Zero Pairs Practice Worksheet 01
Grade 7 Math • CCSS 7.NS.A.1 Day 1: Tuesday Review
Zero Pairs Clash
Name: ______________________
Date: _________ Period: _____
Adding Integers (7.NS.1b)
• Same signs: Add absolute values, keep common sign.Different signs: Subtract absolute values, keep sign of larger magnitude (\(p + q\)).
Subtracting Integers (7.NS.1c)
Subtracting is adding the additive inverse (opposite):
A
Model with Counters & Number Lines
1. Evaluate: \(5 + (-8)\) [Counters]
Draw \(+\) and \(-\) chips to show zero pairs:
Final Sum =
2. Evaluate: \(-3 - 4\) [Number Line]
Rewrite as addition, then plot vectors:
-8-6-4-202
Final Answer =
B
Fluency Sprint: Adding & Subtracting
3. \(-14 + 9 =\)
4. \(27 + (-15) =\)
5. \(-19 + (-23) =\)
6. \(18 - 31 =\)
7. \(-12 - 16 =\)
8. \(-8 - (-14) =\)
9. \(45 - (-25) =\)
10. \(-52 + 52 =\)
11. \(-100 - (-45) =\)
12. \(6 - 19 + 4 =\)
13. \(-7 + (-11) - 5 =\)
14. \(15 - (-8) - 12 =\)
GRADE 7 MATH • CCSS 7.NS.A.1 • TUESDAY WORKBOOK PAGE 1 OF 2
Grade 7 Math
Word Problems & Distance |p - q| (7.NS.1d)
Day 1 Review • 55-Min Class
C
Real-World Problem Solving
15. Submarine Exploration: A research submarine starts at sea level (0 ft), descends 420 feet, ascends 175 feet to take water samples, and then descends another 85 feet.
Expression & Solution:
Depth: ft
16. Bank Balance Overdraft: Maya has \(\$48\) in her checking account. She purchases groceries for \(\$65\), and the bank applies a \(\$25\) overdraft penalty fee. What is her new account balance?
Expression & Solution:
Balance:
D
Distance as |p - q| (CCSS 7.NS.1c)
17. Distance Formula: The distance between two points \(p\) and \(q\) is \(|p - q|\). Find the distance between \(-14\) and \(9\).
Distance =
18. Elevation Change: Mount Whitney is \(+14,505\text{ ft}\) and Badwater Basin is \(-282\text{ ft}\). What is the total elevation difference?
Difference = ft
!
Spot the Blunder (Error Analysis)
Student Claim: -15 - (-8) = -23
Identify the conceptual mistake the student made and provide the correct evaluation with reasoning.
Tuesday Confidence Meter:
⚪ 1: Need Help ⚪ 2: Getting There ⚪ 3: Mastered Addition & Subtraction
GRADE 7 MATH • CCSS 7.NS.A.1 • TUESDAY WORKBOOK PAGE 2 OF 2
Zero Pairs Key Teacher Guide KEY
Grade 7 Math • CCSS 7.NS.A.1 Day 1: Tuesday Review
Zero Pairs Worked Key
Target: Addition & Subtraction
7th Grade Instructional Focus & Pacing (55-Min Period)
Target CCSS 7.NS.A.1c : Emphasize that subtraction is simply adding the additive inverse (\(p - q = p + (-q)\)) . When students encounter \(a - (-b)\), have them explain verbally that subtracting a negative is equivalent to adding a positive distance. Guard against the misconception that "two negatives make a positive" in addition.
Part A: Visual Modeling Solutions (7.NS.A.1b)
1. \(5 + (-8) = \mathbf{-3}\)
5 (+) chips & 8 (-) chips:
(+) (+) (+) (+) (+)
(-) (-) (-) (-) (-) (-) (-) (-)
5 zero pairs cancel out, leaving 3 negative chips (\(-3\)) .
2. \(-3 - 4 = \mathbf{-7}\)
Rewrite: \(-3 + (-4)\)
Start at 0, move 3 left to \(-3\). Move another 4 left to land on \(\mathbf{-7}\).
Vector 1: \(0 \to -3\) | Vector 2: \(-3 \to -7\)
Part B: Fluency Sprint Step-by-Step Solutions
Prob 3: \(-14 + 9\)
\(= -5\)
Diff signs: \(14 - 9 = 5 \to -5\)
Prob 4: \(27 + (-15)\)
\(= 12\)
Diff signs: \(27 - 15 = 12\)
Prob 5: \(-19 + (-23)\)
\(= -42\)
Same signs: \(19 + 23 = 42 \to -42\)
Prob 6: \(18 - 31\)
\(= -13\)
Rewrite: \(18 + (-31) = -13\)
Prob 7: \(-12 - 16\)
\(= -28\)
Rewrite: \(-12 + (-16) = -28\)
Prob 8: \(-8 - (-14)\)
\(= 6\)
Rewrite: \(-8 + 14 = 6\)
Prob 9: \(45 - (-25)\)
\(= 70\)
Rewrite: \(45 + 25 = 70\)
Prob 10: \(-52 + 52\)
\(= 0\)
Additive inverse property
Prob 11: \(-100 - (-45)\)
\(= -55\)
\(-100 + 45 = -55\)
Prob 12: \(6 - 19 + 4\)
\(= -9\)
\(6 - 19 = -13\); \(-13 + 4 = -9\)
Prob 13: \(-7 + (-11) - 5\)
\(= -23\)
\(-18 - 5 = -18 + (-5) = -23\)
Prob 14: \(15 - (-8) - 12\)
\(= 11\)
\(15 + 8 = 23\); \(23 - 12 = 11\)
GRADE 7 MATH • CCSS 7.NS.A.1 • TUESDAY KEY PAGE 1 OF 2
Grade 7 Teacher Key
Word Problems & Error Analysis Solutions
CCSS 7.NS.A.1c,d
Sign Squad Practice Worksheet 02
Grade 7 Math • CCSS 7.NS.A.2 Day 2: Wednesday Review
Sign Squad Showdown
Name: ______________________
Date: _________ Period: _____
Multiplication & Division Rules (7.NS.2a,b)
• Same signs: Result is always POSITIVE (+) Different signs: Result is always NEGATIVE (-)
Powers of Negative Bases & Chains
• Even count of negative factors \(\to\) Positive Odd count of negative factors \(\to\) Negative Caution: \((-4)^2 = (-4)(-4) = 16\) whereas \(-4^2 = -(4 \cdot 4) = -16\).
A
Sign Patterns & Exponent Traps
1. \((-3)^3\)
2. \(-5^2\)
3. \((-2) \cdot (-3) \cdot (-4)\)
4. \((-1)^{15}\)
B
Fluency Sprint: Multiply & Divide
5. \(-7 \times 8 =\)
6. \(-12 \times (-6) =\)
7. \(9 \times (-11) =\)
8. \(-72 \div 9 =\)
9. \(-84 \div (-7) =\)
10. \(0 \div (-13) =\)
11. \(\frac{-96}{12} =\)
12. \(\frac{-120}{-8} =\)
13. \(-15 \div 0 =\)
14. \(-4 \times 13 =\)
15. \(-15 \times (-5) =\)
16. \(\frac{144}{-12} =\)
GRADE 7 MATH • CCSS 7.NS.A.2 • WEDNESDAY WORKBOOK PAGE 1 OF 2
Grade 7 Math
Multi-Step Operations & Rate Problems
Day 2 Review • 55-Min Class
C
Rate of Change & Averages (CCSS 7.NS.A.2)
17. Temperature Drop: In Fairbanks, Alaska, the temperature dropped at a steady rate of \(4^\circ\text{F}\) every hour for 7 consecutive hours. If the starting temperature was \(15^\circ\text{F}\), what was the final temperature?
Calculations:
Temp: \(^\circ\text{F}\)
18. Golf Scorecard Average: A golfer recorded scores relative to par over 4 rounds: \(-3\), \(+2\), \(-5\), and \(-2\). Find the golfer's mean (average) score per round.
Calculations:
Mean:
D
Multi-Step Integer Evaluation
19. Evaluate: \(\frac{-48}{-6} + (-4)(3)\)
Answer =
20. Evaluate: \((-2)^4 - (-18 \div 3)\)
Sign Squad Key Teacher Guide KEY
Grade 7 Math • CCSS 7.NS.A.2 Day 2: Wednesday Review
Sign Squad Worked Key
Target: Multiply & Divide
7th Grade Instructional Focus: Exponents & Division by Zero
Target CCSS 7.NS.A.2a,b : Remind students that \((-x)^2 \neq -x^2\). Parentheses bind the negative sign inside the base, whereas \(-x^2\) is the opposite of \(x^2\). Also reinforce rational number definitions: \(0 \div n = 0\) (0 shared among groups), but \(n \div 0 = \text{undefined}\) because no number multiplied by 0 equals a non-zero \(n\).
Part A: Sign Patterns & Exponent Traps Solutions
1. \((-3)^3\)
\(= -27\)
\((-3)(-3)(-3)\)
2. \(-5^2\)
\(= -25\)
\(-(5 \times 5)\)
3. \((-2)(-3)(-4)\)
\(= -24\)
3 neg factors \(\to -\)
4. \((-1)^{15}\)
\(= -1\)
Odd exponent \(\to -1\)
Part B: Fluency Sprint Step-by-Step Solutions
Prob 5: \(-7 \times 8\)
\(= -56\)
Different signs \(\to\) negative
Prob 6: \(-12 \times (-6)\)
\(= 72\)
Same signs \(\to\) positive
Prob 7: \(9 \times (-11)\)
\(= -99\)
Different signs \(\to\) negative
Prob 8: \(-72 \div 9\)
\(= -8\)
Different signs \(\to\) negative
Prob 9: \(-84 \div (-7)\)
\(= 12\)
Same signs \(\to\) positive
Prob 10: \(0 \div (-13)\)
\(= 0\)
Zero divided by any # is 0
Prob 11: \(\frac{-96}{12}\)
\(= -8\)
Different signs \(\to\) negative
Prob 12: \(\frac{-120}{-8}\)
\(= 15\)
Same signs \(\to\) positive
Prob 13: \(-15 \div 0\)
Undefined
Cannot divide by 0
Prob 14: \(-4 \times 13\)
\(= -52\)
Different signs \(\to\) negative
Prob 15: \(-15 \times (-5)\)
\(= 75\)
Same signs \(\to\) positive
Prob 16: \(\frac{144}{-12}\)
\(= -12\)
Different signs \(\to\) negative
GRADE 7 MATH • CCSS 7.NS.A.2 • WEDNESDAY KEY PAGE 1 OF 2
Grade 7 Teacher Key
Rates, Multi-Step & Truth-Lie Solutions
CCSS 7.NS.A.2
Part C: Real-World Rates & Averages Solutions
Mixed Ops Practice Worksheet 03
Grade 7 Math • CCSS 7.NS.A.3 Day 3: Thursday Review
Mixed Ops Gauntlet
Name: ______________________
Date: _________ Period: _____
7th Grade Test-Day Master Checklist: All 4 Operations & PEMDAS
Add (+): Same sign \(\to\) Add & Keep. Diff sign \(\to\) Subtract.
Subtract (−): Add the opposite: \(p - q = p + (-q)\).
Multiply (×): Same sign \(\to +\), Diff sign \(\to -\).
Divide (÷): Same sign \(\to +\), Diff sign \(\to -\).
A
Mixed Quick-Fire Circuit
1. \(-16 + (-24)\)
2. \(-16 - (-24)\)
3. \(-6 \times (-8)\)
4. \(-96 \div 6\)
5. \(35 - (-15)\)
6. \(-14 \times 5\)
7. \(-75 \div (-5)\)
8. \(-42 + 60\)
B
Order of Operations (PEMDAS)
9. Evaluate: \(-8 + 4 \cdot (-3)^2 - (-10)\)
Answer =
10. Evaluate: \(\frac{-30 - (-6)}{(-2)^3 + 4}\)
Answer =
11. Evaluate: \(5 - [ -3 \cdot (-2 - 6) ]\)
Answer =
12. Evaluate: \(|-15 + 7| - 3(-4)\)
Answer =
GRADE 7 MATH • CCSS 7.NS.A.3 • THURSDAY WORKBOOK PAGE 1 OF 2
Grade 7 Math
Test Simulation & Error Analysis (7.NS.A.3)
Day 3 Review • 55-Min Class
C
Test Readiness Multiple Choice
13. Which expression has the greatest value?
A) \(-14 - (-20)\)
B) \(-4 \times (-2)\)
C) \(-36 \div (-4)\)
D) \(| -12 | - 5\)
Selected Answer:
14. If \(x = -3\) and \(y = -5\), what is \(2x^2 - y\)?
A) \(13\)
B) \(23\)
C) \(-23\)
D) \(-13\)
Selected Answer:
D
Test Traps: Error Analysis
15. Student Work on Test Question:
Problem: Evaluate \(-4 - 2(3 - 8)\)
Line 1: \(-4 - 2(-5)\)
Which line contains the first error? Explain what went wrong and provide the correct result.
✓
Friday Test Readiness Check
I can add/subtract without sign confusion.
I remember \((-a)^2 \neq -a^2\).
I know division by zero is undefined.
I follow PEMDAS step-by-step.
GRADE 7 MATH • CCSS 7.NS.A.3 • THURSDAY WORKBOOK PAGE 2 OF 2
Mixed Ops Key Teacher Guide KEY
Grade 7 Math • CCSS 7.NS.A.3 Day 3: Thursday Review
Mixed Ops Worked Key
Target: All Operations & Test Prep
7th Grade Test-Eve Strategy & PEMDAS Discipline
Target CCSS 7.NS.A.3 : Multi-step real-world and mathematical operations. Have students work through Part A independently in 5 minutes to test instant sign-rule recall. When tackling PEMDAS in Part B, demand that they underline or circle the specific operation performed at each step to eliminate skipped signs or subtraction-before-multiplication errors.
Part A: Mixed Speed Circuit Solutions
1. \(-16 + (-24)\)
\(= -40\)
2. \(-16 - (-24)\)
\(= 8\)
3. \(-6 \times (-8)\)
\(= 48\)
4. \(-96 \div 6\)
\(= -16\)
5. \(35 - (-15)\)
\(= 50\)
6. \(-14 \times 5\)
\(= -70\)
7. \(-75 \div (-5)\)
\(= 15\)
8. \(-42 + 60\)
\(= 18\)
Part B: Order of Operations Step-by-Step
9. \(-8 + 4 \cdot (-3)^2 - (-10)\)
• Exponent: \((-3)^2 = 9\)
• Multiply: \(4 \cdot 9 = 36\)
• Add/Sub (left-to-right): \(-8 + 36 = 28\)
• Subtract neg: \(28 - (-10) = 28 + 10 = \mathbf{38}\)
Answer: 38
10. \(\frac{-30 - (-6)}{(-2)^3 + 4}\)
• Numerator: \(-30 + 6 = -24\)
• Denominator exponent: \((-2)^3 = -8\)
• Denominator sum: \(-8 + 4 = -4\)
• Divide: \(\frac{-24}{-4} = \mathbf{6}\)
Answer: 6
11. \(5 - [ -3 \cdot (-2 - 6) ]\)
• Inner parentheses: \(-2 - 6 = -8\)
• Inside bracket multiply: \(-3 \cdot (-8) = 24\)
• Subtract: \(5 - 24 = 5 + (-24) = \mathbf{-19}\)
Answer: -19
12. \(|-15 + 7| - 3(-4)\)
• Inside absolute value: \(-15 + 7 = -8\)
• Absolute value: \(|-8| = 8\)
• Multiply: \(3(-4) = -12\)
• Subtract: \(8 - (-12) = 8 + 12 = \mathbf{20}\)
Answer: 20
GRADE 7 MATH • CCSS 7.NS.A.3 • THURSDAY KEY PAGE 1 OF 2
Grade 7 Teacher Key
Test Item Rationale & Error Analysis Solutions
CCSS 7.NS.A.3
Part C: Test Readiness Multiple Choice Rationale
13. Greatest Value: C (\(-36 \div -4 = 9\))
• A: \(-14 - (-20) = -14 + 20 = 6\)
• B: \(-4 \times (-2) = 8\)
• C: \(-36 \div (-4) = \mathbf{9}\) (Greatest value)
