About This Worksheet
This worksheet helps sixth-grade students connect greatest common factor work with the distributive property. Students first find the GCF of each pair of addends, then factor that value out and rewrite the expression as a product. This shows them how common factors can be used to reorganize a sum without changing its value. The activity is an important bridge between number theory and algebraic thinking. It helps students see that factors are useful for more than just listing or comparing numbers.
What Students Practice
Students examine pairs of whole numbers in addition expressions and identify the greatest factor shared by both terms. They then divide each addend by the GCF and place the resulting values inside parentheses. This creates an equivalent expression in factored form using the distributive property. Students practice GCF, division, equivalent expressions, and mathematical structure all in the same problem. The repeated format also helps them recognize how a common factor can be “pulled out” of a sum.
Why This Matters
Factoring with the distributive property is one of the first places students see number theory connect directly to algebra. Instead of viewing GCF as an isolated skill, students learn that it can be used to rewrite expressions more efficiently. This prepares them for later work with algebraic factoring and equivalent expressions. It also strengthens their understanding that multiplication can be distributed over addition in both directions. Seeing that connection now makes more advanced algebra feel less unfamiliar later.
Teaching Tips
Have students find the GCF first and write it outside the parentheses before doing anything else. Then ask, “What do I multiply this GCF by to get each original addend?” Encourage students to check their work by distributing the outside factor back through the parentheses. If the original expression returns, they know the factoring was correct. This reverse check is a simple way to connect factoring and distribution as opposite processes.
Curriculum Standards
This worksheet directly supports CCSS.MATH.CONTENT.6.NS.B.4, which asks students to use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. The activity also reinforces finding greatest common factors as part of the same standard. Because students rewrite expressions into equivalent forms, it also supports early algebraic reasoning. It is well suited for classroom instruction, independent practice, homework, or review before students begin more formal algebraic factoring.