As has been discussed in two of our previous newsletters, we really like the work of Marion Small in Good Questions: Great Ways to Differentiate Mathematics Instruction published by NCTM in 2009. This newsletter contains our application of Ms. Small's approach to tasks contained in Books G, H, and I (Grades 6-8) of Making Sense of Problem Solving, published by Teacher to Teacher Publications, Inc.

Links to open and parallel tasks for grades 3 to 5 can be found in our October 2009 Newsletter.  Our August 2009 Newsletter provides links to open and parallel tasks for Kindergarten through grade 2.

In order to meet the diverse needs of students, Marion Small proposes a strategy of using Open and Parallel tasks related to the big ideas in each mathematical strand.  Teacher to Teacher’s Making Sense of Problem Solving program is built around the big ideas presented in the National Council of Teachers of Mathematics Curriculum Focal Points, which have been used in the development of standards in many states.  Teacher to Teacher has an underlying belief in the importance of differentiation. In each unit, we start with Warm Ups that introduce or reinforce concepts the students will need in order to fully engage in the problem solving task.  Then students solve the main task. Finally, we offer at least one Extension to challenge the thinking of students who are ready to go beyond the basic math concepts embedded in the problem solving task.

Marilyn Small defines open tasks in this way: "A task is open when it is framed in such a way that a variety of responses or approaches are possible."  She explains parallel tasks as "Sets of tasks, usually two or three, that are designed to meet the needs of students at different developmental levels, but that get at the same big idea and are close enough in context that they can be discussed simultaneously."

We encourage you to take the following ideas and use them to adapt other problems. We'd love to hear from our newsletter readers if you create a set of related differentiated tasks that works well with your students.

We have developed three options for each problem: one "open" task and two parallel tasks. The open task generally targets students who are proficient, but is open enough to allow all students to participate.  The Option 1 parallel tasks are designed for students who are struggling, and Option 2 parallel tasks provide additional challenge for students who are ready to go beyond grade level expectations.  When presenting these to students, we suggest mixing up the order, so that students consider all options when they choose a task.  Be sure to include a journaling activity as a follow-up that asks students to explain why they chose the numbers they did in an open problem or the parallel task option that they chose.

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