Long Division and More in Class 10 Math

Long Division and More in Class 10 Math

As the Class 10 students entered Room 214, an upbeat song streamed from a laptop, setting the tone for a fun and engaging morning in Integrated Math III, a required course for this grade that delves more deeply into algebra, geometry and precalculus with a specific focus on functions.

“Find a seat, please,” Upper School Math Teacher Shaw Driggers told the group, switching off the music. “And grab a writing utensil.”

When the class was ready, Mr. Driggers directed their attention to the board as he wrote 3 ⟌583 in red marker. As the students worked through this problem collectively, he encouraged them with questions like “Who remembers what we do next?” and “Can someone pick up the process?”

After this review, Mr. Driggers expanded to a new topic. “We’re going to move to the realm of polynomial variables,” he explained, handing out a practice packet. “Let’s jump right in. I’ll meet you on page two.”

Polynomials, the students learned, are algebraic expressions consisting of variables that can be added, subtracted and multiplied (for example: x2 + x – 12).

At the top of the second page, a challenge awaited our scholars: Divide P(x) by D(x). P(x) = 2x2 – 5x – 7; D(x) = x – 2. “How many 2x2 does x go into?” he asked when the problem was projected for all to see. Again, he expected his students to contribute to this collaborative exercise and, soon enough, the correct sequence of numbers and symbols filled the board.

“Remember to keep terms like x in the same column,” he stressed before advancing to the next problem:

8 + 30x – 27x2 – 12x3 + 4x4
x + 2

“Who’s feeling brave?” Mr. Driggers asked with a smile. Several students raised their hands to demonstrate their understanding. Others asked questions to clarify steps they weren’t sure about. In this supportive and collegial environment, everyone had the chance to shine.

For the next few minutes, the students worked on their own to tackle a tricky problem in their packets, drawing on the skills they had learned in earlier lessons. Their teacher walked around the desks, checking in with each person. “This is great. Now repeat the process,” he said to a girl by the door. “You want to subtract here,” he noted to another.

Then it was time to come together again. In quick succession, Mr. Diggers called on a handful of students to share their calculations. Their pride was unmistakable as was their interest in and aptitude for this unit.

“I got a perfect match with two terms!” one student exclaimed. “Can I keep going?” another asked. When the period ended moments later and the class dispersed, a couple of students stayed behind to continue talking about math with Mr. Driggers.

In upcoming lessons, these Class 10 students will investigate more function relationships including quadratic, exponential, inverse and logarithmic. As evidenced by their strong effort in today’s class, they continue to be confident, proficient and curious mathematicians.