Distributive Property with GCF


With our Distributive Property with GCF lesson plan, students learn how to find the greatest common factors and least common multiple and then use them with the distributive property.

Included with this lesson are some adjustments or additions that you can make if you’d like, found in the “Options for Lesson” section of the Classroom Procedure page. One of the optional additions to this lesson for more advanced students is to add in more than two terms to find the GCF or increase the quantity of variables.

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What our Distributive Property with GCF lesson plan includes

Lesson Objectives and Overview: Distributive Property with GCF teaches students how to find the greatest common factor and then use it with the distributive property. At the end of the lesson, students will be able to find the greatest common factor and the least common multiple and then apply it to the distributive property. This lesson is for students in 6th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. If your students are more advanced, you can add in more than two terms to find the GCF or increase the quantity of variables. You could have any students who struggle with multiplication use a multiplication table to help them find the GCF. Finally, you can teach your students how to find the GCF on their calculators.

Teacher Notes

The teacher notes page includes a paragraph with additional guidelines and things to think about as you begin to plan your lesson. This page also includes lines that you can use to add your own notes as you’re preparing for this lesson.


Distributive Property with GCF

The Distributive Property with GCF lesson plan includes three content pages. The distributive property states that a(b + c) = ab + ac. Though this looks like a complicated equation, it’s actually quite easy to use with a little practice. This equation tells us that you can distribute the multiplication (by a) over the sum (b + c), multiplying the numbers b and c separately by a before adding them together as the last step.

Many students will have used the distributive property before without even realizing it. For example, you can rewrite 4 x 26 as 4(20 + 6). To solve the problem this way, you multiply 20 and 6 by 4 separately and then add those sums together: 4 x 20 + 4 x 6 = 80 + 24 = 104.

Greatest Common Factor (GCF)

To express a sum as a product, you can find the greatest common factor (GCF). You can do this using something called prime factorization. The lesson shows an example of this. For the problem 20 + 15, you use prime factorization to find the GCF, or the largest number that they have in common. 5 is the GCF for these two numbers because it’s the only number in common. The GCF is 5, so 5 goes outside of the parenthesis. To figure out what goes inside the parenthesis, you should think of what number you need to multiply by the GCF to get the original numbers. 5 x 4 = 20 and 5 x 3 = 15, so the final equation is 20 + 15 = 5(4 + 3).

The lesson includes another example to illustrate this concept before diving into factoring, which is when we use the distributive property backwards. For example, we can look at the expression 5x + 10 and rewrite it as 5(x + 2). To do this, we took the sum (5x + 10) and rewrote it as a product (5(x + 2)). A product is a factor times a factor; in this case, it’s 5 times the quantity (x + 1).

We can rewrite the sum 16x + 24 as the product 8(2x + 3). To check your work, you just need to multiply: 8 x 2x + 8 x 3 = 16x +24. The more you practice finding the GCF and using the distributive property, the better you’ll get!


The Distributive Property with GCF lesson plan includes three worksheets: an activity worksheet, a practice worksheet, and a homework assignment. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.


For the activity worksheet, students will first solve all of the problems on the worksheet on their own. They will then work in small groups to compare their answers and decide on a single answer to write on the tablecloth in front of them.


The practice worksheet asks students to complete two short exercises. For the first, they will use the GCF and the Distributive Property to express each sum as a product, showing their work. For the second, they will find the missing number in each equation.


For the homework assignment, students will use GCF and the Distributive Property to express each sum as a product.

Worksheet Answer Keys

This lesson plan includes answer keys for the activity worksheet, the practice worksheet, and the homework assignment. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

Additional information


6th Grade



State Educational Standards