, and gaming scores.
During a game of "Quest for Gold," Marcus has a score of -150 points. On his next turn, he successfully solves a riddle to earn 320 points. However, he then lands on a trap tile and loses 210 points. What is Marcus's score after these turns?
In a football game, the Eagles start on their own 25-yard line. They lose 7 yards on an incomplete screen pass, complete a deep route for a gain of 18 yards, and then get penalized for holding, pushing them back 10 yards. What is their net yardage change, and what yard line are they on now?
Detailed Steps
Net change: \(-7 + 18 - 10 = +1\) yard net change
1. Play sequence: \(25 - 7 = 18\) yard line | 2. Deep pass: \(18 + 18 = 36\) yard line
The highest temperature ever recorded in Death Valley, California was a blistering 134°F. In contrast, the lowest temperature ever recorded in California was -45°F in Boca. Write a subtraction expression to find the distance (difference) between these two extreme temperatures, and solve.
Detailed Steps
Expression: \(134 - (-45)\)
1. Subtracting a negative is equivalent to adding: \(134 + 45\)
A research weather balloon floats high in the atmosphere at 5,400 feet above sea level. Directly below it, a deep-sea ocean probe floats at -280 feet (280 feet below sea level). Write a subtraction expression and calculate the total vertical distance between them.
Detailed Steps
Expression: \(5,400 - (-280)\)
1. Subtracting a negative is equivalent to adding: \(5,400 + 280\)
Operations Mastery Signed Numbers Relative Distance
Integer Ledger Answer Keys Page 2 of 2
Final Answer:
Self-Check Checklist:
Did I apply the sign rules correctly? Did I write final units ($, ft, °F, pts)?
Integer Scales Worksheets Page 2 of 2
Detailed Steps
Equation: \(-35 \times 12\)
1. Rate of descent \((-35)\) times elapsed time \((12)\).
2. Calculation: \(35 \times 12 = 420\). Different signs yield a negative product: \(-420\) feet.
Final Answer:
-420 ft
6
A science weather balloon starts descending from high altitude. Its height changes by a steady rate of -12 feet per second. If it descends for exactly 25 seconds, what is the total change in the weather balloon’s height?
Detailed Steps
Equation: \(-12 \times 25\)
1. Descent velocity: \(-12\) times travel time: \(25\) seconds.
2. Calculation: \(12 \times 25 = 300\). The sign is negative: \(-300\) feet change.
Final Answer:
-300 ft
Section 4: Averages & Multipliers
7
Over the course of 6 consecutive winter nights, the total temperature change in a mountain peak town was recorded as -42°F. What was the average temperature change per night?
Detailed Steps
Equation: \(-42 \div 6\)
1. Divide total negative temperature change \((-42)\) by total count of nights \((6)\).
2. Calculation: \(42 \div 6 = 7\). Negative divided by positive is negative: \(-7°F\).
Final Answer:
-7°F
8
In a retro arcade game, landing on a purple skull multiplies the player's current score by -3. If Leo has a current score of -250 points and lands on the purple skull, what is his new score?
Detailed Steps
Equation: \(-250 \times (-3)\)
1. Identify the signs: Negative score \((-250)\) times Negative multiplier \((-3)\).
2. Multiplying two negative numbers yields a positive product: \(+750\) points!
