Students will apply the area and perimeter formulas for rectangles in order to create a fence in which to house a (make-believe) pet.

### Class

Fourth Grade

### Duration

Two class periods

### Materials

- Graph paper
- Graph paper transparency
- Overhead machine
- Circulars with fence prices or access to the Internet

### Key Vocabulary

Area, perimeter, multiplication, width, length

### Objectives

Students will apply the area and perimeter formulas for rectangles in order to create a fence and calculate how much fencing they are required to buy.

### Standards Met

4.MD.3 Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

### Lesson Introduction

Ask students if they have pets at home. Where do the pets live? Where do they go when you are at school and the adults are at work? If you don’t have a pet, where would you put one if you had one?

### Step-by-Step Procedure

- This lesson is best done after students have an initial understanding of the concept of area. Tell students that they are going to create a fence for their new cat or dog. This is a fence where you want the animal to have fun, but it has to be enclosed so that they are safe during the day.
- To begin the lesson, have students help you create a pen with the area of 40 square feet. Each square on your graph paper should represent one square foot, which will enable students to just count the squares to check their work. Begin by creating a rectangular pen, which enables you to review the formula for area. For example, the pen can be 5 feet by 8 feet, which will result in a pen with an area of 40 square feet.
- After you create that simple pen on the overhead, ask students to figure out what the perimeter of that fence would be. How many feet of fencing would we need to create this fence?
- Model and think aloud while doing another arrangement on the overhead. If we wanted to make a more creative shape, what would give the cat or dog the most room? What would be most interesting? Have students help you construct additional fences, and always have them check the area and calculate perimeter.

- Remark to students that they’ll need to buy fencing for the area they are creating for their pet. The second day of class will be spent calculating the perimeter and cost of the fencing.
- Tell students that they have 60 square feet to play with. They should work alone or in pairs to make the most interesting and also spacious area for their pet to play in, and it has to be 60 square feet. Give them the rest of the class period to choose their figuration and draw it on their graph paper.
- The next day, calculate the perimeter of their fence shape. Have a few students come to the front of the classroom to show their design and explain why they did it this way. Then, break students into groups of two or three in order to check their math. Don't proceed to the next section of the lesson without accurate area and perimeter results.
- Calculate the fence costs. Using a Lowe's or Home Depot circular, have students select a particular fence that they like. Show them how to calculate the price of their fence. If the fencing they approve of is $10.00 per foot, for example, they should multiply that amount by the total length of their fence. Depending on what your classroom expectations are, students may use calculators for this part of the lesson.

### Homework/Assessment

Have students write a paragraph at home about why they arranged their fences like they did. When they are finished, post these in the hallway along with students' drawing of their fences.

### Evaluation

An evaluation of this lesson can be done as students are working on their plans. Sit down with one or two students at a time to ask questions such as, "Why did you design your pen this way?" "How much room will your pet have to run around?" "How will you figure out how long the fence will be?" Use those notes to decide who needs some extra work on this concept, and who is ready for more challenging work.