Perimeter

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Objective

SWBAT measure the perimeter of the shape by using a formula or counting the units around it.

Big Idea

Perimeter can be measured by using a formula or counting the units on each side of a shape.

Whole Class Discussion

15 minutes

I begin by reviewing what we learned on the previous day.  I say, "We talked about area yesterday.  We learned that the formula for area is A = L x W. Can someone raise their hand and tell me what area means?"  Student response:  Area is what you count on the inside of a shape.  I ask, "What are some things you may need to find the area for?"  Student responses:  when you put down a new floor, to hang something on the wall, and when you put new counters in your house.   

I go on to say, we know area is the inside of a two dimensional shape.  Today, we learn about perimeter.  Perimeter is the outside of the shape.  In this room where we are now standing and sitting in is the area.  Along the wall of this room is the perimeter.  For instance, if someone wanted to put a fence in their yard.  They need to know the perimeter because it is the outside border of the yard.  They need to know the length and width of the yard.  

On the board, I display the Teaching Tool - Perimeter.  I point out that the width of the rectangle is 3 feet.  I ask, "If the width is 3 feet on this side of the rectangle, what is the width on the opposite side?"  The students all knew that it is also 3 feet.  "We should know that those sides are the same length on a rectangle.  If the length of the rectangle is 4 feet on this side, then what is it on the opposite side?"  Again, the students know that it is 4 feet.  

There is a formula we can use to find the perimeter of rectangles and squares.  I write the formula P= (2 x L) + (2 x W).  We just discussed that the opposites are the same, so we can multiply by 2 to double the length or width.  I make it clear to the students that they can only use this formula for rectangles, squares, and other 4 sided shapes that have opposites that are the same (such as the rhombus).  

On the board, I demonstrate how to take the formula and insert the numbers.  I write (2 x 4) + (2 x 3).  I let the students help me multiply and add to find the perimeter of 14 feet for this shape. I explain to the students that because we are adding the different sides, we write "feet" for our unit of measure, not "square feet".  I explain to the students that if they forget the formula, then just add all the way around the shape to get the perimeter.

To give the students more practice, we find the perimeter to a shape with more than 4 sides.  I explain to the students that they can not use the formula for this shape because the sides are different lengths.  

To find the perimeter, you should add all of the sides.  I ask the students to help me count the number of sides.  (This is important because sometimes when students add numbers, they may skip a number.  If they know how many sides are on the shape, they can make sure that they add that many numbers.)  Together, we count 6 sides to this shape.  I tell the students that they must add 6 numbers.  On the Smart board, I write all 6 numbers as the students call them out to me.  Together, we add to find 12 inches for the perimeter of this shape.

 

 

Skill Building/Exploration

20 minutes

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

I give each pair a Perimeter Activity Sheet.  The students must find the perimeter of the shapes on the activity sheet.  In the Video - Perimeter, you can see and hear a student trying to come up with the perimeter of a triangle.  This student emerged as the leader of the group.  However, she struggled with finding the perimeter of a triangle because she wanted to use the formula, p= (2 x L) + (2 x W).  I question the students to lead them to the correct answer.

As the class works, I monitor and assess their progression of understanding through questioning. 

1. What is the formula for the perimeter of a square or rectangle? 

2. How many numbers will you add for this shape?

3. How did you get your answer?

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

Misconceptions:

I had to correct a few students on writing the answer for the perimeter.  Because we wrote "square feet or inches" for area, they wanted to put the word "square" in their answer.  I reminded the students that when you add 4 feet plus 2 feet, you get 6 feet.  The answer is not squared because you added the two numbers.  For area, you measure to find the square unit because you are finding the total amount of space on the inside of the shape.  

Closure

15 minutes

To close the lesson, I bring the students back together as a whole class.  I feel that it is very important to let the students share their answers as a whole class.  This gives those students who still do not understand another opportunity to learn it.  I like to use my document camera to show the students' work during this time.  Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

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, as well as work that may have incorrect information.   In this sample of student work, Student Work - Using Formula for Perimeter, you can see that the students used the formula to find the perimeter.  The students went step by step to find the correct answer.  The students labeled their answer with the correct unit of measure.  In this sample of student work, Student Work - Perimeter, the students did a good job on most of the problems.  However, as you can see, the students added 4 numbers to find the perimeter of a triangle.  This is a red flag to me because it tells me that these students think that there should always be 4 addends for the perimeter.  Because more than one student may have had the same misconception, during the closing of the lesson, I remind the students that to find the perimeter of a shape using adding, your addends must equal the number of sides of the shape.  For example, if it is a triangle, then you should add 3 numbers.  I also reiterate to the whole class that the answer does not include the word "square" because we are adding to find the total number of feet or inches that make up the perimeter of a shape.