By Katie Gibbons and Sarah B. Bush, Posted May 11, 2015 – 

I learned about algebra tiles (see fig. 1) in my college mathematics methods course, but I wasn’t convinced they would be helpful to my students. I didn’t fully see the pedagogical benefit of using them as a visual representation of variables because I didn’t use them when I was learning the foundations of algebra. However, I didn’t want to rely solely on the ways I was taught and knew that different hands-on strategies could enhance my students’ learning.

Fig. 1 Algebra tiles

Once I used algebra tiles in my classroom, my thoughts drastically changed. Because my sixth graders worked on compound area and perimeter earlier this year, they picked up on the naming of each tile (see fig. 2) rather quickly. The first step for my students was to create a unit, defining each side of the small square as a length of 1. But when they tried to use multiple unit squares to represent a longer tile piece, the students found that a row of individual units lined up next to the long tile piece did not fit the length exactly. (We discussed whether to use an estimated fraction, but agreed that this was too imprecise, so we decided to call that length “x”.) At that point, students were ready to explore the perimeters and areas because they saw the connection among the side lengths of the three different types of tiles.

Fig. 2 Naming the tiles

Discussing the fact that algebra tiles (like base-ten blocks) are named by their respective areas allowed students to discover the ability to name each tile. We did this as a class by color-coding the sides of each tile (see fig. 2). This helped my students see exactly where each of the names came from. For example, students can be asked the following question:

Write an expression for the perimeter and the area of this shape (see fig. 3).

Fig. 3 A perimeter and area arrangement

Figure 4 is a possible student response for the perimeter; figure 5 illustrates a student response for area.

Fig. 4 A perimeter expression

Fig. 5 An area expression

I never imagined that a battle could be won using algebra tiles to model with mathematics. My next adventure is to incorporate algebra tiles into my students’ exploration of expressions with integers.

Katie Gibbons teaches sixth-grade mathematics at Noe Middle School in Louisville, Kentucky. She strives to maintain a student-centered classroom in which students are challenged each and every day.

Sarah B. Bush, sbush@bellarmine.edu, is an assistant professor of mathematics education at Bellarmine University in Louisville, Kentucky. She is a former middle- grades mathematics teacher who is interested in interdisciplinary, relevant, and engaging math activities.