Equivalent Equations Exit Ticket
Formative Assessment
Equivalent Equations
Quick Exit Ticket • Distributive Property & Like Terms
Student Name
Date
Directions: For each equation below, analyze the algebraic steps (distributing and combining terms). Select exactly TWO equivalent equations from the choices provided.
1 Which equations are equivalent to the equation below?
Select TWO
\[20(7 - d) + 11d = 113\]
\(140 - d + 11d = 113\)
\(140 - 20d + 11d = 113\)
\(140 + 10d = 113\)
\(140 + 9d = 113\)
\(140 - 9d = 113\)
2 Which equations are equivalent to the equation below?
Select TWO
\[15(6 - x) + 8x = 74\]
\(90 - x + 8x = 74\)
\(90 - 15x + 8x = 74\)
\(90 + 7x = 74\)
\(90 - 7x = 74\)
\(90 - 23x = 74\)
3 Which equations are equivalent to the equation below?
Select TWO
\[12(8 - y) + 5y = 81\]
\(96 - y + 5y = 81\)
\(96 - 12y + 5y = 81\)
\(96 - 7y = 81\)
\(96 + 7y = 81\)
\(96 - 17y = 81\)
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Equivalent Equations Answer Key
Teacher Resource • Answer Key & Diagnostic Guide
Equivalent Equations Key
Formative Assessment Grading • Distributive & Combining Terms
Subject: Algebra 1 / Grade 8 Math
Target Errors: Distribution & Negatives
How to use this key: Use this single-page key to quickly grade student exit tickets. It identifies the correct choices and tracks exact misconceptions for any incorrect choices made.
1 Original Equation: \(20(7 - d) + 11d = 113\)
Correct Answers: B & E
\(140 - d + 11d = 113\) Distributive Error: Missed multiplying second term \((-d)\) by 20
\(140 - 20d + 11d = 113\) [CORRECT] Distributed step correctly
\(140 + 10d = 113\) Combining Error: Simple adding/subtracting error
\(140 + 9d = 113\) Sign Error: Subtracted 11 from 20 but gave positive sign (\(+9d\))
\(140 - 9d = 113\) [CORRECT] Fully simplified equivalent form
2 Original Equation: \(15(6 - x) + 8x = 74\)
Correct Answers: B & D
\(90 - x + 8x = 74\) Distributive Error: Missed multiplying second term \((-x)\) by 15
\(90 - 15x + 8x = 74\) [CORRECT] Distributed step correctly
\(90 + 7x = 74\) Sign Error: Combined \(-15x + 8x\) to get positive \(+7x\)
\(90 - 7x = 74\) [CORRECT] Fully simplified equivalent form
\(90 - 23x = 74\) Combining Error: Added terms ignoring signs (\(-15 - 8\))
3 Original Equation: \(12(8 - y) + 5y = 81\)
Correct Answers: B & C
\(96 - y + 5y = 81\) Distributive Error: Missed multiplying second term \((-y)\) by 12
\(96 - 12y + 5y = 81\) [CORRECT] Distributed step correctly
\(96 - 7y = 81\) [CORRECT] Fully simplified equivalent form
\(96 + 7y = 81\) Sign Error: Combined \(-12y + 5y\) to get positive \(+7y\)
\(96 - 17y = 81\) Combining Error: Added terms ignoring signs (\(-12 - 5\))
Single-page quick diagnostic key matching the streamlined Exit Ticket Answer Key
