Find the Area of the Model House Day 3

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

Big Idea

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

Teacher Demonstration

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 continued finding the area of your home plan by focusing on one room at a time. Today, we are going to continue the same process. Remember... if we want to figure out how much flooring we need for our home plans, we first have to find the area of each room! 

Grid Paper

I pass out a couple pieces of grid paper to each student and explain: Today, we are going to continue finding the area of all the remaining rooms in our houses so that we can walk into a store like Home Depot and successfully get flooring! 

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 a prior lesson, 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 revisit a list of required rooms on the board from yesterday's lesson. All students already have these six rooms in their home plans. Many students went on to create even more rooms! I explain: Today, I'd like for you to finish finding 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.

Student Practice

70 minutes

Calculating Square Footage Chart

I pass out the Calculating Square Footage chart so that students can begin keeping track of the area of each room in their houses. I model how to complete the chart by filling in the following into each of the columns:

  • Room: Living Room
  • Expression: (10 x 15) + (2 x 15)
  • Area: 180 feet squared

Students follow along using recorded information from their math journals from the last couple of lessons. They love having a way to organize all of the rooms!

Students then move on to finding the area of their next rooms. As I walk around, I am so proud of students diligently working: Student Decomposing Rooms.

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). 

  1. What did you do first? 
  2. Can you explain why you _____? 
  3. What do you see?
  4. What did you just learn?
  5. 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 Work

Here are two examples of the Calculating Square Footage Chart: Student Chart Example and Student Chart Example 2.

Some students finish the six required rooms and move onto other rooms: Higher Level Student Example.