Open and Parallel Tasks for Grade 7 and 8 Students

The discussion today is open and parallel tasks, specifically I will be using the example of "Pepperoni on a Pizza" to discuss the ideas of open and parallel tasks for a grade 7 class; and "number of rocks in the elementary class's playground" as an example of open/parallel tasking in a grade 8 class.

Grade 7 "Pepperoni on a Pizza"
Marion Small's Big Idea: Number and Operations, "Numbers Tell How Much or How Many"

Open Question: "How many pepperoni are on a pizza? (personal size 12"/30cm)

Parallel Task:
Task A- "Decide on a number of how many pepperonis might be on an extra large pizza (16"/40cm), then create a formula that can show tell people how many pepperonis are on ANY size pizza"
Task B- "What is a fraction that best describes the Pepperoni to Cheese ratio?"

Rationale:

Students are interested in this idea because of a couple reasons, one might be that they get pizza afterwards (hint, hint); whereas another being that maybe its just not something they ever really thought about. While all students are specifically focused on the number of pepperoni-there is a task B that is mean't to be more difficult because it is relying on the use of fractions. To fathom the task itself the students are expected to step back and break the pizza up into a fraction/slices, afterwards decide what an appropriate fraction might be that represents the number of pepperoni on the pizza; divide that between the number of slices and then relate the number of pizza slices with more cheese than pepperoni on them. This is also a great opportunity to get students started with manipulatives as it is a bit of a broader idea.

Grade 8 "Number of Pebbles on the Playground"
Marion Small's Big Idea: Number and Operations, "There are many equivalent representations for a number or numerical relationship. Each relationship may emphasize something different about the number or relationship."

Open Question:"What is the weight of a single pebble?"

Parallel Task:
Task A- "What do you think the number of pebbles on the playground is?"
Task B-Devise a way of measuring the number of pebbles in the on the playground as efficiently as possible.

Rationale:

Students are working on data management; measurement as well as number sense and numeration depending on the relationships between size and volume. The students will most likely have difficulties when try to fathom a task like counting those stones and then creating a formula to show its possible growth based on the size of the playground.

I came up with these ideas while I was reading through Marion Smalls and ___ text, "More Good Questions: How to Differentiate Secondary Mathematics Instruction". I was reading through, trying to really grasp and understand the purpose as well as meaning of the open/parallel questions. Having the examples really made it applicable for me.

More information:

http://www.teachertoteacher.com/newsletter-archive/jan2010-newsletter.html