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.
Checking for Correctness
This lesson is a continuation of the lesson, Estimating Flooring Costs. Prior to moving on, I want to make sure all students have a completed journal entry and the correct estimates for each flooring type: Completed Chart. For example, when looking at this journal, I notice a student correctly estimated each type of flooring, except for the laminate flooring at the bottom of the chart. She wrote: $1.39 = about $2.00.
This is the perfect opportunity for students to compare flooring costs estimations before going on to the next activity. Students go through each flooring type and discuss estimated costs. Discrepancies in answers provide students with the chance to defend their thinking. This is such an important part of mathematics!
Reviewing Dollar and Cents Signs
This student, Dollar Signs vs. Cent Signs, correctly estimated each type of flooring, but seemed to be confused when to use the dollar sign and the cent sign. Knowing that this is common at the 4th grade level, I want to review these concepts before moving on with our lesson. So, I wrote the following examples on the board.
C: (cent sign) 1.89
D: 1.89 (cent sign)
E: $1.89 (cent sign)
F: (cent sign) 89
G: 89 (cent sign)
I ask students to turn and talk: Which examples are correct? Which examples are incorrect?
After students have time to converse with a nearby peer, we then discuss each example as a class, crossing off incorrect examples. Only A and G are correct.
Goal & Lesson Introduction
To begin, I introduce today's goal: I can estimate the cost of flooring in each room of my home. I explain: Now that you have estimated the cost per square foot of each flooring type, it's now time to estimate the cost of installing flooring in your home!
I continue: In real life, why would we want to estimate the cost of flooring instead of finding the actual amount? (To quickly calculate the cost so we can figure out if we have enough money.)
Flooring Cost Chart
I pass the Flooring Cost Chart to students and I demonstrate how to complete the charts using the student's Square Footage of Rooms from a previous lesson. I explain: Today, you can pick two types of flooring for your whole house. The top half of the Flooring Cost Chart paper is for calculating the cost of one type of flooring and the bottom half of the paper is for a second type of flooring.
I chose a flooring option (Thoroughbred Carpet). Then I fill in the estimated cost per square foot ($1.00). I chose the easiest estimated flooring cost so that all students can easily understand the directions. Then, I wrote the name of the room (Living Room) in the first column of the chart, the square footage in the next column (220 square feet), and I show students how to calculate the estimated cost of flooring the room for the final column (220 square feet x $1.00 = $220.00).
To bring this number back to the real-world application, I state: So it would cost $220.00 to install flooring in my living room.
This may seem like a simple calculation, however, it was such an "Ah-ha" moment for many students. Many students were eager to share their thinking. One student says: That's cheap! Another student says: For the whole living room?
Students are excited to start calculating the cost of their own rooms! I am reminded of the power of student ownership.
Before students begin working, I explain to students that they will be given a budget! They respond with astonished eyes and expressions, "What?!" I continue: You'll be given $2,000 to install flooring in the 6 required rooms of your house... the living room, kitchen, dining room, bedroom, bathroom, and laundry room. If you get done with these rooms, I will give you more money to install flooring in the remaining rooms!
In no time, students are off and ready to complete their charts!
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).
Here's an example of one student, Calculating Estimated Cost, who has her Square Footage of Rooms paper, Estimated Cost of each Flooring Type chart, and her Flooring Cost Chart spread out on her desk. I love watching students sort through information and apply previous learning to complete this task.
During this time, students were working at different levels. Some students struggle with calculating the estimated costs. Others successfully find the cost of flooring for all six required rooms rather quickly and were able to calculate the total cost of flooring their entire houses (including many "extra" rooms)! I gave these students $2,000 more to account for the added space.
Here, a student excitedly goes beyond the six required rooms: Student Explanation of Tasks.