When engaging students in problem solving and I hope you are doing so often, it is important to think about the types of tasks you give them. Which of the following two will give you the most information about your students?
Example 1: (closed)
Nathan finds 6 pink eggs, 1 yellow egg and 3 blue eggs during the backyard Easter egg hunt. How many eggs does he find in all?
Example 2: (open)
Nathan finds 10 eggs in the backyard Easter egg hunt. Some of the eggs are pink and some of the eggs are blue. How many of each could he have found? What are the possibilities?
Both of these problems have a purpose, but when my goals are problem solving and fluency with numbers the second example is the task type I will provide the most often. Learning how to open up a closed task is an important skill that becomes easier with practice and collaboration with other educators.