Understanding Area of a Rectangle Conceptually

Let's tackle Area of a Rectangle conceptually using a series of visual prompts to help students generate the formula for finding the area of ANY rectangle!

In this Math Is Visual Prompt, students are given the opportunity to wrestle with the idea of area in particular the area of a rectangle through a concrete and visual set of curious experiences. In order to maximize the concreteness of this activity, my suggestion is for square tiles or linking cubes to be out and available and have students try to make their estimates using the concrete materials.

Let’s get started…

Spark Curiosity: What Do You Notice? What Do You Wonder?

Ask students “What do you notice? What do you wonder?” to spark curiosity and pause where indicated in this video.

Here’s an image of what students/children will be looking at when you are instructed to pause the video:

Math Is Visual - Area of a Rectangle Visual Prompts.006 What Do You Notice What Do You Wonder?

After students share what they notice and wonder, you can then show them the next portion of the video until you’re instructed to pause.

Math Is Visual - Area of a Rectangle Visual Prompts.012 - How many of these will it take to cover that

Here, students are now able to go ahead and try to make an estimate using spatial reasoning skills only. Having manipulatives out is a huge help. You could also simply cut out squares and have them try their best to represent based on what they see in order to help them build their diagrammatic skills and manipulation skills.

After students are given time to share their initial estimates, you can reveal the following visual prompt:

Math Is Visual - Area of a Rectangle Visual Prompts.019 Update your estimate

Share out again, then show this:

Math Is Visual - Area of a Rectangle Visual Prompts.020 Update your estimate again

Boom. Give children some think time and have them CONVINCE you of their most recent estimate. Are any students willing to GUARANTEE their estimate is precise? How come?

Act 3: The Big Reveal

Students can now celebrate when they see how many squares can actually cover the rectangle:

Math Is Visual - Area of a Rectangle Visual Prompts.045 act 3

Visual Prompts – Set 2:

Let’s give them another go!

Math Is Visual - Area of a Rectangle Visual Prompts.049 How many of these does it take to cover that

Math Is Visual - Area of a Rectangle Visual Prompts.058 Update your prediction

The Big Reveal:

Math Is Visual - Area of a Rectangle Visual Prompts.078 act 3 it takes 18 of these to cover that

Visual Prompts – Set 3:

Math Is Visual - Area of a Rectangle Visual Prompts.082 visual prompt 3

More information:

Math Is Visual - Area of a Rectangle Visual Prompts.091 update your estimate

Act 3: The Big Reveal

Math Is Visual - Area of a Rectangle Visual Prompts.104 act 3 it takes this many squares to cover the rectangle

Visual Prompts – Set 4:

In the last visual prompt set, we give students the length and width of the rectangle in square tiles. Now, students are encouraged to determine how many.

Math Is Visual - Area of a Rectangle Visual Prompts.110 how many and how do you know

Notice that I haven’t used the language estimate since students have enough information to determine precisely how many squares it will take to cover the area of the blue rectangle. However, also notice that I haven’t used the word calculate and instead use the softer words: how many?

Act 3: The Big Reveal…

Math Is Visual - Area of a Rectangle Visual Prompts.129 7 groups of 5 squares

Note here that I’ve shown 7 groups of 5 here, but I’m also asking for students to try to calculate another way.

Math Is Visual - Area of a Rectangle Visual Prompts.139 5 groups of 7 squares

The hope for this set of visual prompts is to give students an opportunity to “play” with area without being pre-taught ahead of time. This is a simple inquiry-based way to introduce the idea using their prior knowledge, intuition and spatial reasoning.

From here, we can now start formalizing these student generated solutions to come up with the formula for the area of a rectangle:

Area of a Rectangle = Length x width


A = l x w

Pretty awesome what mathematics can do when we approach it from a concrete and visual standpoint first to solidify our conceptual understanding before moving on to steps, procedures, and algorithms!

Coming up next, we’ll extend this idea to the area of a triangle. How do you think we might go about introducing that idea?

How’d It Go?

Thanks for watching and reading!

Did you use this in your classroom or at home? How’d it go? Post in the comments!

Math IS Visual. Let’s teach it that way.


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