Integer Jungle Worksheet Integer Jungle
Navigating the World of Positive and Negative Numbers
Explorer:
Date:
Field Guide: Addition
Rule A: Same Signs
Add the numbers together and keep the original sign.
Example: (-3) + (-2) = -5
Rule B: Different Signs
Subtract the smaller number from the larger. Keep the sign of the larger absolute value.
Example: (-8) + 12 = 4
1
(-12) + 7 = ________
2
(-5) + (-9) = ________
3
15 + (-6) = ________
Field Guide: Subtraction
The "Keep-Change-Change" Secret:
Turn every subtraction problem into an addition problem!
5 - 8 → 5 + (-8) = -3
4
(-20) - 4 = ________
5
8 - 13 = ________
Field Guide: Double Negatives
Subtracting a negative is like adding! The two minus signs combine to make a plus sign.
10 - (-3) → 10 + 3 = 13
6
(-4) - (-4) = ________
7
10 - (-3) = ________
8
(-1) - (-15) = ________
Field Guide: Mixed Challenges
Step-by-Step Navigation:
When solving a long expression, go left to right.
9
(-2) + 11 - 5 = ________
10
14 + (-20) - (-6) = ________
Survival Tip: When you get stuck, draw a quick number line! Adding means moving to the right (getting warmer), and subtracting means moving to the left (getting colder).
Integer Jungle Answer Key Integer Jungle
Answer Key & Teacher Reference
ANSWER KEY
Addition Guide
Same signs: Sum + Keep Sign
Diff signs: Difference + Larger Absolute Sign
Subtraction Guide
Change to Addition: a - b = a + (-b)
Double Negative: a - (-b) = a + b
Jungle Trek Solutions
(-12) + 7 = -5
Subtract: 12 - 7 = 5. Keep negative (-12 is larger).
(-5) + (-9) = -14
Same signs: 5 + 9 = 14. Keep negative.
15 + (-6) = 9
Subtract: 15 - 6 = 9. Keep positive (15 is larger).
(-20) - 4 = -24
Think: (-20) + (-4). Moving further left.
8 - 13 = -5
Think: 8 + (-13). Start positive, move past zero.
(-4) - (-4) = 0
Think: (-4) + 4. Opposites cancel out.
10 - (-3) = 13
Double negative: 10 + 3 = 13.
(-1) - (-15) = 14
Double negative: (-1) + 15 = 14.
(-2) + 11 - 5 = 4
Step 1: (-2) + 11 = 9. Step 2: 9 - 5 = 4.
14 + (-20) - (-6) = 0
Step 1: 14 - 20 = -6. Step 2: (-6) - (-6) = 0.
Integer Jungle • Integer Operations Worksheet
10/10: Jungle Expert 8/10: Path Finder 6/10: Needs Map
Integer Jungle Slides Integer Jungle
Navigating Positive & Negative Operations
Add
Subtract
The Two Sides of Zero
0
Negative ()
Positive ()
Think of Positives as your "Army" and Negatives as the "Opposition." Who will win the battle?
Rule 1: Same Signs
The Rule:
ADD the numbers.
KEEP the sign.
If everyone is on the same team, the team just gets bigger!
Negative Team
(-3) + (-4) = -7
Positive Team
5 + 2 = 7
Rule 2: Different Signs
The Rule:
SUBTRACT the values.
KEEP the sign of the larger "army."
Battle: Positives Win
(-8) + 12 = 4
12 is bigger than 8!
Battle: Negatives Win
10 + (-15) = -5
15 is bigger than 10!
Subtraction is a Secret
Subtraction is just adding the opposite!
5 - 8 Original
5 + (-8) Added Opposite
KEEP the first
CHANGE to plus
CHANGE the sign
The Double Negative
When you subtract a negative, it turns into ADDITION.
"Taking away debt is the same as giving money!"
Example 1
10 - (-2)
10 + 2 = 12
Example 2
(-3) - (-5)
(-3) + 5 = 2
Jungle Challenge
(-6) + (-4) ?
15 + (-7) ?
(-2) - 8 ?
4 - (-3) ?
(-10) - (-10) ?
(-1) + 12 - 5 ?
Check your answers with your trek leader!
Jungle Peak Worksheet Jungle Peak
Advanced Operations & Real-World Navigation
Mountain Guide:
Date:
Field Guide: Chain Expressions
Strategy: Consolidation
When expressions get long, you can combine all positives and all negatives first! Then do one final battle.
(-3) + 10 + (-5) + 4 → (10 + 4) + [(-3) + (-5)] → 14 + (-8) = 6
1
(-15) + 24 + (-9) + 6 = ________
2
40 - (-12) + (-25) - 10 = ________
3
(-100) - 50 + (-25) - (-75) = ________
Field Guide: Grouping Symbols
The Inner Peak:
Always clear the parentheses first. Treat them like their own mini-jungle trek before joining the rest of the team.
20 + [(-5) - 3] → 20 + (-8) = 12
4
50 + [(-15) - (-5)] = ________
5
(-8) - [(-12) + 20] + 15 = ________
6
-[(-5) + 12] - [8 + (-10)] = ________
Field Guide: Real World Context
Positive (+)
Deposit, Elevation, Gaining, Rising, Warming up.
Negative (-)
Withdrawal, Debt, Depth, Losing, Falling.
7
An explorer starts at 450 feet above sea level. They climb down a cliff and drop 600 feet. What is their new elevation?
8
Your bank account has -$25 (you owe money). You deposit $80, but then spend $120 on hiking gear. What is your final balance?
9
The temperature in the jungle peaks at 32°C during the day and falls 40°C by midnight at the summit. What is the midnight temperature?
10
A submarine is at -200 meters. It descends another 150 meters, then rises 80 meters. What is its final depth?
Jungle Peak Answer Key Jungle Peak
Answer Key & Teacher Reference
ANSWER KEY
Chain Expressions
(-15) + 24 + (-9) + 6 = 6
Steps: (24 + 6) + [-15 + (-9)] = 30 + (-24) = 6
40 - (-12) + (-25) - 10 = 17
Steps: 40 + 12 + (-25) + (-10) = 52 + (-35) = 17
(-100) - 50 + (-25) - (-75) = -100
Steps: (-100) + (-50) + (-25) + 75 = -175 + 75 = -100
Grouping Symbols
50 + [(-15) - (-5)] = 40
Steps: 50 + [(-15) + 5] = 50 + (-10) = 40
(-8) - [(-12) + 20] + 15 = -1
Steps: (-8) - [8] + 15 = -16 + 15 = -1
-[(-5) + 12] - [8 + (-10)] = -5
Steps: -[7] - [-2] = -7 + 2 = -5
Real-World Navigation
7. Elevation Change
450 - 600 = -150 feet
8. Bank Balance
(-25) + 80 - 120 = -$65
9. Temperature Shift
32 - 40 = -8°C
10. Submarine Depth
(-200) - 150 + 80 = -270 meters
Jungle Peak Slides Jungle Peak
Multi-Step Expressions & Real-World Peaks
Chain Reactions
Strategy: The "Big Battle" Method
1. Positives
10 + 4 = 14
2. Negatives
-3 + -5 = -8
Final Battle
14 + (-8) = 6
Inside the Fortress (Grouping)
The Fortress Rule:
Always clear [ Grouping Symbols ] first.
Think of them as a separate, mini-trek you must complete before re-joining the main group.
20 + [(-10) - 5]
Clear the fortress!
20 + (-15) = 5
Real World Navigation
The Climb
Deposits, Rising Elevation, Temperature Increases.
+ POSITIVE
The Drop
Withdrawals, Descending, Debt, Falling Temps.
- NEGATIVE
The Summit Challenge
A hiker is at 500 ft.
FINAL ELEVATION?
Think: 500 - 650 + 100 = ...
Abyss Descent Worksheet Abyss Descent
The Final Boundary: Absolute Value & Unknowns
Abyss Explorer:
Date:
Field Guide: Absolute Value \( |x| \)
Absolute value is the distance from zero. Distance is always positive! Think of the bars \( | \quad | \) as a "positivity machine."
| -10 | = 10 \quad \text{and} \quad | 5 | = 5
Note: If there is a negative outside the bars, like \( -| -8 | \), the answer is -8 because the machine makes it 8, then the outside negative hits it.
1
| -45 | + (-15) = ________
2
| 20 - 30 | - 15 = ________
3
- | -8 + 3 | = ________
4
| -12 | - | -20 | = ________
Field Guide: Algebraic Substitution
Replace the letter with its value using parentheses. This prevents "sign accidents."
If x = -5, then x - 10 \rightarrow (-5) - 10 = -15
Solve for the following if a = -12 and b = 8:
5
a + b - 10 = ________
6
| a | - b = ________
7
b - a = ________
Field Guide: Missing Value Puzzles
Think backward! What value would satisfy the "battle" to get the result?
(-5) + \square = -12 \quad \rightarrow \quad \square = -7
8
(-14) + \square = 10
□ =
Show thinking below
9
\square - (-8) = -12
□ =
Show thinking below
10
| x | = 25 \quad \text{and} \quad x < 0
x =
Explain why
Abyss Master: You have reached the bottom of the integer system. Accuracy is your oxygen—always double-check your signs before you resurface!
Abyss Descent Answer Key Abyss Descent
Answer Key & Teacher Reference
ANSWER KEY
Absolute Value Solutions
1. | -45 | + (-15)
45 - 15 = 30
2. | 20 - 30 | - 15
| -10 | - 15 = 10 - 15 = -5
3. - | -8 + 3 |
- | -5 | = - (5) = -5
4. | -12 | - | -20 |
12 - 20 = -8
Substitution Solutions (a = -12, b = 8)
5. a + b - 10 \rightarrow (-12) + 8 - 10
-14
6. | a | - b \rightarrow | -12 | - 8
4
7. b - a \rightarrow 8 - (-12)
20
Abyss Puzzle Solutions
8. (-14) + \square = 10
Thinking: "What is 10 steps right of -14?" or 10 - (-14)
24
9. \square - (-8) = -12
Thinking: \square + 8 = -12 \rightarrow -12 - 8
-20
10. | x | = 25 and x < 0
Thinking: Absolute value 25 means 25 or -25. Given x < 0.
-25
Abyss Descent Slides Abyss Descent
The Final Frontier of Integers
The Positivity Machine
Absolute Value \( |x| \)
The machine measures distance from zero.
Always outputs a positive!
Solve everything inside first.
Input: Negative
| -15 | = 15
Input: Expression
| 5 - 12 | = 7
The Trap: External Negatives
Danger Zone
What happens when the minus is outside?
- | -8 | = -8
The "positivity machine" makes the inside 8...
Abyss Puzzles: Working Backward
Can you solve for x?
(-10) + x = -2 x=8
x - (-5) = -15 x=-20
The Secret Strategy:
"Balance the Scale"
If you are at -10 and need to get to -2, you must move right 8 steps.
MISSION COMPLETE
Jungle
Basic Operations Mastered
Peak
Complex Expressions & Real World
Abyss
Absolute Value & Logical Puzzles
You are now a certified Integer Explorer.
Base Camp Homework Assignment Base Camp Review
Expedition Homework: Master Your Skills
Explorer:
Mission: Complete these 5 mission-critical challenges to prepare for tomorrow's trek. Show all your steps in the work areas provided.
1
(-18) + 32 = ________
Calculations
2
14 - (-9) = ________
Calculations
3
(-5) + 12 - (-3) + (-10) = ________
Calculations
4
| (-25) + 10 | - 5 = ________
Calculations
5
The temperature at the summit is -12°C. A sudden warm front causes the temperature to rise by 15°C, but by nightfall, it drops 8°C. What is the final temperature?
Answer:
Expedition Integer • Gear Check: Pencil, Eraser, Sharp Mind
Base Camp Homework Answer Key Base Camp Review
Answer Key & Grading Guide
Answer Key
1
(-18) + 32 = 14
Reasoning: Different signs. Subtract the values: 32 - 18 = 14. Keep the positive sign because 32 is the larger "army."
2
14 - (-9) = 23
Reasoning: Double negative rule. Subtracting a negative turns into addition. 14 + 9 = 23.
3
(-5) + 12 - (-3) + (-10) = 0
Step-by-Step:
Change subtraction to addition: (-5) + 12 + 3 + (-10)
Combine positives: 12 + 3 = 15
Combine negatives: -5 + (-10) = -15
Final Battle: 15 + (-15) = 0
4
| (-25) + 10 | - 5 = 10
Step-by-Step:
Solve inside absolute value: (-25) + 10 = -15
Apply absolute value: | -15 | = 15
Subtract 5: 15 - 5 = 10
5
Final Temperature: -5°C
Equation: (-12) + 15 - 8
-12 + 15 = 3 (Morning rise)
3 - 8 = -5 (Nightfall drop)
5 Correct
Summit Master
3-4 Correct
Solid Climber
0-2 Correct
Needs Gear Check
