Area of Squares and Rectangles

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SWBAT measure the area of a shape by counting the square units.

Big Idea

Area can be found by counting square units or by using the area formula, A= l x w.

Whole Class Discussion

15 minutes

In today's lesson, the students learn to use a formula to find the area of rectangles and squares (4.MD.3A).

I let the students know that in today's lesson, we continue on with what we learned about area.  To review, I ask the students to raise their hands and tell me what they have learned so far about area.  Student responses:  1) It is the middle of the shape, 2) We count the squares inside of the shape to find the area, and 3) We put pieces together to make a whole square unit.  I let students know, that yes, area is the inside of the shape and I remind them that we talked about replacing the tile floor in the classroom.  Before the floor can be replaced, we need the area to know how much tile is needed.  

I say, "Today, we will learn to use a formula to find the area.  I have heard some of you mention length and width, so that I am sure you a familiar with this skill from third grade.  In today's lesson, we specifically learn how to find the area of rectangles and squares."  The students are at their desks with paper and pencil so that they can work along with me.  The power point is displayed on the Smart board.  We begin with problem 1.  I point out to the students that I did not give them the measurements for this shape, but there are square units.  The formula for area  is length x width (I point to the length and width on the shape).  I ask the students, "If you forget which one is length and which one is width, does it matter?"   Student response:  No.  I ask, "What property tells us this?"  I let the students call out their answers.  I finally hear a student say, "commutative property."  I remind the students that the commutative property lets us change the order of the factors and still gives us the same product.  If we are going to use a formula for this problem, we can count the pieces to find the length and the width.  Together, we count the number of boxes in the length to get 3.  Then we count the number of boxes in the width to get 5.  I tell the students to first write down the formula A = l x w.  Next, replace the letters with the correct numbers. A = 3 x 5.  The answer to this problem is 15 square units.  I point out to the students that when you are multiplying units by units, you must write "square units" in your answer.

In problem 2, I let the students know that we do not have boxes to count.  I remind them that because they know the formula to area, they can find the area of this rectangle. Again, I write the formula for area on the board as the students write it on their papers.  I say, "In order to work a problem that does not have square units, replace the letters with the correct numbers for the length and width."  Together, we solve the problem to find that  the areaq is 24 square feet.  At this point, I explain to the students that if they have a unit of measure (such as inches or feet), then they should make sure that they use it in their answer. 

Before I send the students to their seat, I realize that I wanted to show them one more example that is not in the power point.  On the Smart board, I draw a rectangle and put the length as 3 inches.  I leave the width blank, but I tell the students that the area is 15 square inches.  I have the students write down the formula for area.  Next, they replace A with 15 and L with 3.  The students now have 15 = 3 x W.  I ask, what is the width?  All of the students yell out 3.



Skill Building/Exploration

20 minutes

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

I give each pair an Area of Squares and Rectangles activity sheet and a ruler.  The students must find the area of the squares and rectangles on the activity sheet.  Also, the students must work together to measure their desks, then find the area of their desks. In the Video - Area of Squares and Rectangles, you can hear the students justifying their answers.

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

1. What is the formula for area? 

2. How many numbers are you multiplying to find the area?

3. What word must you write in your answer?

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.


I had a few students trying to multiply 4 numbers.  I reminded the students of the importance of using the formula.  The formula lets you know that it is only 2 numbers being multiplied.



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 Student Work - Area and Student Work, as well as work that may have incorrect information.  In this sample of Student Work - Area, this student did not use the formula.  Even though he used a strategy that would allow him to get the correct answer, it is important to use the formula to make sure you are finding the area.  You can number your boxes to justify that your multiplication calculations are correct.  

More than one student may have had the same misconception. During the closing of the lesson, all misconceptions that were spotted during the group activity will be addressed whole class.  In this particular lesson, I reiterate to the whole class the importance of using the formula to find the area.  I let them know that by using the formula, it reminds you of which numbers should be used to find the area.