Integer Chains Worksheet
Math Mastery Series • Pre-Algebra
Integer Chains Worksheet
Adding and Subtracting Four Integers Using Strategic Grouping
Name:
Date: Period:
Key Strategies for 4-Integer Expressions
1 Add Opposites & Group Signs
Rewrite minus as adding the opposite: \( a - b = a + (-b) \).
Then group: \( (\text{all positives}) + (\text{all negatives}) \).
2 Pair & Simplify in Halves
Split into two pairs: \( [1\text{st} \pm 2\text{nd}] + [3\text{rd} \pm 4\text{th}] \).
Evaluate each bracket first, then combine both results.
A Guided Scaffolding: Group Positives & Negatives
Fill in each step to reach the final sum.
1. \( 14 - 19 + 8 - 6 \) Strategy: Sort by Sign
Step 1: Rewrite Sums
\( 14 + (-19) + 8 + (-6) \)
Step 2: Total Positives
\( 14 + 8 = \text{______} \)
Step 3: Total Negatives
\( (-19) + (-6) = \text{____} \)
Final Sum
Ans: ______
2. \( -12 - (-7) + 15 - 20 \) Remember: \( -(-7) = +7 \)
Step 1: Rewrite as +
Step 2: Total Positives
Step 3: Total Negatives
Final Sum
Ans: ______
B Paired Grouping Method: Solve in 2 Halves
Work out each bracketed pair, then combine.
3. \( [(-15) + 22] + [(-8) - 14] \)
Pair 1: \( (-15) + 22 \)
Pair 2: \( (-8) - 14 \)
Combine Pair 1 + Pair 2: Answer: ________
4. \( [32 - 45] + [16 - (-9)] \)
Pair 1 Work
Pair 2 Work
Combine Pair 1 + Pair 2: Answer: ________
5. \( (-26) - 14 + (-18) + 50 \)
Pair 1 Work
Pair 2 Work
Combine Pair 1 + Pair 2: Answer: ________
6. \( -38 + (-12) - (-30) - 17 \)
Pair 1 Work
Pair 2 Work
Combine Pair 1 + Pair 2: Answer: ________
Rule of Signs: Adding negatives gives a negative sum. Adding opposite signs uses difference of absolute values. Page 1 of 2 • Continue to Part II →
Part II
Independent Fluency, Error Analysis & Modeling
Name: Show all steps clearly
C Independent Integer Chains
Use whichever grouping strategy works best for each problem.
7. \( 18 - 26 - 14 + 35 \)
Show work:
Answer: ____________
8. \( -35 + (-15) + 60 - 22 \)
Show work:
Answer: ____________
9. \( -9 - (-25) - 16 + (-11) \)
Show work:
Answer: ____________
10. \( 75 + (-50) - 30 - (-15) \)
Show work:
Answer: ____________
11. \( -100 + 46 - (-54) - 33 \)
Show work:
Answer: ____________
12. \( (-18) - 32 + (-20) - (-80) \)
Show work:
Answer: ____________
Error Detective: Spot & Fix the Mistake
Critical Reasoning
Devon's Incorrect Solution:
Problem: \( -10 - 6 + (-4) - (-12) \)
Step 1: \( -10 - 6 = -16 \)
Step 2: \( -16 + (-4) = -20 \)
Step 3: \( -20 - (-12) = -32 \quad \text{[Error!]} \)
Describe Devon's mistake in Step 3:
Correct Answer: _________
E Real-World Application: The Submersible Log
Depth Modeling
A marine research sub logs four consecutive vertical maneuvers over a testing mission:
Stage 1 Ascend +70 m
Stage 2 Dive -130 m
Stage 3 Ascend +85 m
Stage 4 Dive -45 m
Write expression & show work:
Net elevation change: ________ meters
Self-Reflection:
Confident Minor mistakes Need more practice
Integer Chains Worksheet • Page 2 of 2
