Factoring numerical sums using the distributive property is an essential Grade 6 math skill that connects greatest common factors (GCF) with equivalent numerical expressions. This printable worksheet guides students through rewriting sums of whole numbers as products, using the greatest common factor to produce a fully factored expression.

Students move beyond simply finding common factors. They practice choosing the largest common factor, dividing each addend correctly, and checking that the numbers remaining inside parentheses have no common factor greater than 1. For example, 36 + 24 can be rewritten as 12 × (3 + 2). This approach builds a clear connection between whole-number factors and the distributive property.

From Finding Factors to Complete Factoring

The worksheet begins with a short lesson introduction explaining the reverse distributive property and how to factor numerical sums completely. Students then apply the method to whole numbers from 1 to 100, progressing from direct calculations to checking and justifying equivalent expressions.

The activities include:

• GCF factoring practice: Find the greatest common factor and rewrite each numerical sum as an equivalent product.
• Multiple-choice questions: Identify the correctly factored form among plausible alternatives.
• Expression sorting: Classify numerical expressions according to whether they are equivalent to a given sum.
• Error analysis: Examine fictional students' work, identify mistakes involving common factors or division, and correct the solutions.
• Written explanations: Justify why an expression is equivalent to the original sum and whether it is fully factored.

Why Complete Factoring Matters

Students sometimes use a common factor without checking whether it is the greatest common factor. An expression such as 6 × (4 + 6) is equivalent to 24 + 36, but it is not completely factored because 4 and 6 still share a common factor. The worksheet addresses this distinction directly, giving learners opportunities to recognize incomplete factoring and explain how to correct it.

Other questions focus on accurate division when taking out the GCF. By analyzing incorrect solutions, students can see why both addends must be divided by the same factor to preserve the original value.

What Is Included

• A printable Grade 6 math worksheet focused on numerical sums and the distributive property.
• Introductory lesson notes with a worked factoring example.
• Practice involving equivalent products, common factors, and mathematical reasoning.
• Student Notes lines at the bottom of the worksheet.

Classroom Teaching Ideas

Use the introductory notes during a lesson on the greatest common factor, then assign the factoring exercises for individual practice. The expression-sorting activity works well for checking whether students can recognize equivalent forms, while error-analysis questions provide useful discussion prompts for small groups.

The written reasoning tasks can also serve as a formative assessment, revealing whether students understand the difference between an equivalent expression and a completely factored expression.

Curriculum connection: Common Core Mathematics 6.NS.B.4, including using the distributive property to express a sum of whole numbers with a common factor as a multiple of a sum with no common factor.