Equation Balance Worksheet
Algebra 1 Review Scaffolded Practice
Equation Balance
Solve 1-step equations using inverse operations to keep the balance level.
Name:
Date:
Period: Page 1 of 2
⚖️
The Golden Rule of Balance Whatever you do to one side, you must do to the other side!
\(+\) Add ↔ \(-\) Subtract
\(\times\) Multiply ↔ \(\div\) Divide
1
Level 1: Launch & Balance (Add / Subtract)
Inverse: undo addition or subtraction
#1 Undo \(+7\) with \(-7\)
\(x + 7 = 15\)
Left: \(x + 7\) ⚖️ Right: \(15\)
Show Work:
Answer: \(x =\) _____
#2 Undo \(-9\) with \(+9\)
\(y - 9 = 14\)
Left: \(y - 9\) ⚖️ Right: \(14\)
Show Work:
Answer: \(y =\) _____
#3 Real World Snack Money
Jordan had \(m\) dollars. After spending $8 on snacks, he has $13 remaining:
\(m - 8 = 13\)
Show Work:
Starting Money: \(m = \$\) _____
2
Level 2: Equal Sharing (Multiply / Divide)
Inverse: undo multiplication or division
#4 Undo \(\cdot 4\) with \(\div 4\)
\(4k = 28\)
\(k\) \(k\) \(k\) \(k\)
Total = 28
Show Work:
Answer: \(k =\) _____
#5 Undo \(\div 5\) with \(\times 5\)
\(\frac{w}{5} = 6\)
1 part = \(6\) ➡️ All 5 parts
Show Work:
Answer: \(w =\) _____
#6 Real World Pizza Party
Three friends evenly split a giant party pizza. Each person paid $9:
\(\frac{p}{3} = 9\)
Show Work:
Total Price: \(p = \$\) _____
💡 Pro Tip: Check your work by substituting your answer back into the original equation!
Turn to Page 2 ➡️
Part 2
Challenge & Check
Apply balance skills to mixed signs, error spotting, and reflection.
Student: Page 2 of 2
3
Level 3: Proficient (Mixed Operations & Sign Checks)
Watch integer rules
#7 Addition with Negatives
\(n + 12 = 5\)
Show Work & Check:
Answer: \(n =\) _____
#8 Multiplication with Negatives
\(-6x = 42\)
Show Work & Check:
Answer: \(x =\) _____
#9 Division with Negatives
\(\frac{b}{-4} = -8\)
Show Work & Check:
Answer: \(b =\) _____
#10 Real World Skateboard Savings
Maya wants a $95 board. She has saved $48 so far.
\(48 + s = 95\)
Show Work:
Still needs: \(s = \$\) _____
🔍
Error Analysis: Balance Detective
Spot & Fix
Marcus's Solution:
\(x - 6 = 15\)
\(- 6 \quad\quad - 6\)
\(x = 9\) ❌
1. What mistake did Marcus make?
2. Correct Solution:
True value: \(x =\) _____
🎯 How do you feel about solving 1-step equations today? Circle one:
🟢 I got this! Can solve on my own
🟡 Getting there! Need to watch signs
🔴 Need help! Confused on inverses
My reminder for tomorrow:
Equation Balance Answer Key
Teacher Resource Full Solutions & SPEd Guide
Equation Balance Answer Key
Complete step-by-step solutions, check steps, and targeted instructional cues.
Algebra 1 Intervention Page 1: Levels 1 & 2
💡
Key SPEd Intervention Strategy: Emphasize the vertical "river" or line down the equal sign. Have students draw a vertical dashed line through \(=\) to ensure they perform the exact same inverse operation on both sides of the balance scale.
1 Level 1 Solutions: Addition & Subtraction
Undo \(+\) with \(-\) | Undo \(-\) with \(+\)
#1 Solution \(x = 8\)
\(x + 7 = 15\)
\(\quad - 7 \quad - 7\)
\(x = 8\)
Check: \(8 + 7 = 15\) ✔️
Prompt: "What removes \(+7\)? We subtract 7 from both sides."
#2 Solution \(y = 23\)
\(y - 9 = 14\)
\(\quad + 9 \quad + 9\)
\(y = 23\)
Check: \(23 - 9 = 14\) ✔️
Prompt: "Opposite of minus 9 is plus 9. Add 9 to 14."
#3 Real World \(m = \$21\)
\(m - 8 = 13\)
\(\quad + 8 \quad + 8\)
\(m = 21\)
Check: \(\$21 - \$8 = \$13\) ✔️
Context: Jordan started with $21 before buying snacks.
2 Level 2 Solutions: Multiplication & Division
Undo \(\cdot\) with \(\div\) | Undo \(\div\) with \(\cdot\)
#4 Solution \(k = 7\)
\(4k = 28\)
\(\div 4 \quad \div 4\)
\(k = 7\)
Check: \(4(7) = 28\) ✔️
Visual prompt: "4 groups equal 28, so 1 group equals 7."
#5 Solution \(w = 30\)
\(\frac{w}{5} = 6\)
\(\cdot 5 \quad \cdot 5\)
\(w = 30\)
Check: \(\frac{30}{5} = 6\) ✔️
Prompt: "Fraction line means division. Inverse is multiply."
#6 Real World \(p = \$27\)
\(\frac{p}{3} = 9\)
\(\cdot 3 \quad \cdot 3\)
\(p = 27\)
Check: \(\frac{\$27}{3} = \$9\) ✔️
Context: 3 friends paying $9 each means the pizza was $27.
⚠️ Common Misconception in Level 1 & 2:
Students frequently want to do the operation they see rather than the inverse (e.g., seeing \(+7\) and adding \(7\) to \(15\)). Prompt them: "Cover the variable. What number is next to it? How do we cancel that number to zero (or one)?"
