SWBAT use smaller rectangles to find the area of a room.

Decomposing is a useful strategy that helps students find the area of larger rectangles.

20 minutes

**Unit Explanation**

During the first section of this unit, students will construct a house plan, find the area of the house plan, and calculate flooring costs. While finding the area is the focus of this unit, the first few lessons (where students explore the meaning of a polygon, construct house plans, and decompose rectangles into smaller rectangles to find the area) lay the foundation for finding the area of their home plans later on. This also provides students with a meaningful and purposeful context to find the area.

During the second section of this unit, students will investigate dog pen designs and will primarily focus on finding the perimeter, or amount of fencing needed for different dog pens. Students will also explore odd-shaped polygons by finding the area and perimeter of odd-shaped dog pens.

**Goal & Introduction**

I begin by reviewing our learning goal: *I can use smaller rectangles to find the area of a room. *I explain: *Yesterday, you all chose a room from your home plan to decompose into smaller rectangles in order to find the total area of the room. Can anyone remind me why we're finding the area of our home plans? *A student says, "Because we are going to pick out flooring and we need to know how big each room is to buy flooring."

**Grid Paper**

I pass out a couple pieces of grid paper to each student and explain: *Today, we are going to find the area of all the other rooms in our houses so that we can walk into a store like Home Depot and successfully get flooring! Remember how we reconstructed one room yesterday using grid paper? First, you determined the length and width of the room in your home plan. Then, you created the same room on grid paper. This way, you could use scissors to decompose the room into smaller rectangles! *

**Grid Paper Explanation**

During previous lessons, all students created a home plan like this example: House with Walls Example 1. If a student has a dining room that is 12 x 9 in her home plan, she cuts out a 12 x 9 rectangle using grid paper: Example of Cutting out Room. She will then be able to decompose her room into smaller rectangles with a pair of scissors: Example of Decomposing Room.

Why the grid paper? I want students to be able to work with and focus on one room away from the rest of the house plan outside of the confined space in-between walls. I also want students to be able to find the area of the room by physically cutting the room into smaller rectangles.

**Getting Ready**

I ask students to get ready by getting their student math journals and home plans. Referring to the anchor chart from yesterday, Anchor Chart: Decomposing Rooms, I review the math journal entry process that I want students to complete for each of the remaining rooms in their home plans:

1. Room Name

2. Decompose using Grid Paper

3. Equation

4. Total Area

I purposefully skip the step 5 explanation on the anchor chart. If I required an explanation on each room, students would get tired easily and lose the motivation to complete the task. Also, I didn't want this assignment to drag on for too long!

Here's an example of the expected student journal entry: Dining Room Example.

**Required Rooms**

Next, I write a list of the required rooms on the board. All students already have these six rooms in their home plans. Many students went on to create even more rooms! I explain: *For the next couple of days, I'd like for you to find the area of the required rooms first. If you get done early, you can find the area of the remaining rooms in your house as well. *This gives students an attainable goal while at the same time, higher-achieving students can "go above and beyond" by finding the area of every room.

1. Living Room

2. Kitchen.

3. Dining Room

4. Bathroom

5. Laundry Room

6. Bedroom

**Common Core Connection**

This lesson is a great way to engage students in Math Practice 4: Model with mathematics as students are solving a real-world problem arising in everyday life as they determine the area of a home to figure out flooring costs. Ultimately, students learn more when math is meaningful and connected to the real world.

70 minutes

To set students up for success, I suggest that students begin with smaller rooms and work their way up to the larger rooms.

Students don't waste any time getting right to work!

**Monitoring Student Understanding**

Once students begin working, I conference with every group. My goal is to support students by asking guiding questions (listed below). I also want to encourage students to construct viable arguments by using evidence to support their thinking (Math Practice 3).

- What did you do first?
- Can you explain why you _____?
- What do you see?
- What did you just learn?
- Are you using friendly numbers? How do you know?

More specifically, here's what I look for as I conference with individual students today:

**Decomposing**** Look-Fors**

- Did the student cut the room into smaller rectangles?
- Are the dimensions labeled?
- Does the student specify the measuring unit (ft)?
- Did the student find the area of each rectangle?
- Did the student correctly add the areas of the smaller rectangles to get the area of the room?

**Equation Look-Fors**

- Does the student have only one equals sign?
- Does one side of the equation equal the other?

**Area Look-Fors**

- Did the student correctly label the area, such as "square feet" or "feet squared?"
- Did the student calculate the area correctly?
- Does the student have a solid understanding of the goal?

**Student Conferencing**

During one conference with one student, I notice he is confused about one square foot vs. one foot. We make a model together and then I ask him to explain it to another student: One Foot vs One Square Foot. I was so proud of him! To help solidify this concept, I ask him to measure the area of our classroom rug using a square foot: Measuring the Area of our Rug.

**Student Journal Examples**

Decomposing a Kitchen.jpg: This student does a great job decomposing a 14' x 7' room using friendly numbers: (10 x 7) + (4 x 7) = 98 feet squared.

Decomposing a Living Room.jpg: This student shows how to decompose a 7 x 12 into several smaller rectangles: 4(2 x 12) + (3 x 9) + (3 x 3). This gets a little complicated, but in the process, her number sense is certainly growing!

Decomposing a Dining Room.jpg: This student does a beautiful job decomposing the 10 x 12 dining room into (10 x 10) + (10 x 2), but miscalculates the total area.

Decomposing a Bedroom.jpg: This student decides to decompose a 16 x 16 bedroom into four rectangles: (10 x 10) + (10 x 6) + (6 x 6) + (10 x 6) to get a total area of 256 square feet.