Integer Operations Anchor Packet
Stage 1 of 4 Discovery & Brain Dump
Integer Brain Dump Studio
Unload everything you know, remember, or wonder about adding and subtracting signed numbers.
Name:
Date:
Subject: Grade 7 Math • Integers
Driving Question: When combining or subtracting positive and negative numbers, how do we know the sign and value of our answer?
Brain Dump Goal: Jot down terms, models (counters, number lines, thermometers), real-life connections (money, elevation, sports), and what confuses you. No erasing—get ideas on paper!
1. Integer Keywords & Ideas
Math terms
• Positive (\(+\)) and Negative (\(-\)) Numbers
• Zero Pairs (\(+1\) and \(-1\) cancel to make \(0\))
• Absolute Value (\(|-8| = 8\), distance from zero)
• Opposite Numbers (\(5\) and \(-5\))
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2. Sketches & Visual Models
Doodle models here
← Left = Negative / Subtract Right = Positive / Add →
-3-2-10+1+2+3
- Pos. Counter − Neg. Counter = 0 (Zero Pair)
Sketch your own thermometer, football field, or debt model here
3. Real-Life Examples & Stories
Where do we see this?
• Bank Account: Having \(\$15\) vs. owing \(\$20\) (\(+15 - 20 = -\$5\))
• Temperature: At \(4^\circ\), temp drops \(9^\circ\) (\(4 - 9 = -5^\circ\))
• Football: Gained \(6\text{ yd}\), then lost \(8\text{ yd}\) (\(6 + (-8) = -2\))
• Elevation: \(12\text{ ft}\) above sea level, scuba diving \(15\text{ ft}\) below
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4. Tricky Parts & Misconceptions
Common mistakes
? Trap: Saying "two negatives make a positive" for \(-4 + (-3)\)!
? When do we add absolute values vs. subtract them?
? Why does subtracting a negative like \(6 - (-2)\) equal \(+8\)?
? Confusing subtraction sign with the negative sign!
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Stage 1 Milestone:
Reviewed key integer terms Noticed zero pairs & number lines Added 1 personal question/idea
Integer Operations Anchor Toolkit Page 1 of 4 • Stage 1
Stage 2 of 4 Categorize & Define
Sift, Sort & Spotlight
Group integer operations into 3 clear cases and spotlight essential tools.
The Big Discovery: Every integer addition & subtraction problem falls into one of three core cases. Identify the case before calculating!
A. The 3 Core Cases of Integer Operations
Identify the pattern
Case 1: Same Signs
Both positive OR both negative
Rule: ADD & KEEP SIGN!
\(4 + 5 = +9\)
\(-3 + (-6) = -9\)
"They are on the same team!"
Case 2: Different Signs
One positive AND one negative
Rule: SUBTRACT & WINNER WINS!
\(-8 + 3 = -5\) (Negatives win by 5)
\(9 + (-4) = +5\) (Positives win by 5)
"Tug-of-war battle!"
Case 3: Subtraction (K-C-C)
Minus sign between numbers
Rule: ADD THE OPPOSITE!
\(3 - 8 \rightarrow 3 + (-8) = -5\)
\(5 - (-4) \rightarrow 5 + 4 = 9\)
"Keep - Change - Change!"
B. Key Vocabulary Anchor Cards
Must-know concepts for the chart
Zero Pair \((+1) + (-1) = 0\)
One positive counter and one negative counter combine to have a net value of exactly zero.
"Earning \$1 then spending \$1 leaves you at \$0."
Absolute Value \(|x|\) (Distance)
A number's distance from zero on the number line. Distance is never negative!
\(|-7| = 7\)
"Walking 5 steps backward is still 5 steps of walking."
C. Wall Filter: Must-Have on Poster vs. Keep in Notebook
Prevent chart clutter
MUST BE ON CLASS POSTER (Top 3 Visuals)
1. Tug-of-War / Battle model for different signs
2. Keep-Change-Change (K-C-C) 3-step subtraction rule
3. "Warning: Two negatives DO NOT make a positive in addition!"
KEEP IN PERSONAL NOTES (Too bulky for the wall)
1. Long word problem story paragraphs
2. Large numbers (use simple digits like \(-8, +5\) on the wall)
3. Multiplication & division rules (don't mix them in!)
Integer Operations Anchor Toolkit Page 2 of 4 • Stage 2
Stage 3 of 4 Classroom Co-Creation
The Master Chart Blueprint
Draft the actual classroom poster design before making it on giant chart paper.
Poster Title: INTEGER ADDITION & SUBTRACTION NAVIGATION
Color Code: Yellow = Pos (+) Red = Neg (−)
Class Poster Layout Model (Modeled Layout for Wall Chart)
Notice the 3-panel split
HOW DO WE COMBINE SIGNED NUMBERS?
First look at the operation: Is it Addition (+) or Subtraction (−)?
Case 1: Same Signs Both (+) or Both (−)
ADD & KEEP SIGN "Combine team points"
\(3 + 4 = \mathbf{+7}\)
\(-5 + (-2) = \mathbf{-7}\)
Owe \$5 + owe \$2 = owe \$7!
Case 2: Different Signs One (+) and One (−)
TUG-OF-WAR MATCH
+ TEAM vs − TEAM
SUBTRACT & KEEP WINNER
\(-8 + 5 = \mathbf{-3}\) (− wins by 3)
\(7 + (-2) = \mathbf{+5}\) (+ wins by 5)
Case 3: Subtraction (−) Never subtract directly!
ADD THE OPPOSITE K - C - C
Keep the 1st number
Change − to +
Change 2nd number's sign
\(4 - (-3) \rightarrow 4 + 3 = \mathbf{7}\)
COMMON TRAP WARNING: "Two negatives make a positive" is ONLY true when subtracting a negative (e.g., \(-(-5) = +5\)). When ADDING negatives (\(-3 + (-4)\)), you are combining debts, so the answer is \(-7\)!
Class Blueprint Discussion Pitch:
(What should our class anchor chart make sure to emphasize?)
When building our wall chart, I want to make sure the: section is biggest
Because when 7th graders see a problem like \( -6 - 9 \), they often forget to:
Integer Operations Anchor Toolkit Page 3 of 4 • Stage 3
Stage 4 of 4 Test-Drive & Reflect
Audit, Test & Reflect
Test our new anchor chart on real problems and cement your understanding.
Put It to Work: An anchor chart is only helpful if you use it during independent work. Solve the problems below by following the exact steps on our blueprint!
A. Anchor Chart Usability Audit (Rate Our Finished Chart)
Score 1 (Poor) to 4 (Super Clear)
1. Fast Recognition
Can you immediately tell Same Signs vs. Different Signs?
1 2 3 4
2. Tug-of-War Clarity
Does the model show why \(-8 + 5 = -3\) without guessing?
1 2 3 4
3. K-C-C Actionable Steps
Can someone rewrite \(5 - (-9)\) step-by-step?
1 2 3 4
4. Misconception Shield
Does the warning stop students from writing \(-4 + (-3) = +7\)?
1 2 3 4
B. The Test-Drive: Apply the Chart to Solve Two Problems
Show work and tag the chart section
Problem 1: Evaluate \(-11 + 4\) Addition
Identify Case → Show counters / Tug-of-War reasoning:
Answer: ________
Chart Section Used:
Same Signs Tug-of-War K-C-C
Problem 2: Evaluate \(5 - (-8)\) Subtraction
Rewrite with Keep-Change-Change (K-C-C) first:
Answer: ________
Chart Section Used:
Same Signs Tug-of-War K-C-C
C. Personal Metacognitive Reflection
Lock in your strategy
1. The difference between adding \(-6 + (-3)\) and subtracting \(-6 - (-3)\) is:
2. When I see a problem with DIFFERENT signs (like \(-14 + 9\)), my brain will picture:
3. During an independent quiz or test, I will glance at our anchor chart whenever I see:
Integer Operations Anchor Toolkit Page 4 of 4 • Stage 4
