 # Supporting Pattern Exploration and Algebraic Reasoning through the Use of Spreadsheets

Ayhan Kursat Erbas (Middle East Technical University, Turkey), Sarah Ledford (Kennesaw State University, USA), Chandra Hawley Orrill (University of Massachusetts Dartmouth, USA) and Drew Polly (University of North Carolina at Charlotte, USA)
DOI: 10.4018/978-1-4666-4086-3.ch015

## Abstract

As teachers prepare to teach the Common Core State Standards for Mathematics (CCSSM), students’ exploration of patterns and relationships between numbers has gained more importance. Specifically, students’ conceptual understanding of numerical patterns is critical in middle school, as it lays a groundwork for fostering mathematical thinking at all levels. Educational technologies can enhance student’s explorations of patterns by providing opportunities to represent patterns, test conjectures, and make generalizations. In this chapter, the authors illustrate how spreadsheets can support students’ explorations of both arithmetic and geometric patterns in the middle grades.
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## Using Patterns To Explore Arithmetic Sequences

Investigating arithmetic patterns can support students in making connections among mathematical concepts as well as connecting classroom mathematics to the world around them. Since arithmetic patterns change by a fixed amount, arithmetic sequences are fairly simple to observe and study. However, they are also robust enough to support students as they make sophisticated conjectures and generalizations. Mathematical software can facilitate the analysis and interpretation of arithmetic patterns. For example, spreadsheets allow students to extend arithmetic patterns by working numerous, rote calculations freeing students to focus on developing generalizations based on the patterns in the spreadsheet. Spreadsheets also allow students to perform manipulations on a pattern and quickly view the effect of the manipulations on the rest of the numbers in the pattern. Clearly, this is beneficial in allowing students to test conjectures. Below is one example of an investigation that exemplifies the value of using technology for solving patterns:

A cruise line has 3-day, 4-day, and 7-day cruises. After each cruise, a ship returns for one day and repeats the pattern. If one cruise of each type leaves today, when will all three cruises leave again on the same day? Generalize your solution for x-day, y-day, and z-day cruises.

The day that each cruise line leaves can be represented as an arithmetic pattern. One possible method of exploring this pattern includes the teacher leading a whole-class discussion in which students are challenged to see the relationships for each cruise line which lasts 3, 4, and 7 days. Another pathway for exploration could be to engage students in a “think-pair-share” strategy in which the students analyze the problem for relevant information and calculate an answer to the first question on their own, then discuss their answer in a pair. In this pair, they could also extend this exploration by generating strategies for solving the problem for x, y and z days. The goal before the technology is used is for the students to develop an initial conjecture that they will be able to test and refine with the technology.

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