Adding Subtracting Integers Slides
Real-World Mathematics
Visual Concept Deck
Adding and Subtracting Integers
How positive and negative numbers power real-world elevations, freezing temperatures, and financial balances.
Elevation Temperature Money & Debt
The Vertical Number Line
+2,000 m Peak (+) 0 m Sea Level (0) -500 m Submarine (-)
Key Insight: Integers aren't just abstract symbols—they tell us direction, depth, temperature, and money!
VOCAB Core Terminology
Notation: | x |
Absolute Value
1
Definition
Distance from Zero
How many steps a number is from zero on the number line.
2
Rule
answer is ALWAYS POSITIVE
Because distance can never be negative!
Measuring the Distance Distance ≥ 0
5 units away 5 units away 0 -5 +5
|-5| = 5
|5| = 5
Both -5 and +5 have the exact same distance of 5 from zero!
Independent Practice
Evaluate Each Absolute Value
Single Integer Examples
1
\(|-6|\)
2
\(|14|\)
3
\(|-25|\)
4
\(|9|\)
5
\(|-18|\)
6
\(|32|\)
7
\(|0|\)
8
\(|-47|\)
9
\(|83|\)
10
\(|-100|\)
IXL Next Step: Online Practice
When finished, log in to IXL and search these three skill codes:
Skill 1
NSB
Skill 2
ABP
Skill 3
KGR
Golden Strategy
Step 1: Check Signs
Look at the signs of the numbers
Case 1
Same = Add
Both positive or both negative? Add the numbers and keep their sign!
(-4) + (-5) = -9
Case 2
Different = Subtract
One positive and one negative? Subtract the absolute values!
(-7) + 11 = +4
★ ★ ★ ★ BIGGEST absolute Value goes on top ★ ★ ★ ★
When subtracting different signs, place the number with the larger absolute value on top to find the difference!
Example 1
Adding Two Integers
Same Signs (Both Negative)
(-4)
(-5)
1. Check Signs
Both numbers are negative (same sign team).
2. Add Values
Add the absolute values: 4 + 5 = 9.
3. Keep Sign
Keep the shared negative sign: -9.
Final Solution: (-4) + (-5) = -9
Example 2
Adding Two Integers
Different Signs (Negative + Positive)
(-7)
(+11)
1. Check Signs
Signs are different (one negative, one positive).
2. Subtract Values
Subtract smaller from larger: 11 - 7 = 4.
3. Bigger Absolute Value
|11| > |-7|, so the answer is positive!
Final Solution: (-7) + 11 = +4
Your Turn
Solve Each Addition Problem
5 Problems
1
(-8) + (-6)
Same signs?
2
12 + (-5)
Different signs?
3
(-15) + 9
Which team is bigger?
4
(-10) + 10
Opposites sum?
5
(-14) + (-13)
Add & keep sign!
Rule Recap: Same signs \(\rightarrow\) Add and keep sign. Different signs \(\rightarrow\) Subtract absolute values and take the sign of the larger value!
Watch Out!
Common Integer Mistakes
Avoid These Traps
Trap 1
"Two Negatives Make Positive"
(-4) + (-5) = +9
(-4) + (-5) = -9
Why: In addition, combining two debts creates a bigger debt!
Trap 2
Picking the Wrong Sign
(-12) + 5 = +7
(-12) + 5 = -7
Why: |-12| > |5|. The negative number has more magnitude!
Trap 3
Negative Absolute Value
|-8| = -8
|-8| = +8
Why: Distance from zero can never be negative!
Pro Tip: Before computing, ask yourself: "Are the signs teaming up (same) or battling (different)?"
Independent Assignment
Homework Practice
Time for Homework!
Head to IXL and begin your assigned integer practice.
IXL SKILL
Search 3-Letter Code:
QFU
Skill: Add Integers
SHOW ALL WORK!
- ✓ Write each problem down on your lined paper or notebook.
- ✓ Label the signs: Same or Different.
- ✓ Show your addition or subtraction before typing in your answer!
Completion Goal: Earn a 100 or work for 40 minutes. Whichever occurs first.
100 or 40 Mins
Subtracting Integers Slides
Operation Transformation
Visual Concept Deck
Subtracting Integers
Notice the subtraction sign (−) between two numbers? That is your signal to use Keep • Change • Change!
1. KEEP 2. CHANGE 3. CHANGE
The Superpower Switch
Notice Subtraction: (-4) − (+5) K • C • C Solve as Addition: (-4) + (-5)
The Golden Secret: You never actually have to subtract signed numbers! We rewrite every subtraction as addition.
OPERATION ALERT Identify Before You Solve
Trigger: a − b
Look for the Minus Sign Between Numbers
Addition Problem
Already Addition!
(-6) + 9
✓ No KCC needed. Just look at the signs (different signs \(\rightarrow\) subtract absolute values).
−
Subtraction Problem
ALERT: Subtraction Sign!
(-6) − 9
⚡ STOP! Subtraction between numbers means you MUST use Keep • Change • Change!
First step on every integer problem: Look between the numbers. Is it plus or minus?
Anchor Chart
How Keep • Change • Change Works
Left to Right
1
KEEP
Keep the first integer completely alone. Never change its sign!
(-8) ⟶ (-8)
2
CHANGE
Change the subtraction sign into an addition sign.
− ⟶ +
3
CHANGE
Change the second integer into its opposite sign.
(-5) ⟶ (+5)
Example: (-8) − (-5) rewrites to
(-8) + 5 = -3
Subtracting is adding the opposite!
Golden Strategy
Step 2: Check Signs of New Problem
Look at the signs of the numbers
Case 1
Same = Add
Both positive or both negative? Add the numbers and keep their sign!
(-4) + (-5) = -9
Case 2
Different = Subtract
One positive and one negative? Subtract the absolute values!
(-7) + 11 = +4
★ ★ ★ ★ BIGGEST absolute Value goes on top ★ ★ ★ ★
When subtracting different signs, place the number with the larger absolute value on top to find the difference!