Dividing through the year—inside the classroom

I do not tend to remember the past in detail, but I will vividly remember this particular moment from my year of service with City Year. On one of my first days as a near-peer mentor in September, I was working with Aaron, a fifth-grade student, on division story problems. In particular, Aaron struggled with the following problem:

There are three delivery vans and 65 pizzas. The boss told the drivers that they should put an equal number of pizzas on each van and that they could split the remaining pizzas equally. How much of a leftover pizza does each of the 3 drivers get?

He called me over with a dejected hand and an obligatory rather than authentic ask for help. I kneeled down and smiled, “Which part of the problem is confusing you?”

Aaron responded with the same deflated tone, “Everything.” The way Aaron’s head was drooped over on his desk combined with his sad eyes and worn-down pout told me that he was expecting me to do the heavy lifting on this problem for him.

With little time remaining in our math block, I crouched down and encouraged him to start by re-reading the problem together with me. His demeanor continued to be just as flat, but he was able to figure out the equation and the answer. However, when asked how to split the leftover two pizzas between three people, Aaron let out a frustrated, “I don’t know,” and forcibly put his head down on his desk in the crook of his elbow.

Right then, the teacher called for the students to transition to writing. I patted Aaron on the shoulder and reassured him, “We’ll get it tomorrow!”

As it happened to be, Aaron was placed on my academic focus list of students for me to work with. Through the next ten months, I spent over 1000 minutes working with him in a one-on-one and small group setting. Together, we mastered his use of a ratio table for multiplication and division and worked on deepening his understanding of fractions. Aaron started to compile many 3s in his workbook, a score that represents understanding of the concept. At first, it was with my guidance, but gradually, Aaron completed his workbook pages independently and correctly, rarely asking me for help.

Before I realized it, the end of the school year was approaching. My first memory of Aaron came full circle as we returned to division story problems with remainders but this time, three-digit by two-digit division.

Aaron raised his hand, his desk coincidentally situated in the back of the room as before. I suddenly recalled the moment from earlier in the year. However, this time, Aaron was sitting upright and gestured to his workbook while asking, “Is this right?” I looked down at a perfectly executed ratio table to solve this division problem, including his representation of the remainder as a fraction. With a warm smile, I looked him in the eyes and responded, “Yes. Good work, Aaron.”