Using Stories to Explore Patterns and Think Algebraically
Patterns are everywhere: in nature, in art, and in stories. First and second graders have been exploring patterns, identifying different types, and then extending them. At the beginning of this theme unit of patterns and algebraic thinking, most students were only familiar with repeating patterns, for example, ABABAB or AABAAB. Through hands-on activities and lots of observation, first and second graders were introduced to growing (increasing) patterns and decreasing patterns. They observed how patterns can increase or decrease by a constant, and even practiced explaining and writing rules for pattern growth. Once they felt comfortable explaining the way a pattern increases or decreases, they were introduced to a number of ways to represent patterns, including t-charts, graphing, and algebraic equations. With the right hands-on materials, visuals, and a suitable environment (where they can learn from each other and make mistakes freely), we see that algebra can be taught at any age.
Picture books served as another vehicle for identifying and extending patterns. During this theme unit, we read the book One Grain of Rice by Demi. This book tells the story of a clever girl who tricked a greedy raja into giving her just one grain of rice, and then doubling the previous day’s amount for thirty days. Students explored this exponential growth pattern through a rice collage activity, learning how to use the calculator to multiply by two. They also graphed this pattern on graph paper, writing their own numbers for the x and y axis, and then plotting the dots and connecting them to see the upward curve.
Another book we studied was Two of Everything by Lily Toy Hong, a retelling of an old Chinese folktale. In the story, a poor farmer finds a magical pot that doubles anything that falls inside. To explore this pattern, students created their own magic pots, choosing a rule that challenged them. They learned about input and output, as well as the fact that numbers can be represented by letters and shapes. By writing the magic pot rule as both n+n and nx2, all students could access it, including those who were not yet ready for the concept of multiplication. When students were given the opportunity to create their own pot, they were able to use their personal understanding of operations and wrote rules such as, n-3, n+12 and nx3.
After exploring many other stories and situations, students were tasked with creating their own pattern to convert into a narrative similar to the fables they heard. After the first round of pattern completion, students were asked if they felt appropriately challenged by their work. Many students realized they could push themselves further, and continued to develop their ideas in greater complexity. Some students created repeating patterns, while others created increasing or decreasing ones.
At first, I was concerned about the abstract nature of this challenge, and approaching the story writing process with only a pattern to guide them. This was the reverse of how we had been exploring patterns in our class. However, the students surprised me by coming up with some very creative plots that fit their patterns exactly. As a class, we also discussed characters, setting, problem, and solution. One first grader created a decreasing pattern that looked like this: 3,2,1,0.
In his story, a man who owns three jellyfish discovers that they are escaping through a pipe in his house. One jellyfish escapes each day. They end up in a graveyard where any army uses them to fight off zombies.
A second grader created a challenge pattern that looked like this: 1,16,31,46,61,76,91,106.
His story takes place in a high school, where the temperature increases by 15 degrees Fahrenheit each day. A special task force is hired to solve the mystery and cool everyone down.
This interdisciplinary project gave first and second grade students the chance to apply what they had learned and challenge themselves at their own level. They also explored the parts of writing a story and were able to choose their own characters, setting, and plot, giving them creative expression to share what they were passionate about. We look forward to sharing these stories with visitors at our exhibition in a few weeks!