Algebra Blueprint Worksheet Algebra Blueprint
Topic: Systems of Equations (Substitution)
Name:
Date:
Phase 1: Warm-up
Solve the multi-step equation below. Show every step!
2(x + 3) = 10
Phase 2: Video Investigation
The 5 Steps of Substitution
1
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2
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3
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4
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5
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Example 1: Standard Case
y = 10 - x
Follow along with the video to solve.
The "Check" Step
Why does Justin emphasize checking your work?
Phase 3: Blueprint Practice
Practice A: The Direct Path Guided
y = 2x + 1
Step 1: y is already isolated. Substitute (2x+1) for y in the second equation.
Practice B: The Isolation Chamber With a Partner
x - y = 3
Hint: Neither variable is isolated yet. Which equation and which variable is the easiest to get by itself?
Phase 4: Substitution Relay
Collaborative Task
Rules: Partner A solves Step 1, then passes the paper. Partner B solves Step 2, and so on. Check each other's work before moving on!
System: y = x - 4 and 2x + y = 5
Step 1: Substitute & Solve for x
Step 2: Plug back in & Solve for y
Step 3: State Solution & Verify
System: x = 2y + 6 and 3x - 4y = 28
Step 1: Substitute & Solve for y
Step 2: Plug back in & Solve for x
Step 3: State Solution & Verify
Substitution Solution Slides 8th Grade Mathematics
Substitution
Solution
Solving Systems of Linear Equations Algebraically
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Phase 1: Warm-up
Review: Solving multi-step equations with one variable.
2(x + 3) = 10
1 Distribute the 2
2 Subtract from both sides
3 Divide to isolate x
Phase 2: Video Investigation
Watch & Learn
Embedded media
Pause at 1:13 (Steps)
Pause at 3:10 (Example 1)
Pause at 6:21 (Special Cases)
The Substitution Method
1
Isolate a variable in one equation.
2
Substitute that expression into the other equation.
3
Solve the new equation for the single variable.
4
Plug the value back in to find the second variable.
5
Verify your solution in both original equations.
Phase 3: Standard Case
Class Demo Problem
y = 2x + 1
Step 1 & 2: Substitute
3x + (2x + 1) = 11
The Goal
We want to turn two equations into ONE equation with only ONE variable.
Phase 4: Substitution Relay
Partner A
Substitutes the expression and solves for the first variable.
The Pass
Hand the paper to your partner. They check your math first!
Partner B
Plugs the value back in to solve for the second variable.
System Solve Exit Ticket Exit Ticket
Solving Systems: Substitution
Name:
Target: 8.EE.C.8.B
1
Solve the system of equations below using the substitution method.
y = 3x - 5
Show Your Work
2
Check Your Solution
Use the solution (x, y) you found in Problem 1 and plug it into both original equations to verify it is correct.
Verify in Equation 1:
Verify in Equation 2:
Final Solution
(_____, _____)
Substitution Teacher Guide Teacher Blueprint Guide
Lesson: Substitution Solution (8th Grade Math)
Lesson Pacing & Key Moments
Section Time Key Actions Warm-up 5 min Focus on the distributive property and isolating a variable. Video Viewing 10 min Pause at 1:13 (Steps), 3:10 (Checking), and 6:21 (No Solution). Guided Practice 15 min Model Practice A. Scaffolding Practice B by asking "which is easiest to isolate?". Relay Activity 10 min Partners must physically swap papers. Emphasize peer-checking. Exit Ticket 5 min Individual formative assessment.
Answer Key: Worksheet
Warm-up:
2(x + 3) = 10 → 2x + 6 = 10 → 2x = 4 → x = 2
Practice A:
3x + (2x + 1) = 11 → 5x = 10 → x = 2. Plug in: y = 2(2) + 1 = 5. Solution: (2, 5)
Practice B:
Isolate x: x = y + 3. Substitute: 2(y + 3) + 3y = 21 → 2y + 6 + 3y = 21 → 5y = 15 → y = 3. x = 3 + 3 = 6. Solution: (6, 3)
Relay Problem 1:
2x + (x - 4) = 5 → 3x = 9 → x = 3. y = 3 - 4 = -1. Solution: (3, -1)
Common Misconceptions
Distributive Error:
Students often forget to distribute a negative sign when substituting (e.g., -3(10-x) becomes -30-3x instead of -30+3x).
Substitution Choice:
Students may substitute an expression into the same equation they used to isolate the variable, resulting in an identity like 6=6.
The Half-Finished Answer:
Remind students that a solution to a system is an ordered pair (x, y) , not just one variable.
Exit Ticket Key
System:
y = 3x - 5
Steps:
2x + (3x - 5) = 15x = 4
y = 3(4) - 5 = 12 - 5 → y = 7
Final Answer: (4, 7)
