Filling in the Middle

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Objective

SWBAT understand the term area and differentiate perimeter and area.

Big Idea

Perimeter is the outside, and area is the inside of a figure. Students can use both concepts to work with geometric shapes.

Warm Up

15 minutes

The students have been introduced to finding the perimeter of a field. Today we will introduce finding the area of that same field. 

I ask students if they remember the farmer with the bunny who ate his lettuce? I tell them that today we are going to look in on the farmer again. The farmer is tired of planting lettuce and he has decided that it would be easier to grow hay for his cow on the field. 

When the video is over, I ask students if they remember creating arrays? Finding the area of a shape is a lot like making and counting an array. I draw an array on the board and we count the squares to find the area, or total number of squares inside the figure. 

Teaching the Lesson

15 minutes

I draw a large rectangle on a piece of graph paper. I ask students how I can find the area of my rectangle. I tell them I am like the farmer and I want to fill in all of my rectangle but don't know how to figure out how big it is. 

Students who make the connection to the farmer in the field, will be able to tell me to count the squares. We count together and find the area of the shape. I ask students what it might remind them of (arrays). If no one comes up with the idea of an array, I try writing the the repeated addition sentence ( 2 + 2 + 2) on the board next to my rectangle. This helps students see the connection between the array and the area.

I ask students how many of them remember doing arrays? I tell them that finding the area of a rectangle is just like finding the total of an array.

I draw a second rectangle on the graph paper. I ask how we might find the area? (counting the inside). I help students count the total number of squares. I also ask if anyone could figure out the total the way to count an array? I ask for a volunteer to show us how they might use repeated addition, or multiplication to solve the array. 

I ask students if the area and the perimeter are the same? How could we figure that out? (count the outside - like the farmer with his fence). We count and find the two numbers are different.

I draw a last example for us to compare perimeter and area. When I feel that most students are understanding how to find area and perimeter, I stop and explain the centers we will work with today.

 

Centers

30 minutes

Today students will circulate through 4 centers. They will work with perimeter and area at each center. 

Center 1: Students will roll 2 dice and use chips to fill in rows and columns of an array on graph paper. They will trace around the outside of their shape and then write the area (the number of squares that contain colored chips) inside the figure. Students will continue to build shapes and count the area of each one.

Center 2: Students will use geoboards to build shapes. They will build rectangular shapes on the geoboard by rolling 2 dice. The first will be the number of sides of the shape, and the second is the number of pegs on each side. When the shapes have been built, each student will then add the sides to get the total perimeter of the shape.

Center 3: The students will be given a number of shapes drawn on graph paper. They will count the perimeter and area of each shape and figure out which is larger. Today I have them use only squares and rectangles. We have not talked about how they might find the area by counting when the shape has diagonal lines. 

Center 4: I tell students to draw a large block letter for one of the letters in their name, on a piece of graph paper. The students then count the blocks by numbering to find the area of the letter. They can also count around the outside to find the perimeter of their letter.