It was one question that united Tottenham Public School students: Mrs. Nichol’s class had 2 caterpillars in her classroom. If 2 caterpillars eat 5 leaves, how many leaves would 12 caterpillars eat?¹
The result: a mathematical celebration of how students learn, and how they continually build their knowledge throughout the whole elementary school math program as they move towards high school.
All of the Tottenham teachers, regardless of grade, asked students this one math question. And while all grades found the same answer, the methods used were quite different.
In Grade 1, students were expected to identify, describe, extend and create repeating patterns to solve the problem. Fast forward to Grade 8, where students used linear growing patterns with graphs, algebraic expressions and equations to find their answer. This shows the connection that exists between these seemingly different learning expectations.
Throughout the learning process, students use manipulatives and pictures to help them develop concrete and hands-on representations of patterns. As students build on this conceptual skill over the years, they can represent the pattern with numbers. Once in high school and beyond, they can think about patterns in more abstract ways.
In the photo gallery below you can see evidence of this continuum of learning. Students are using math manipulatives, drawing leaves and caterpillars, informal and more formal t-charts, multiplication, unit rate, graphs and finally, algebraic expressions and equations to solve the shared problem.
These math samples are interesting because they clearly illustrate that learning math is a cumulative process and depends greatly on a team approach. This team is made up of every teacher a student encounters along the way as well as their families, school staff and principals.
This example also shows that while knowing the fundamentals of math is very important, there is more going on. Students are expected to read and understand a written question, which sometimes has multiple steps. They are expected to develop a plan for solving the problem, carry out their plan and represent their solution in a clear manner to others.
Really interesting problems also bring in many types of mathematics. For example, in the caterpillar question we see growing patterns, graphing, repeated addition, multiplication and algebra.
Our school communities work as a team to celebrate student success, learn from our mistakes and help students build on their understanding at each stage of the process. This is a tough task, but together we are better!
¹ Smith, Margaret Schwan., and Mary Kay. Stein. 5 Practices for Orchestrating Productive Mathematics Discussions. Reston, VA: National Council of Teachers of Mathematics, 2011. Print.