Equivalent Expressions With the Distributive Property
Written by Adi Ackerman, Head Teacher
"Equivalent Expressions With the Distributive Property" is written for 6th Grade (Ages 11-12), and it covers Common Core 6.EE.A.3. If your student is a year younger but already steady on algebra, the page still works. You may just need to read the instructions out loud. And if they are older and equivalent expressions never quite stuck, this is a short review rather than busywork.
6th grade math worksheet: expand 8 expressions like 5(2y minus 3) and factor 8 more like 24a + 36 with the distributive property. Answer key included. Part of our equivalent expressions algebra collection. Aligned to Common Core standards.
How do I use this worksheet?
Start with terms, coefficients and constants so students can name the parts. Then do the distributive property and like terms pages, and use the matching page as a check.
What students will practice
- Students will expand 8 expressions with the distributive property, such as 3(x + 4) = 3x + 12.
- Students will factor 8 expressions using the greatest common factor, such as 12y minus 8 = 4(3y minus 2).
- Students will see that expanding and factoring write the same expression two equivalent ways.
Curriculum Links
Common Core State Standards
Expressions and Equations · 6th Grade
Standard: Apply the properties of operations to generate equivalent expressions.
View all 6.EE.A.3 worksheets →Find this in the curriculum
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FAQ
How do I use this equivalent expressions worksheet?
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Start with terms, coefficients and constants so students can name the parts. Then do the distributive property and like terms pages, and use the matching page as a check.
What does this worksheet teach?
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Expand 8 expressions like 5(2y minus 3) and factor 8 more like 24a + 36 with the distributive property. The distributive property lets you multiply each term inside the parentheses: 2(w + 9) = 2w + 18, and 2w + 18 factors back to 2(w + 9). The directions on the page read: Use the distributive property to write an equivalent expression. An answer key is included.
Can I use this equivalent expressions worksheet for homeschool or classroom?
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Yes, both. We made it for 6th Grade algebra, and the page works the same whether it lands on a kitchen table or a center rotation. At home, most families go through it together and talk the answers out loud, and that talking is where most of the learning happens with equivalent expressions. In class it runs well as independent work while you pull a small group. Print one copy or thirty, whichever the day needs.
What are equivalent expressions?
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They are expressions that have the same value no matter what number the variable is. 4(2x minus 1) and 8x minus 4 are equivalent because the distributive property turns one into the other.
How do you combine like terms?
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Add or subtract terms that have the same variable part, and add the constants separately. In 4x + 7 + 2x minus 3, the x terms make 6x and the constants make 4, so the expression simplifies to 6x + 4.
What is a coefficient?
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A coefficient is the number that multiplies a variable. In 7x + 3y minus 12, the coefficients are 7 and 3 and the constant is negative 12. A variable on its own, like b, has a coefficient of 1.
Is there an answer key?
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Yes. All 4 equivalent expressions worksheets have an answer key.
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