6th Grade Equivalent Expressions and the Distributive Property Test Solutions and Scoring (PDF)

6th Grade math test solutions: Equivalent Expressions and the Distributive Property – Maths PDF

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This grade 6 equivalent expressions test answers for 6th Grade covers equivalent expressions and the distributive property (Common Core 6.EE.A.3, 6.EE.A.4), with a free PDF to print.

Use this key to score the equivalent expressions test out of 20 points. Each solution is fully worked, and the scoring line explains how to award each point and partial credit for correct steps.

Grade 6 · Common Core State Standards: 6.EE.A.3, 6.EE.A.4

Grade 6 equivalent expressions test answers: worked solutions

Question 1 – Distributive property [2 pts]

(a) \(7x + 14\). (b) \(12a – 20\).

Scoring: 1 point for each expression.

Question 2 – Factor [2 pts]

(a) GCF 6: \(6(3 + 4y)\). (b) GCF 3: \(3(3m – 2)\).

Scoring: 1 point for each expression.

Question 3 – Combine like terms [2 pts]

\(6x + 2x = 8x\) and \(4 – 1 = 3\).

\(8x + 3\)

Scoring: 1 point for the x-terms; 1 point for the constants.

Question 4 – Area model [2 pts]

\(3(x + 6)\) and \(3x + 18\).

The area is 3x + 18.

Scoring: 1 point for each expression.

Question 5 – Equivalent or not [2 pts]

\(4(x + 1) = 4x + 4\) by the distributive property.

Test: \(4(3 + 1) = 16\) and \(4 \cdot 3 + 4 = 16\).

Yes, equivalent.

Both are 16.

Scoring: 1 point for the method; 1 point for the correct conclusion.

Question 6 – Spot the error [2 pts]

The student did not multiply 3 by 5. \(5(x + 3) = 5x + 15\).

Scoring: 1 point for the explanation; 1 point for the correct expression.

Question 7 – Simplify [2 pts]

\(4x + 8 + 3x = 7x + 8\).

Scoring: 1 point for distributing; 1 point for combining.

Question 8 – Fencing [3 pts]

\(2(x + 4) + 2 \cdot 3 = 2x + 8 + 6 = 2x + 14\).

For \(x = 6\): \(2 \cdot 6 + 14 = 26\).

Scoring: 1 point for each equivalent expression; 1 point for 26 feet.

Question 9 – Multi-step simplify [3 pts]

\(2(5x – 3) = 10x – 6\) and \(4(x + 2) = 4x + 8\).

\(10x – 6 + 4x + 8 = 14x + 2\).

Check: \(2(2) + 4(3) = 16\) and \(14 + 2 = 16\).

Scoring: 1 point for each distribution; 1 point for the final expression.

Total score

Total

20 points

Key facts behind this grade 6 equivalent expressions test answers

Key facts

Equivalent expressions have the same value for every value of the variable.
Distributive property: a(b + c) = ab + ac.
Like terms have the same variable part and can be combined.
Factor out the GCF to reverse the distributive property.
Substitute values to test whether two expressions are equivalent.

How to use this grade 6 equivalent expressions test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 6 chapters: Grade 6 math.

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