Area and the Distributive Property

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SWBAT: • Define product, sum, and distributive property • Represent the area of a rectangle whose sides may be variables • Identify and create equivalent expressions by using the distributive property • Use area models to help factor an expression

Big Idea

The area of a rectangle is x^2 + 10x. How can you represent this area as a product? Students apply their knowledge of area and the distributive property to expand and factor algebraic expressions.

Do Now

7 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.   Today I want students to review the work students did with equivalent numerical expressions in the first unit of the year.  I want to see if students can apply their knowledge of area and order of operations to identify the correct expressions.  A common mistake is for students to think that the two expressions in problem 2 are equivalent.  I push students to use their knowledge of order of operations to prove that they are not equivalent.

I call on students to share their ideas.  I call on other students to share whether they agree or disagree with their classmates and why.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Vocabulary Review

8 minutes

We fill out these notes together.  I ask students how the picture connects to perimeter and area.  I want students to realize that the amount of fence represents the perimeter of the yard while the amount of grass represents the area of the yard. 

We review the distributive property.  I want students to be able to see that the distributive property says that the product a(b+c) can also be represented by the sum of ab +bc.  In the past, students have been able to add the two values inside the parentheses and then multiply it by the outside factor.  Today we are working with variables, so students will not be able to do this.  

Area and Length Expressions

7 minutes

We work on these problems together.  I ask students how we can represent the area of a rectangle that is 3 units by a units.  If students struggle, I remind them of their work with the algebra tiles.  When we tripled x, the result was 3x. 

Students complete the rest of the problems independently.  They participate in a Think Pair Share to share and compare their work.  I present the answer to problem four as 2x.  This is a common mistake and I want students to recognize that x times x results is x squared, not 2x.  

Group Work

18 minutes


  • Before this lesson, I use the data from the previous lesson’s ticket to go to Create Homogeneous Groups.
  • I use a Group Work Rubric with each group to give students feedback on their cooperation and behavior.
  • I Post a Key so groups can check their work as the complete problems.

I explain that they are going to be working with their group to apply the distributive property to finding the area of figures.  This work is not easy, but their work with algebra tiles and number tricks will help them.  I explain that when their group completes a page they need to raise their hands and check in with me before moving on.  Students move into groups and I pass out the Group Work Rubrics. 

As students work I walk around and monitor student work and behavior.  Students are engaging in MP1: Make sense of problems and persevere in solving them and MP7: Look for and make use of structure.

Some students may initially say they are confused and that they don’t understand the problems.  I tell them to look at their notes and use their group members to help them.  I want students to use the resources that they have to help them reason through the problems.

If a group successfully completes a page, I briefly scan their work and send them to the key.   If students successfully complete all of the work, they move on to the challenge problems.

Closure and Ticket to Go

10 minutes

I ask students to flip to challenge problem 3.  Students participate in a Think Pair Share.  I want students to apply their knowledge of the distributive property to factor this expression in multiple ways.  If students struggle, I encourage them to draw their own rectangle to model the problem.  I call students up to share their ideas and show their work under the document camera.  Students are engaging in MP3: Construct viable arguments and MP7: Look for and make use of structure.

I pass out the Ticket to Go and the Homework.