# Favorite lessons create an intellectual need

As the math interventionist in our building I have the luxury of co-teaching with an incredible group of 6-8 math educators. When the 6th grade math teachers meet face-to-face much of our PLC time is spent examining student work and reflecting on what went well in today’s lesson and what can be improve upon.

Today we discussed with our counterparts the results of our attempt to give students a “headache” and create an intellectual need for vocabulary when learning about exponents. Our original plan was to go straight to the notes as a mini-lesson then introduce the vocab but, as my colleague and I were discussing over email, we decided to introduce exponents within the context of a real world situation.

Here’s what today’s lesson looks like from our lesson plans in Google Drive.

Here’s a summary of our discussion in our PLC tracking document.

Our improved instructional design of the lesson wasn’t perfect, but it was a much better learning experience than simply launching with notes followed by practice.

Here’s how we framed the learning. We began by posing to the class the problem in the image below and constructed meaning using a team teaching think-aloud. I read the problem, my co-teacher Cathy modeled confusion and read the problem again, and discovered a starting point. I interjected that there are many ways to represent problems and suggested we use a tree diagram to get us started.

As we created the tree diagram we eventually stopped to emphasize that the pattern continued. At that point we asked the class (and fell out of the think-aloud mode!) how to represent the continuing pattern for Thursday and Friday. Then we finished creating the tree diagram.

My co-teacher Kathy mentioned to the class that her eyes were beginning to look at the rows of “F’s and we counted the numbers in each row.

We then looked at the diagram, noted the values and introduced the vocabulary term “Standard Form” by labeling that column.

Next  we noticed two was a factor in 2, 4, 8, and 16. We introduced the vocabulary term “Expanded Form” and began with 2 x 1. Students quickly shared 2 x 2 = 4, but to write the expanded form of 8 most students wanted us to write 2 x 4 instead of 2 x 2 x 2. We had a discussion on only focusing on using 2.

After expanding each of the numbers, we worked from the bottom to complete the Exponential Form column noting 2 x 2 x 2 x 2 is equivalent to 2^4. Students quickly caught on as we worked our way up the column. Comprehending that 2^0 is equivalent to 1 was a bit troublesome for a few students. I don’t have the image but we then attached meaning to the vocabulary words base, power and exponent.

The goal for the original lesson was to acquire new vocabulary. We could have accomplished it using only notes followed by independent practice, but providing a context for learning and creating an intellectual need for the vocabulary made the lesson more meaningful.

I wonder, however,  if too much vocabulary was shared in the lesson. I hope not. Students were only asked to identify the base, power, and exponent in their practice. The next day they examined more closely the terms standard form, expanded form and exponential form.