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.
Finding the Area
In today's lesson, students will begin constructing rooms in their made up house plans. Over the next two days, students will use a guide to determine the appropriate sizes of rooms. Then they will begin creating these rooms based on length and width dimensions. This will set the foundation for finding area of each room and the entire house in future lessons.
To prepare for today's lesson, I build a model house ahead of time using grid paper, cardboard, and cardstock. I create this model house plan using my own house as I knew students would be more interested:
I tape graph paper together and create a basic plan of my house. Each square represents one foot squared.
I cut around the house plan to tape it on cardboard.
Next, I cut strips of white card stock for walls.
To fold the walls, I line up a white card stock strip, mark with a pencil, and fold.
I tape the strips together and secure the strips to the house plan.
Using this method, I enclose each room. For fun, I made little flaps for doors.
It was easiest to work from one side of the house to another (instead of putting all exterior walls in place first).
Interior House Video
I want to make sure students can visualize every room so I set out to make a video of my house. However, I find a video of the interior of my home on YouTube. Sometime relators post videos online: My House Video.
I begin by showing students My House Video. While the video plays, I explain how I want to update my house with new paint and new flooring. For the purpose of this lesson, I focused on the flooring itself.
I then show students my model home. I allow time for students to ask questions and to share stories. This is all part of heightening student engagement!
At this point, we develop a simple definition for area as a class, Array: a rectangle with grids.
When I teach vocabulary, I try to use TPR (Total Physical Response). As a class, we will develop a simple definition for a vocabulary word as well as hand movements. TPR activates multiple parts of the brain and promotes a stronger memory connection. Often, students are able to recall the meaning of vocabulary words by recalling the hand movements.
Today, we discuss and come up with the following definition and hand movements: Array! A rectangle (draw a rectangle in the air) with grids (make grid lines in the rectangle).
Next, we practice the new vocabulary word several times. To review the meaning of area, throughout the unit I say, Turn and Talk: What is an array? Students will use the hand movements to recall the definition!
To help students recall the meaning of array throughout the rest of the year, I hang a vocabulary posters on our math wall: Array.
I excitedly announce to students: Guess what! You get to build your own houses today! Excitement fills the air! They couldn't wait! I invited students to the front carpet for a closer look at my example model home. I explained: First, you will need to make a floor plan using graph paper. In my plan, each of the squares represents one foot squared. This means that one side of each square represents one foot. To demonstrate this, I grab four rulers and make a square using the rulers.
Starting with the Living Room
In order to scaffold this huge project and break the tasks down into smaller parts, I ask students to start planning the living room first. I ask students to turn and talk: How big should a living room array be? What do you need to help you make more informed building decisions? After some time, a student suggests, "We need to look up how big living rooms are!" Another student suggests, "We can go measure our living rooms tonight." This was the perfect opportunity to pass out the Room Sizes Guide to each student (found at the following link).
Using the Room Sizes Guide, students point out that a large living room would measure 22 x 28 feet and that a small living room would measure 12 x 18 feet. Some students ask if they can create a great room instead or a family room, so I open up the options to include a living room, family room, or great room. I knew students would love having more choices!
Next, I ask students to turn and talk: Where should your living room go in your house? I ask this question because I know that some students will create the living room in the very middle of their graph paper, leaving little room for others rooms in the house! We discuss the layout of different houses. For example, one student plans to place her great room right next to the front entrance because her house is set up that way.
I create the following checklist on the board to provide students with clear assignment expectations. Students don't write it down anywhere... it's just a way for students to monitor their own learning!
1. Living room is drawn correctly, walls are straight and on the lines
2. Length is correctly labeled (Example: 18 ft)
3. Width is correctly labeled (Example: 12 ft)
4. Room is labeled (Explain: beginning with capital letters)
I pass out one piece of graph paper per student and show students how they can tape extra pieces of graph paper together later on if needed. Students got right to work!
Common Core Connection
While this task may seem simple, this lesson is taught during the first month of school. In fact, students are truly engaged in Math Practice 1 (Make sense of problems and persevere in solving them) as they are having to make many decisions about room type, room size, door placement, room location in the house, etc.
Monitoring Student Understanding
Once the class began working, I conference with as many students as possible. My goal is to support students by providing them with the opportunity to explain their thinking and by asking guiding questions. I also want to encourage students to construct viable arguments by using evidence to support their thinking (Math Practice 3).
Also, I encourage students to take doorways into consideration. For example, if a student has a 20 foot wall separated into three sections (wall + doorway + wall), I ask students to label eact section separately. This was a great opportunity to discuss the average size of doorways (3 feet).
One student has a 10 foot wall, then a 3 foot doorway, and then another 7 foot wall. However, he labels the 10 foot wall "20 feet." The student simply ask, "So what you are saying is that this wall is 20 feet, right?"
I will often show students my example model house or the blueprints for my house, and they quickly realize what they need to do.
Here's a sample of a living room: Living Room Example. This student earned all 4 points for meeting the above expectations.
As students finish, I ask them to walk around the room and check their points with three students. This provides me with a little more time to help struggling students and to check for student understanding.