Lesson objective: Fluently use the distributive property and the greatest common factor to write equivalent expressions.

This lesson helps to build fluency with the distributive property. Prime factorization is used here because it supports finding the greatest common factor of two numbers in an efficient manner. This work develops students' understanding that writing a sum of two products is equivalent to** **the product of their greatest common factor and the sum of their remaining factors.

Students engage in Mathematical Practice 7 (look for and make use of structure) as they understand the structure of a factored expression to be a equivalent to the sum of each addend with common factors. Students will break numbers down into products with common factors and will also break numbers down into prime factors to find the greatest common factor.

**Key vocabulary:**

- distributive property
- equivalent expression
- greatest common factor