Functional Thinking as an Entry Path into Algebra

The Squares and Vertices Problem

Students in third grade used one-inch square tiles to create a growing pattern by adding one additional tile to each consecutive pattern configuration. Tiles were placed vertex-to-vertex. Then students created a function table to record and analyze the relationship between the number of tiles and the number of vertices in their growing pattern. For example, in one pattern, for 2 tiles, there were 7 vertices, and for 3 tiles, there were 10 vertices, and so on. Students realized that once they recognized the abstract numerical pattern in their function charts, they could predict the growing pattern for any number of tiles without having to actually create further concrete models.

Functional thinking is an important entry point into algebra, and allows students to generalize and express relationships quantitatively. Natural language can be used to describe and express these relationships. Students were asked, “How would you describe the relationship between the number of squares and the number of vertices in your repeating pattern diagram?” Students compared various ways of describing their numerical relationships. We also analyzed the statement: “The number of vertices is equal to three times the number of squares, plus one”  v = 3s + 1




Family Math Night at LREI

Students and Parents look forward to Family Math Night every year.  

Students in grades one through four celebrate mathematics, as well as continue to hone their fluency in combination facts by playing fun games. Fourth grade students create their own math games as a capstone experience, and then teach them to family and friends during Family Math Night. Continue reading

Area, Perimeter & Little Red Square Park

Third Graders Explore Area and Perimeter by Measuring a “Pocket Park”

As part of their study of area and perimeter, third graders in Elaine and Jessie’s class measured the perimeter of “Little Red Square”, the small pocket park that lies just in front of LREI on Sixth Avenue. Each class divided into small groups and used trundle wheels to measure the four sides of the park. Then they calculated the perimeter by adding up the side dimensions. When the class looked at the set of data, they realized that their perimeter data varied, and they attributed this to the inexactness of using the trundle wheel. They decided to use the middle number of the data set (the median) as their “working” perimeter for the park. Continue reading

Student-to-Student Mathematical Discussion in the Classroom


Young mathematicians need to be able to “Construct viable arguments and critique the reasoning of others”, according to the National Council of Teachers of Mathematics. This philosophy aligns with LREI’s progressive educational goals of placing an emphasis on student voice, and creating a classroom culture of engaging student-to-student discussions. Students take on the role of leaders who believe that they can actively defend their own mathematical ideas, and help shape the ideas of their colleagues in a supportive, nurturing environment. Continue reading