Understanding Area

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SWBAT understand how to count square units to find the area.

Big Idea

Counting the square units inside of a shape will give you the area.

Whole Class Discussion

15 minutes

In today's lesson, the students review how to find the area of shapes by counting the square units.  This aligns with 3.MD.C5A  because the students learn that a square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area.

To begin, I let the students know that today's lesson is understanding area.  We begin by reviewing the vocabulary:

Area – The number of square units needed to cover a region. I let the students know that we could discuss the area of the classroom.  When we say the number of square units needed to cover the region of the classroom, the floor is a perfect example because there are square units on our classroom floor.  If the school wanted new tile to cover the floor, they would need to know how many square units are needed.  I go on to tell the students that if someone wants to put down new carpet in their house or put down a marble floor, they need to know the area of the room in order to do it.

 Estimate- an approximate calculation or judgment of the value, number, quantity, or extent of something.  I let the students know that an estimate is not the exact answer, it is about how much you have.  For example, if you have a cake with 1 slice missing, then you have about 1 whole cake.

Exact - not approximated in any way; precise.  I tell the students that when I say precise, it is the answer.  I did not round to get it, nor did I add something to it.  For example, 7 x 5= 35.  I tell the students that 35 is the exact answer. 

To find the area, all you have to do is count the square units inside the shape.  The power point is displayed on the Smart board.  I tell the students to look at the shape on the board. If I want to find the area of this shape, all I have to do is count the square units.  The students count out loud, as I number the blue squares.  The area of this shape is 13 square units.  I tell the students that when finding the area, be sure to include the word "square" in your answer.  I go on to ask the students, "Is this an exact answer or is this an estimate?"  I tell the students to raise their hands if they think that this is an exact answer.  All of the students raise their hands.  I call on one student to explain.  She says, "We counted 13 in all, and there were 13 squares."  I add on that we did not have to put pieces together to form a whole square unit.  

I display another shape on the Smart board.  I ask the students to count the pieces out loud.  Before we begin numbering, I point out to the students that some of the pieces are not completely shaded in.  I ask the students to start out by counting all of the whole pieces first.  As they count, I number the whole square units.  We count a total of 10 whole pieces.  Then, we put the smaller pieces together.  I point to one of the smaller pieces and ask the students what fraction of the piece is shaded.  Student response:  1/2.  I ask, "If I take this one half and put it with another 1/2, how much would that make?"  Student response:  1 whole.  Together, we add the halves together to form wholes.  The students find that area for this shape is 13 square units.  I ask, "Is this an exact answer or an estimate?"  Student response:  estimate.



Skill Building/Exploration

20 minutes

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

I give each pair an activity sheet.  The students must find the area of the shape by counting, then tell if it is an exact answer or an estimate.  

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

1.  What is the area? 

2. Is it an exact answer or an estimate?  How do you know?

3. Which pieces can you put together to make a whole?

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


A lot of the students had difficulty with problem 2 on the activity sheet.  Finding the area of the circle proved to be difficult for the students, as I knew that it would.  I feel that it is important to have the students struggle as they learn.  If they do not struggle, then it may be a skill that they have already learned.


15 minutes

To close the lesson, I let the pairs call out the answers to problems 1, 3, and 4.  I knew that problem 2 was difficult, therefore, we discussed it last.  Most of the pairs estimates for problem 2 fell between 21 and 25 square units.  I let the students know that they did a good job of estimating problem 2 because it was difficult.  (I try to encourage my students at all times because I do not want them to feel defeated when trying to learn a skill.  Besides, they worked really hard putting pieces together to form a whole.  They were very dedicated to trying to solve this problem.)  I let the students know that my estimate of the problem is about 24 square units.

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), as well as work that may have incorrect information (Student Work - Area).  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.