Lesson objective: Understand how we can use the distributive property and common factors to write equivalent expressions.

Students bring prior knowledge of properties of multiplication from Grade 3 (3.OA.5). This prior knowledge is extended to formalizing the distributive property as students build understanding of the eqivalency between *ab + ac *and *a(b+c)*. A conceptual challenge students may encounter is thinking they only multiply the first addend by the factor when distributing, when the factor is really being multiplied by the sum of the addends, so each addend needs to be multiplied by the factor. Students have this misconception due to not understanding that the expression 3(2+5) represents the same area model as 3x7.

The concept is developed through work with an area model, which help students form a concrete understanding of the abstract distributive property. This work helps students deepen their understanding of equivalence because they will explore how numbers can be decomposed in equivalent ways and how choosing the appropriate equivalence helps solve problems.

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they look at the structure of a factored or distributed expression and understand it to be a numerical way to express the equal relationship between the area models of the factors.

**Key vocabulary:**

- area model
- distributive property
- equivalent
- factor
- product
- sum