Nine and three-fourths is another task on my list of favorites. Students are always intrigued with it, as are colleagues who tackle it in workshop settings. It has been one of my go-to tasks for quite awhile. I do have to be honest and say that I have no idea where I found it. However, I want to extend my thanks to the author, as well as, my sincere apologies for losing track of whose work it is. It is an awesome task.
It is an awesome task because everyone can play. Everyone can join in the conversation and the learning. Everyone has ideas to investigate, think about, and share with others.
This past June, more than forty K – 5 teachers spent some time with this task during a five-day summer math camp. We used nine and three-fourths to kick off our two-day conversation centered around the big ideas in fractions.
WEDNESDAY MORNING’S TASK
Choose one or more pattern blocks to represent one unit. Based on the unit you selected, create a picture that is worth 9 and three-fourths units.
- Identify the unit you selected
- Trace and color your picture
- Justify that your picture does have a value of 9 and three-fourths units
The morning session began with an exploration of the patterns blocks and the relationships that exist among the various blocks in the set. The set of pattern blocks we used included all of the blocks shown, as well as, the brown trapezoids from the add-on set. We talked about the task itself; which including a discussion of an example of a picture worth nine and three-fourths, when the yellow hexagon is worth 1. The picture was comprised of nine yellow hexagons and 3 brown trapezoids (not shown in the picture above). We agreed that we would not use the yellow hexagon, or an equivalent, as the unit. And they were off; working, building, talking, re-starting, recording, and considering how to share this with students, and what aspect of the task should be used to begin the class discussion. At the conclusion of the morning’s work time, a few of the workshop participants presented their pictures.
The following are representative of the pieces that were shared.
Using the 5 Practices for Orchestrating Productive Mathematical Discussion by Margaret Smith and Mary Kay Stein to build our conversation, we talked about the unit each picture was based on, how three-fourths was represented in each drawing, how and why each picture met the criteria of the task, and how each unit was selected. We discussed the teacher moves used throughout the morning session, the impact they had on the learning, and what adjustments might need to be made when sharing the task with students. The morning session concluded with a conversation focused on how the task provides opportunities to discuss and tackle some of the misconceptions students have about the big ideas of fractions.
It was a great way to spend a Wednesday morning.