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Introduction
In today’s classroom, technology isn’t just a supplement — it’s a platform for enhancement and discovery. One tool that continues to empower mathematical thinking is the humble spreadsheet. Whether through Microsoft Excel or Google Sheets, secondary students can engage in authentic modeling experiences that promote both procedural fluency and conceptual understanding. In a recent investigation, we explored how spreadsheets bring linear, exponential, and quadratic patterns to life — and how students can use them to take ownership of abstract mathematics.
This post highlights several investigations from our summer methods course, each designed to reinforce algebraic thinking using dynamic spreadsheet environments. The tasks push students to look for structure and explore mathematical generalizations in a tech-integrated setting.
Investigation highlights:
Investigation highlights:
In Investigation 3.1: Choose Your Allowance, we compared three monthly allowance plans:
Plan A: Additive growth of $1/month
Plan B: Increasing additive growth (+$0.25/month/month)
Plan C: Multiplicative growth (10% per month)
With spreadsheets, we could quickly generate tables and graphs to visualize the long-term impact of each plan. This opened the door for discussions on linear vs. exponential growth, predicting values and comparing financial decisions and real-world relevance for budgeting and saving
Furthermore, Investigation 3.2: Spotting Linear Patterns, focused on arithmetic sequences and their closed and recursive forms. We entered sequences like 3, 7, 11, 15... and explored how to compute the common difference, how changes to the initial value affect the sequence and how to write general formulas like f(x) = a + dx. By toggling constants and formulas in the spreadsheet, we were able to make predictions and validated patterns and see how adjusting one cell could dynamically update an entire sequence.
Through Investigation 3.3: Surrounding another pattern, we modeled geometric sequences, beginning with 3, 6, 12, 24… and adjusting both the initial value and the common ratio. Using spreadsheet formulas like = {previous cell term] * ratio, we explored exponential growth and decay and graphing curves in comparison to linear sequences. This helped differentiate exponential thinking from additive patterns, laying groundwork for more advanced exponential functions.
Likewise, in Investigation 3.4: Dealing with Quadratics patterns, one activity involved the sequence 0, 1, 4, 9, 16… which was determined to be a quadratic relationship. based on the ratio of each value being squared (n^2). By calculating the first and second differences, using recursive rules to build a sequence using second differences and developing general formulas of the form f(x) = ax² + bx + c, we could recognize and complete our closed formula concept of this pattern. This activity showed how real-world parabolic shapes (e.g., projectile motion) can be understood from simple difference patterns.
Importance and Relevance:
Importance and Relevance:
Spreadsheets serve as a bridge between numerical, graphical, and symbolic representations. In a high school setting, they can allow students to experiment, revise, and visualize — aligning beautifully with the Mathematical Practices (MP1–MP7) from the Alabama Course of Study. Most importantly, these investigations support mathematical modeling and open-ended thinking. Integrating technology like Excel or Google Sheets into the secondary classroom transforms passive learning into active exploration. By scaffolding problems through patterns, differences, and dynamic tables, students wouldn't just learn functions, they would be constructing them. From deciding on the best allowance plan to modeling quadratic growth, the spreadsheet becomes a “math lab” for enhancement and discovery.
Below is an example of Investigation 3.2: Spotting Linear Patterns:
References:
Martin, W. G., & Harkey, L. (2025). Spreadsheet Lab Investigations 3.1–3.4. CTSE 5040/6040, Auburn University.
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