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.
Today, students will be choosing which flooring they want to install in each room of their home plans by estimating the cost of each. About a week before this lesson, I set out the following flooring samples: Flooring Options 1 and Flooring Options 2. I wanted to inspire student interest and excitement! Each time students line up, they walk by the samples. They can't help but touch them and begin thinking about their favorites!
To begin, I hold up the flooring samples and ask students to turn and talk: Which samples do you like? Why do you like them? Where would you like to install them?
I hear various repsonses from students, including:
"I want to install the maple hardwood floors in my kitchen. I like how it feels and I like the color!"
"I want the linoleum tiles. I really like tiles in the kitchen and the bathroom."
I then hold up the linoleum tile (Flooring Options 2) and ask them how many square feet I was holding. Students pause at first and then began guessing out loud. Several students guess, "One square foot." I grab a couple rulers and held them up to the length and width of the tile to show that it measures one square foot.
Then, we discuss how each sample of flooring is sold by the square foot, even though all samples weren't exactly one square foot.
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.
Real World Application
To really allow students to experience what it is like to pick out flooring at a local hardware store, I create several short clips and share them with students. They absolutely love watching each one!
Video 1: Walking into Home Depot.MOV
Video 2: Picking out Carpet.MOV
Video 3: Picking out Carpet 2.MOV
Video 4: Picking out Linoleum Tile.MOV
Video 5: Picking out Hardwood Flooring.MOV
Video 6: Picking Laminate Flooring.MOV
Lesson Development Challenge
At this point in the unit, I truly have difficulty determing the best learning path in alignment with the new Common Core Standards. Originally, I plan for students to calculate the cost of flooring per room by multiplying the area (such as 130 square foot room) by a decimal number (such as $2.39 per square foot for flooring). However, multiplying by decimal numbers is a 5th grade standard (not 4th)!
So, for this lesson, I decide to have students calculate the estimated cost per square foot for each type of flooring.
Note: Looking back on this unit, I wish that I would have just had the students use calculators to determine the exact cost to install flooring in each room of their home plan.
Goal & Introduction
I continue by sharing today's goal with students: I can estimate the cost of each type of flooring. I explain: Today, you are going to estimate the cost of each flooring type on the board. However, before you begin, we are going to practice estimating prices in a real-world setting... a garage sale! That's right, today... you are going to a garage sale! Turn and talk: Have you been to a garage sale? Do you like garage-saling?
While students were deep in conversation, I projected the following PowerPoint Presentation: Estimating Prices.
I ask: Who has gone to a garage sale before? Several hands shot up.
I continue: When you are at a yard sale, do you ever offer a lower price? Many students respond with great stories about times in which their parents offered less.
Well, I'm having a garage sale today! But all the prices are decimal numbers, like $1.56. The problem is... you only have whole dollars in your pockets. You're going to have to round to the nearest dollar and make me an offer!
I began going through the PowerPoint. On each slide, students raise their hands and ask, "Mrs. Nelson, would you take _____ ($2.00) for the ______ (basketball)?" If they correctly round to the nearest dollar, I will say, Why, yes, I would take $2.00! Students caught on quickly and the activity seems to be more of a review of what they already know than anything!
Students also keep track of their responses in their journals: Student Journal Example: Estimated Prices. This way, I can monitor who needs extra support. It also helps keep all students engaged.
In the middle of the lesson, one student shares a rounding rhyme she remembers from last year: Rounding Rhyme. I celebrate her for sharing and we all practice saying the rhyme together.
I want to also support student reasoning by creating a number line model: Number Line Estimation Model. While the rhyme can be a helpful reminder, I want students to be able to explain why they round up or down ($1.69 is $0.69 away from $1.00 while it's only $0.31 away from $2.00).
At this point, students were very excited to get their hands on these flooring samples! Students were eager just to hold the samples: Interacting with Flooring.
I first model how to organize estimated calculations in student journals. We make a three column chart altogether: Flooring, Actual Cost, Estimated Cost. Here's an example of a finished chart: Student Journal Example.
Estimating Flooring Costs
I pull popsicle sticks to determine team leaders. Then, I ask each team leader to choose which flooring sample they want their group to look at first. Anytime I can, I try to provide students with choices. This always increases student engagement.
Students work together to estimate the cost of each flooring type. When students are finished estimating, team leaders delivered the flooring sample to the next group. We rotate clockwise to eliminate confusion.
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).
Sometimes the more vocal students can take over in a group setting, leaving the quiet students out. I encourage students to involve everyone by asking the whole class: Who is making sure every group member is equally involved?... Who could do a better job at this?
In this video, Student Estimating Flooring Costs, a student explains how she estimated the cost of a flooring option. Overall, students do a great job estimating the cost of each flooring type!