In one of my classes (Bridge to College) there are sets of developed lesson plans that address the standards for the course. Because of agreements with the community colleges in our state, I do have to stick fairly closely to the outline provided. Luckily, the lessons themselves are pretty well thought out and have a huge focus on the practice standards and the idea of more than one right way to solve problems approach that I like to employ in my other classes.

I do, however, take the opportunity to make small additions or adjustments to further the opportunity for student discourse.

For example, we are working on a unit dealing with measurement and proportional reasoning. The seemingly obligatory scale drawing project comes near the end. I printed off a picture, cut it into one inch squares and asked the students to each recreate a square on an 8 inch square. At the end, the pieces would be put together to get one giant image. They didn’t know what they were creating in the beginning.

My small changes: No much in the way of guidance. Each student tried there own method. Halfway through class, I had them find someone who was using a different method to scale up and have a quick chat. After they finished their first squares, they each did another one and had to use a different method. Most did the one from their partner chat, but one or two thought of a totally new way to approach.

After they are assembled into the wall art, the lesson plan lays out the following questions to consider:

Questions:

1. Look at the finished product and evaluate the display. Did the lines match up? Which part looks the best? Which piece would have been the easiest to recreate? The hardest? Why?

2. What is the relationship of the perimeter and area between your original square and the square you created? What is the relationship of the perimeter and area of the original square to the final class project?

3. If we did the project using 4” x 4” squares how would that have affected the perimeter and area?

First will be in the form of a debate:

1. Which method works best for scaling? (Two or three teams depending on how many methods they settle on).

Second will be a group think:

1. What makes a good strategy? (precision, speed, etc)
2. After we come up the list of attributes, they’ll be asked to rank them in importance and have a quick share out why they think so. I’ll pose the debate question again to see if any minds have changed. I’m expecting an ‘it depends’ as a final answer, but a well thought out, justified, and detailed it depends.

Nothing too exciting or revolutionary but by using the debate structure, students spend time doing all the important steps of good discourse: listening, responding, justifying, prompting others, etc. It’ll add a bit of time onto the project, but time well spent. A scale factor project is just not that interesting all on its own. But really thinking about how to choose a strategy and when and why other choices might be better/worse can then be applied in more complex problem situation later.

The squares are starting to go up (This is the point the students figured out what they were creating. I did give them all random inside bits to start with):

What are some of your favorite strategies for increasing meaningful student discourse?

Edited to add the finished product: