Making Math Real and Personal

Recently I visited a 3rd Grade classroom and asked the students to draw a model that showed 1 square inch and 1 square centimeter on their whiteboards. I found that they had no personal visual references in their mind of how much space those measurements covered and had no confidence in their own drawings. So how do you make it real and personal?

The 3rd Grade Common Core Standard states: 

"Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

• 3.MD.5. Recognize area as an attribute of plane figures and understand concepts of area measurement.
  • 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.
  • A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
• 3.MD.6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units)."

Can your students visualize how much space is covered by a particular square unit?  Do they have an internal sense of how much space is covered by a square inch or a square centimeter?

   I want to show you a set of models that I created to assist students in visualizing square units.

First, I went to a hardware store and bought 4 vinyl tiles that measured 12 inches by 12 inches.
This represents the space covered by 1 SQUARE FOOT.

Next, I created a grid of 1 inch by 1 inch square unitson the second tile. In one square foot, there are 144 square units.

Let's not forget about square centimeters. Look how many square centimeters cover one square foot!!

We never talk much about square decimeters, so I made a model of those square units too. There are a bit more than 9 square decimeters in one square foot. 

First, I showed the students  the back of the tile.The students predicted, by writing down a number on their white board,  how many square units would fit in the space of one tile. Then I turned it around to verify how well they had predicted. By having them "wonder or predict" first, it became personal.

 When I turned the tile around to show the square centimeters, one child exclaimed, "Wow, there are a lot of those buggers...more that I thought there would be!"

 Then we discussed a reference we could remember about how large different square units are and the students and I decided that the size of one square centimeter is about the size of the top of your finger.

One square inch is about the size of a quarter.

Lastly, that our school is covered in square feet and all you have to do to remember is to look down at the floor.


We often ask a student whether or not their answer makes sense. Hopefully when they respond that the area of their math book is 19 sq. cm. they will dig into their personal references and think...that just can't be right...let me try again.

Deborah