6th Grade Equivalent Expressions and the Distributive Property Test with Point Values (PDF)

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

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This grade 6 equivalent expressions test 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.

This 45-minute test has 9 questions worth 20 points. It covers the distributive property, factoring, combining like terms, and testing equivalence (Common Core 6.EE.A.3 and 6.EE.A.4). Show your work for full credit.

Time and points

About this test

Grade: Grade 6
Chapter: Equivalent Expressions and the Distributive Property
Standards: 6.EE.A.3, 6.EE.A.4
Time: 45 minutes
Total: 20 points

Grade 6 equivalent expressions test: questions

Question 1 – Distributive property [2 pts]

Write \(7(x + 2)\) without parentheses.
Write \(4(3a – 5)\) without parentheses.

Question 2 – Factor [2 pts]

Write \(18 + 24y\) as a product of the GCF and a sum.
Write \(9m – 6\) as a product of the GCF and a difference.

Question 3 – Combine like terms [2 pts]

Simplify \(6x + 4 + 2x – 1\).

Question 4 – Area model [2 pts]

Rectangle with height 3.

Write two equivalent expressions for the area of the rectangle shown.

Question 5 – Equivalent or not [2 pts]

Are \(4(x + 1)\) and \(4x + 4\) equivalent? Explain using the distributive property or by testing \(x = 3\).

Question 6 – Spot the error [2 pts]

A student’s answer.

A student writes 5(x + 3) = 5x + 3. Explain the mistake and write the correct expression.

Question 7 – Simplify [2 pts]

Simplify \(4(x + 2) + 3x\).

Question 8 – Fencing [3 pts]

A garden.

A garden is a rectangle with length x + 4 feet and width 3 feet. Write two equivalent expressions for the perimeter. Then find the perimeter when x is 6.

Question 9 – Multi-step simplify [3 pts]

Simplify \(2(5x – 3) + 4(x + 2)\). Check with \(x = 1\).

Key facts behind this grade 6 equivalent expressions test

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

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 6 chapters: Grade 6 math.

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