# Perimeter and Area (Are they the Same?)

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## Objective

SWBAT find the area and perimeter of rectangles and determine if they are both the same value.

#### Big Idea

Formulas can be used to find the area and perimeter of rectangles.

## Opener

5 minutes

In today's lesson, the students learn to use formulas to find the area and perimeter of a shape (4.MD.A3).  This week the students learned to find the area by counting square units.  They also learned how to find the perimeter of a shape by counting the square units around the shape.  In today's lesson, the students will use formulas to find the area and perimeter of a shape.  They determine if the shape has the same value for the area and perimeter.

To get the lesson started, I ask, "What have you learned so far about area and perimeter?"  One student responds, "Area is the inside of the shape. We can count the square units to find the area.  Just like when you told us about putting more tile on the floor."  I let the student know that he is correct. "What about perimeter?"  Another student responses, "Perimeter is the outside of the room.  The floor is the area, but the wall is the perimeter."  Next, I show the students a shape (a hundreds block).  I pose the question, "Can this shape have the same area and perimeter?"   I give the students a few minutes to think about the question.  I take a few student responses. From the responses, I know that the students are not sure.  Most students say that the shape can not have the same area and perimeter.

I tell the students, "Let's find out."

## Whole Class Discussion

10 minutes

I call the students to the carpet.  The power point is displayed on the Smart board.  I begin by letting the students know that our lesson for today is using formulas to find the area and perimeter of shapes.

I begin by reviewing important vocabulary for this lesson.  The students will have to know these terms to understand the lesson.

Vocabulary:

area – The amount of space inside the boundary of a flat (2-dimensional) object such as a rectangle or circle.

perimeter – The distance around a two-dimensional shape.

Formula - Numbers and symbols that show how to work something out.

Next, I display a model of a 10 x 10 square on the board.  It is the same as the hundreds block that I held up at the beginning of class.  I revisit the question that I asked earlier, "Does this shape have the same area and perimeter?"  I tell the students that we can find out.  On the Smart board, the formular A = L x W is displayed.  I let the students know that "L" stands for length and "W" stands for width.  I point to the length and width on the Smart board.  I ask, "What is the length of this shape?"  Together, we count to find that 10 is the length.   "What is the width of this shape?"  Together, we count to find that 10 is the width.

On the next slide, we discuss the perimeter of the shape.  I let the students know that since this is a square, we can use the formula p = 4s.  I go on to tell them that they can only use this formula if it is a square.  I ask the students to help me find the perimeter of this shape.

This takes us back to the question.  Does this shape have the same area and perimeter? The students know that this shape does not have the same area and perimeter. (I am really emphasizing the difference of area and perimeter because I want the students to know that they need to be careful when calculating the area and perimeter.  I have found in the past that some students do not stop to think about which measurement they are being asked to give.  They know how to do the area and perimeter, but they may calculate the area for the perimeter.)

Before the students go back to their seats to work in pairs, I give the students another formula for perimeter.  I let the students know that they can use p= 2L + 2W to find the perimeter of a rectangle.  I draw a rectangle on the board with a length of 3 inches and a width of 2 inches.  I let the students help me use the formula to find the perimeter.

Before I send the students to their seats, I ask one last question.  "Can a shape have the same area and perimeter?"  I tell them that they can explore this with their partners.

## Skill Building/Exploration

20 minutes

For this activity, I let the students work as pairs to find the area and perimeter of rectangles.  By doing this, it allows the students to hear their classmates thinking on the skill.

I give each pair an activity sheet and a bag of cut out rectangles.  The students must find the area and perimeter of the shape by using formulas.  The students determine if the area and perimeter are both the same for each shape.  Also, the students are given geometric boards and rubber bands.  The students must work together to form a shape that has the same area and perimeter.

As they work, I monitor and assess their progression of understanding through questioning.

1.  What formula can you use to help you find the area? What is area?

2.  Is there more than one formula to find the perimeter? What is the perimeter?

3.  Does the shape have the same area and perimeter?

As I walk around the classroom, I am questioning the students and looking for common misconceptions among the students.  Any misconceptions are addressed at this point, as well as whole class at the end of the activity.

Any student that finishes the assignment early, can use grid paper to draw shapes.  Then, find the area and perimeter of the shape.

Misconception:

During the activity, I noticed a pair of students trying to find the perimeter of a shape by adding both sides of the shape to multiply by 2.  For example, if the width of the shape is 5, the students added 5 + 5 to get 10.  Then the students put 10 in the formula (2 x 10).  I explained to the students that because they are using the formula, they only need to insert the number 5.  The formula is multiplying by 2 for you.  You do not need to add both sides together.

## Closure

15 minutes

To close the lesson, I bring the class back together as a whole.  I call on different pairs to share the area and perimeter of the shapes.  This gives me another opportunity to reach the students that did not understand the skill.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson.  Students need to see good work samples (Student Work - Area and Perimeter), as well as work that may have incorrect information.  More than one student may have had the same misconception.

Before the students complete their exit ticket, I have the students hold up their geo boards to show me a shape that has the same area and perimeter.  Most of the pairs found the shape 4 x 4 with an area and perimeter of 16.  (Another possible answer:  6 x 3).

Each student is given an Exit Ticket - Area and Perimeter to complete individually.  Group activities are great, but I need to know how well each student is doing on their own. The exit tickets are collected at the end of class (Student Work - Exit Ticket (Area and Perimeter).  This gives me further data on how the students are comprehending individually.

Results of Exit Ticket:

Number of students with correct area:  16 out of 16

Number of students with correct perimeter:  10 out of 16 (63%)

All struggling students identified from the data on the exit tickets will receive further instruction in small group.