Integer Showdown Slides
Grade 7 Math Unit 1: Number Systems
Grid Quest
Integer Showdown
Mastering addition and subtraction using visual zero pairs and number line runway movements.
Positive Forces
-
Negative Forces
Let the simulation begin
Press Space or Arrow Key
01
The Contenders
Concept Setup
What is an Integer?
Integers are whole numbers and their opposite negatives, including zero.
..., -3, -2, -1, 0, 1, 2, 3, ...
No fractions, decimals, or pieces. Only wholes!
Integers in the Wild
Bank Accounts
Depositing $50 (+50) vs. Spending $50 (-50)
Climate Change
10° above freezing (+10) vs. 10° below freezing (-10)
Elevation Levels
Mountain peak altitude (+) vs. Deep sea trench depth (-)
Unit 1: Rational Numbers & Integers Slide 2
02
The Secret Weapon: Zero Pairs
Visual Model 1
What is a Zero Pair?
When one positive counter (+1) and one negative counter (-1) combine, they completely neutralize each other!
The Law of Balance
Adding or removing a Zero Pair from a board changes the physical appearance, but leaves the total numerical value completely unchanged.
Zero Pair Simulation
+1
Positive Counter
Neutralize
-1
Negative Counter
Mathematical Expression: \( (+1) + (-1) = 0 \)
Unit 1: Rational Numbers & Integers Slide 3
03
Adding with Counters
Battle Scenarios
Scenario A Same Signs
\( (-3) + (-2) \)
When signs match, they are on the same team! Just join them together.
-
-
-
-
-
Total: 5 negative counters \(= -5\)
Scenario B Different Signs
\( (+5) + (-3) \)
Opposite teams fight! Pair up positives and negatives to create Zero Pairs, then clear them.
-
0
-
0
-
0
Leftover
Remaining: 2 positive counters \(= +2\)
Unit 1: Rational Numbers & Integers Slide 4
04
The Number Line Runway
Visual Model 2
Flight Rules
STEP 1: Hangar Location
Start at the first number
STEP 2: Addition Action
- Add positive \(\rightarrow\) Fly RIGHT
- Add negative \(\rightarrow\) Fly LEFT
Simulation Run
\( (-2) + (+5) = +3 \)
+5 Right
S
L
-4 -3 -2 -1 0 +1 +2 +3 +4
Start at -2, move right 5 jumps, land safely at +3!
Unit 1: Rational Numbers & Integers Slide 5
05
Subtraction: The Take Away Dilemma
Dilemma & Rescue
The Problem
\( (+2) - (+5) \)
If you have 2 positive counters, how can you take away 5 positive counters?
Error: Not enough counters!
The Rescue
Introduce Zero Pairs!
Add 3 Zero Pairs. This adds exactly 0 to the board, but supplies the necessary positive counters to remove!
-
-
-
Now we have 5 positives and 3 negatives. Take away 5 positives!
Resulting Counters Leftover: 3 Negative Counters = -3
Unit 1: Rational Numbers & Integers Slide 6
06
The Subtraction Shortcut
Add the Opposite
Keep, Change, Change
Adding the Opposite
Subtracting an integer is the exact same as adding its opposite sign.
\( A - B = A + (-B) \)
No need to draw a ton of counters once you learn the system!
Step-By-Step Conversion
1. KEEP \( +4 \)
Keep the first sign
2. CHANGE \( - \rightarrow + \)
Change subtraction to addition
3. CHANGE \( (-3) \rightarrow (+3) \)
Flip the sign of second number
New Problem: \( (+4) + (+3) = +7 \)
Unit 1: Rational Numbers & Integers Slide 7
07
Interactive Warm-Up
Live Challenge
CHALLENGE 01
\( (-6) + (+4) \)
Are signs opposite or matching? Which team is larger?
Model strategy:
Opposites clash: \(-2\)
CHALLENGE 02
\( (-5) - (-8) \)
Try applying the "Keep, Change, Change" shortcut first!
Model strategy:
\( (-5) + (+8) = +3 \)
CHALLENGE 03
\( (-2) - (+4) \)
You start with 2 negatives. Can you take away 4 positives?
Model strategy:
Add zero pairs: \(-6\)
Ready for Battle? Independent Practice Initiated
Integer Clash Worksheet
Student Edition
Integer Clash
Mastering Integer Addition & Subtraction
Name:
Date: Period:
POSITIVE (+1)
Deposits, altitude, heat
-
NEGATIVE (-1)
Debits, depth, cold
-
ZERO PAIR = 0
They cancel each other
A
Zero Pair Arena (Match and Neutralize)
Draw the required positive and negative counters. Loop the zero pairs, and write the remaining value.
1. Draw 4 positive & 2 negative counters #1
Remaining Value:
2. Draw 3 positive & 6 negative counters #2
Remaining Value:
B
Addition Battle Arena (Modeling with Counters)
Solve each problem. Draw circles with "+" or "-" in the modeling boxes, cross out zero pairs, and write the final sum.
\( (+4) + (-3) \) Problem 3
Zero Pairs cleared: Sum =
\( (-5) + (-2) \) Problem 4
Zero Pairs cleared: Sum =
\( (-6) + (+2) \) Problem 5
Zero Pairs cleared: Sum =
\( (-1) + (-4) \) Problem 6
Zero Pairs cleared: Sum =
Unit 1: Integer Operations Integer Clash Practice • Page 1 of 2 Grade 7 Math
Integer Clash
Phase 2: Number Line Navigation & Subtraction
Name:
C
The Number Line Runway
Draw the flight paths for these problems. Plot your start point, draw jump arrows, and write your landing destination.
Start at 1st number • Add Positive: Jump RIGHT ➔ • Add Negative: Jump LEFT
7. Solve: \( (-3) + (+7) \) Problem 7
-6-5-4-3-2-10123456
Landing Destination (Sum) =
8. Solve: \( (+2) + (-5) \) Problem 8
-6-5-4-3-2-10123456
Landing Destination (Sum) =
D
The Subtraction Shortcut (Keep, Change, Change)
Rewrite each subtraction problem as an addition problem by adding the opposite. Then, calculate the final answer.
Problem 9 Subtraction
\( (-4) - (+2) \)
Addition equivalent:
Answer:
Problem 10 Subtraction
\( (+3) - (-5) \)
Addition equivalent:
Answer:
E
Real-World Missions
Read the scenarios, write the math equation, and solve.
Integer Clash Key
Teacher Edition
Integer Operations Guide
Instructional Blueprint & Misconception Map
Grade 7 Mathematics
Lesson: Integer Showdown
Pacing Blueprint
10 MINS
Direct Instruction
Go through Slides 1-4. Establish vocabulary and counter models.
15 MINS
Guided Runways
Slides 5-7. Practice number lines and "Keep Change Change".
18 MINS
Clash Battle
Students solve the independent worksheet. Monitor groups.
7 MINS
Debrief & Exit
Review answers using the key. Complete reflection checklist.
Common Misconception Map
1
Adding Absolute Values Blindly
Error: Student calculates \((-5) + (+2)\) as \(-7\) by adding absolute numbers and preserving the starting negative sign.
Intervention: Point to the Counter Arena. Ask: "If you have 5 negative counters and 2 positive counters, do they join up or fight? How many zero pairs cancel?"
2
Subtracting From Left-to-Right Blindly
Error: Student calculates \((+3) - (-5)\) as \(-2\) by just subtracting \(5 - 3\).
Intervention: Enforce the Keep-Change-Change shortcut: Keep \(+3\), change minus to plus, change \(-5\) to \(+5\). Show that subtraction of a debt is a profit.
High-Yield Questioning Prompts
To Scaffold Visual Models
"When we bring a positive and a negative counter together, why is the result zero? What physical examples can you think of where opposites cancel out?"
To Solidify Subtraction
"Why is taking away a debt the exact same as giving you cash? How does the number line represent 'adding the opposite' when walking backwards?"
ESSENTIAL UNDERSTANDING GOAL
By the end of this lesson, students should transition from physically counting dots to mentally seeing signs battle or move on the scale runway.
Unit 1: Integer Operations Teacher Guide • Page 1 of 2 Grade 7 Math
Integer Clash ANSWER KEY
Comprehensive Solved Reference
Grade 7 Math
Part 1: Counters & Battles
Section A: Zero Pair Discovery
- Problem 1: Draw 4 (+) and 2 (-). 2 zero pairs cancel. Remaining = +2
- Problem 2: Draw 3 (+) and 6 (-). 3 zero pairs cancel. Remaining = -3
Section B: Addition Solutions
- Problem 3: (+4) + (-3) = +1 (3 pairs cleared)
- Problem 4: (-5) + (-2) = -7 (0 pairs cleared)
