Equation Blueprint Reference Sheet Equation Blueprint
One-Step Mastery Reference
KEEP IT BALANCED!
The Golden Rule
Whatever you do to one side of the equal sign, you must do to the other side .
Opposites
X
÷
Opposites
Addition & Subtraction
Example 1: Solving Addition
\(x + 12 = 30\)
\(- 12 \quad - 12\)
\(x = 18\)
Example 2: Solving Subtraction
\(y - 9 = 15\)
\(+ 9 \quad + 9\)
\(y = 24\)
Multiplication & Division
Example 3: Solving Multiplication
\(5m = 45\)
\(\div 5 \quad \div 5\)
\(m = 9\)
Example 4: Solving Division
\(\frac{k}{4} = 6\)
\(\cdot 4 \quad \cdot 4\)
\(k = 24\)
The Solving Blueprint: Step-by-Step
1
LOCATE
Find the variable and identify the operation happening to it.
2
INVERSE
Choose the opposite operation to "undo" the work.
3
BALANCE
Apply the operation to BOTH sides of the equal sign.
4
VERIFY
Plug your solution back in to make sure it works!
Project: Algebraic Foundations
Drawing No: EQ-01
Sheet: Reference A
Blueprint Practice Worksheet Blueprint Practice
Building Equation Mastery
Student:
Period:
Date:
Instructions: Use the Blueprint Boxes below to solve each one-step equation. For each problem, identify the operation, apply the inverse to both sides, and verify your solution.
SPEC 01: ADDITION \(x + 14 = 32\)
OP: ____________
INV: ____________
Solving Area
\(x =\)
Check:
SPEC 02: SUBTRACTION \(y - 18 = 45\)
OP: ____________
INV: ____________
Solving Area
\(y =\)
Check:
SPEC 03: MULTIPLICATION \(7m = 63\)
OP: ____________
INV: ____________
Solving Area
\(m =\)
Check:
SPEC 04: DIVISION \(\frac{k}{5} = 12\)
OP: ____________
INV: ____________
Solving Area
\(k =\)
Check:
Project: Algebraic Foundations
Drawing No: EQ-02
Sheet: Work Package A
SPEC 05: MIXED \(x + 23 = 5\)
OP: ____________
INV: ____________
Solving Area
\(x =\)
Check:
SPEC 06: MIXED \(9h = 108\)
OP: ____________
INV: ____________
Solving Area
\(h =\)
Check:
Construction Challenge
Write and solve your own one-step equation using division. Show all your blueprint steps!
Custom Solving Area
Project: Algebraic Foundations
Drawing No: EQ-02
Sheet: Work Package B
Blueprint Practice Answer Key Answer Key
Blueprint Practice - Internal Use Only
TEACHER FILE
SPEC 01 \(x + 14 = 32\)
OP: Addition
INV: Subtraction (-14)
\(x = 18\)
Check: \(18 + 14 = 32\) (Correct)
SPEC 02 \(y - 18 = 45\)
OP: Subtraction
INV: Addition (+18)
\(y = 63\)
Check: \(63 - 18 = 45\) (Correct)
SPEC 03 \(7m = 63\)
OP: Multiplication
INV: Division (÷7)
\(m = 9\)
Check: \(7(9) = 63\) (Correct)
SPEC 04 \(\frac{k}{5} = 12\)
OP: Division
INV: Multiplication (×5)
\(k = 60\)
Check: \(60 / 5 = 12\) (Correct)
SPEC 05 \(x + 23 = 5\)
OP: Addition
INV: Subtraction (-23)
\(x = -18\)
Check: \(-18 + 23 = 5\) (Correct)
SPEC 06 \(9h = 108\)
OP: Multiplication
INV: Division (÷9)
\(h = 12\)
Check: \(9(12) = 108\) (Correct)
Challenge Problem Key
The challenge problem is open-ended. Ensure students have:
Created a one-step equation using division (e.g., \(x/4 = 3\)).
Identified the operation (Division) and the inverse (Multiplication).
Correctly solved for the variable.
Checked their work by plugging the result back in.
