Equation Trials Worksheet
Algebra Strategy Goal: 75% Mastery
Two-Step Equation Trials
Master inverse operations by working backward: undo addition/subtraction, then multiplication/division.
Name:
Date: Class:
Order of Operations in Reverse (Work Backward) Keep equations balanced by doing the same to both sides
1
Undo Addition / Subtraction
Use inverse: \( + \longleftrightarrow - \)
2
Undo Multiplication / Division
Use inverse: \( \times \longleftrightarrow \div \)
3
Check Your Solution
Substitute back into equation
Guided Model: How to Isolate the Variable Example: \( 3x + 7 = 22 \)
Step 1: Undo Addition
Subtract 7 from each side:
\( 3x + 7 = 22 \)
\( \phantom{3x} - 7 \quad - 7 \)
\( 3x = 15 \)
Step 2: Undo Multiplication
Divide both sides by 3:
\( \frac{3x}{3} = \frac{15}{3} \)
\( x = 5 \)
Step 3: Verification Check
Plug \( x = 5 \) back in:
\( 3(5) + 7 \stackrel{?}{=} 22 \)
\( 15 + 7 = 22 \)
\( 22 = 22 \quad \checkmark \) True!
Part 1: Guided Practice (Fill in the Steps)
Follow the prompts to record inverse operations and solve.
Problem A \( 2x - 5 = 11 \)
Step 1: Undo \( - 5 \) by adding 5 to both sides:
Step 2: Undo multiplication by dividing both sides by 2:
Solution: x = Check: \( 2(\quad) - 5 = 11 \)
Problem B \( \frac{m}{4} + 3 = 9 \)
Step 1: Undo \( + 3 \) by subtracting 3 from both sides:
Step 2: Undo division by multiplying both sides by 4:
Solution: m = Check: \( \frac{(\quad)}{4} + 3 = 9 \)
Part 2: Warm-Up Practice (Before Trials)
Show both inverse operation steps in the work area
1. Practice Equation: \( 6k + 4 = 28 \)
Show inverse operation steps:
Target: Undo +4, then ÷6
Answer:
2. Practice Equation: \( \frac{p}{5} - 2 = 6 \)
Show inverse operation steps:
Target: Undo -2, then ×5
Answer:
Two-Step Equations • Instructional Prep Page Turn page for the 5 official accuracy trials →
Formal Assessment Criterion: ≥ 75% (4 of 5 Correct)
Five-Problem Accuracy Trials
Student:
Trial Date:
Solve each equation below. Use the visual step organizer to show your inverse operation steps and verify your answer.
Trial 1 \( 5x + 8 = 38 \)
Score: Correct Incorrect
Step 1: Undo Addition / Subtraction
Step 2: Undo Multiplication / Division
Step 3: Solution & Check
x = ______
Check: 5(__) + 8 = 38
Trial 2 \( 3y - 7 = 14 \)
Score: Correct Incorrect
Step 1: Undo Addition / Subtraction
Step 2: Undo Multiplication / Division
Step 3: Solution & Check
y = ______
Check: 3(__) - 7 = 14
Trial 3 \( \frac{n}{2} + 6 = 15 \)
Score: Correct Incorrect
Step 1: Undo Addition / Subtraction
Step 2: Undo Multiplication / Division
Step 3: Solution & Check
n = ______
Check: \(\frac{(\quad)}{2}\) + 6 = 15
Trial 4 \( 4a - 11 = 25 \)
Score: Correct Incorrect
Step 1: Undo Addition / Subtraction
Step 2: Undo Multiplication / Division
Step 3: Solution & Check
a = ______
Check: 4(__) - 11 = 25
Trial 5 \( \frac{w}{3} - 4 = 5 \)
Score: Correct Incorrect
Step 1: Undo Addition / Subtraction
Step 2: Undo Multiplication / Division
Step 3: Solution & Check
w = ______
Check: \(\frac{(\quad)}{3}\) - 4 = 5
Trial Performance & IEP Goal Data
Benchmark: 75% accuracy (4 of 5 trials)
Mark Completed Trials:
T1 [ ] T2 [ ] T3 [ ] T4 [ ] T5 [ ]
Accuracy Score
____ / 5 = ____ %
Goal Status:
Met (≥ 75%) Emerging (< 75%)
Teacher / Evaluator Notes:
