Area: Small Word, Big Misconceptions

Markes, A. (2017, November 10). Area dice game
[Photo]. 

This week in class we played a really fun game about area. To play the Area Dice Game, we divided ourselves as well as a piece of chart paper into two teams. One team at a time, rolls two dice. The numbers that come up represent the length and width of the rectangle you have to draw on your team's half. A team wins when they completely fill their side of the chart paper with different rectangles OR when a team cannot create the rectangle with the dimensions that appear when the dice are rolled.

I like this game because it combines elements of competition and learning. I know at my table we were quite competitive about whether the rectangle with the given dimensions would fit in the remaining space. In terms of learning, this game works on knowledge of area and practices spatial management.

So, what is area? Area is the amount of flat space inside a two-dimensional shape (Small, pp. 488). It is measured in square units. This definition is important for students to understand because a common misconception about area is that it is defined as "length times width". While this is how we measure area for certain shapes, this is not a definition of the term. As teachers, we must correct this common misconception because it can create a roadblock to success when figuring out the area of other shapes, such as a triangle or circle both of which have different ways of determining area.

Another common misconception mentioned by Small that I have also seen in practice occurs when students try to convert square meters to square centimeters. Their reasoning is that since there is 100 cm in 1 m, there must be 100 cm² in 1 m² (pp. 507). This is why it is so important to know the proper definition of area instead of just how to calculate it.

If there is a square that measures 1 m² that means its dimensions are 1 m in length and 1 m in width (1x1=1). For the length, we have 100 cm and for the width we have 100 cm as well. Therefore, there are 100,000 cm² or, 100 cm x 100 cm.  This is why, I always tell my students to convert the dimensions before calculating the area.

For many students as well, they confuse the size of a side length with the area, when comparing two shapes. If one side length is significantly larger than the other, students automatically think the shape with the longer side length has the greater area. This however is not always the case. Again, students need to clearly understand the definition of area as the space inside the object and not the shape with the longer side.

Rectangle: Ha Square! Your sides are so short. Square: It's what's on the inside that counts.