What's Going On in That Area

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Objective

4.MD.3 SWBAT apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Big Idea

Students often confuse the terms area and perimeter. In this lesson, students will find the area of figures by counting rows and column and multiplying.

Don't Be a Square

20 minutes

Materials: graph paper.pdf  color tiles.docx

In this lesson I want my students to examine different arrays to determine the formula for the area of a rectangle.  I invite students to the carpet so that we can begin our discussion. 

I point out that the L X W gives the number of unit squares in the partition.  I display a sheet of graph paper on the overhead for students to see that I can calculate the area on an object by counting the number of square units within that object.  I used manipulative to display on top of the graph paper. I proceed to trace the outline of different shapes such as a trapezoid, circle, rectangle, square, and so forth.

I explain that there are two different ways for me to calculate the area. The first is to count all of the units (individual squares within the shape) or I can apply the formula of length times width. I want them to see that either strategy will give an accurate answer to the area of that particular shape. I repeat counting the number of square units; however this time I ask students to count along with me aloud. How many square units are there? How do you know? Students begin to realize the formula of finding the area. To bring them deeper into the lesson, I draw a rectangle with two columns and four rows. I can either count all of the units, let’s count together. 1,2,3,4,5,6,7,8 or I can multiply length which is 2 times width which is 4. Now who can tell me what is 2 times 4? 8. Exactly, either way, I still got the same answer. We continue to find the area of other shapes to ensure that all students understand the objective of this lesson. Now I want to see if students can do this skill in small groups in order to check for mastering the skill.

 

 

 

Rows versus Units

25 minutes

Materials: graph paper.pdf  ruler.pdf

In this portion of the lesson, I want students to move with their assigned partner. I intend for students to investigate multi-step multiplication problem in a context that involves area.  To do this I post a word problem on the board.  

Problem:

 

Kim’s rectangular room is 20 feet by 45 feet, and Tim’s is 25 feet by 40 feet.  Whose garden is larger? 

I ask students to read the problem aloud with me.  I give them about 4 minutes or so to turn and talk with their partner about how and why the formula can help them solve the problem.  After their time is up, I ask student volunteers to explain their solution.  Some students multiply the length and the width to find the area of each rectangular room.  

20 X 45 = 900 and 25 X 40 = 1,000 square feet

Now that you have the total square feet of both rooms, how do we determine which room is larger.  We can find the difference of the two areas.

1,000 – 900 = 100

Can anyone tell me who room is larger?

To assist struggling students in their learning, I draw and illustration on the board that correctly represents the length and width of the given problem. I may point out how to determine the length from the width; however, I prefer scaffolding them through until they can support their own learning.

 

I discuss the meaning of area once again and ask students to explain the formula. Length times width or base times height The students are divided into pairs. Each group is given a ruler and a sheet of graph paper. The students are asked to draw a rectangle that is 4 squares long and 4 squares wide. I remind students to look at the images on the board in case they need refreshing on length and width. I ask students to find the area of that image. All students had 12 for their area, which was outstanding. I also want each of you to draw two additional images of your choice with different dimensions besides what I just gave you. After you draw the images, we will exchange papers for others to apply the formula for area and determine the area of your image. I may invite a couple of students to share. As students are sharing, I encourage students to ask questions.  I use students’ responses to determine what students are thinking so far.

 

Figure That Area

20 minutes

 

In this portion of the lesson I would like for my students to have some added practice.

I display a sheet with four problems. The problems are 2X6..., 3X5...., 6X2..., and 2X5. I explain that the formula is given; however, I would like for everyone to be able to explain and illustrate an image that shows the correct area for this equation.I will do the first one for you. Before I start, Again what is the formula for area? length times width. I draw two rows of squares with six in each column. Now we can add all of the units together, let's count...1,2,3,4,5,6,7,8,9,10,11,12. or we can simply do what? Multiply 2 by 6. To get what? 12. Now I am going to walk around the room and monitor you all as you work in groups to draw the three additional images that goes along with the given formulas. I monitor students as they are working. The students are doing an excellent job with completing the assignment independently.

What's Your Formula

15 minutes

In this portion of the lesson I want to assess students ability to work on their own. I quickly direct their attention back to the intended purpose of this lesson. I tell students to remember to talk their way through the given formula and explain how and why it works.  

To begin, students are given a worksheet where they  are asked to find the area of four figures. I also give them two equations where they are asked to draw the correct figures to illustrate the problem. As a writing extension. I have one problem where I have ...

John is trying to make a sandbox for his son. He wants the area of the sandbox to be 6 by 4. He figured the total square units to be 21. Is he correct? Why or why not? Illustrate and explain.