Math Open Ended Problem Solving Lesson (Grades 5-8)

PROBLEM: An ice cream stand has 9 different flavors. A group of children come to the stand and each buys a double scoop cone with 2 flavors. If none of the children chooses the same combination of flavors and every combination is chosen, how many children are there? Show how you got your answer.

Following Van De Walle's 3 part lesson format, the lesson would be broken down thusly:

BEFORE: Give the problem to the student and go over the problem as a class. Make sure the class understands the question and what it is asking. This is the time to be checking on prior knowledge. In this case, knowledge of addition and multiplication are likely needed. A few review problems may be in order. The class could also do a couple of warm up questions similar to the main problem, but easier. For instance, they could work out how many different ways you could make a dollar out of change, or in a class of eight students, how many different pairs could be made. You could also have everyone make a quick estimate on how many different combinations of ice cream are possible with this problem. They key is to get them thinking about how they are going to work this out.

DURING: This problem can be done individually or in small groups, depending on the level of class behavior. Let them work on it whatever way they think will work. At this point, many different student needs can be met by using different manipulatives. Some students may find it easier to work with cutouts of ice cream scoops. Some may simply want to draw a diagram on paper. Others may want to work it out using a calculator. Whichever way feels best for the student can be used.

In the During stage I would be walking around the room, checking on the different methods being used. If students are having difficulties with the problem, they can be provided with some hints, or possibly an easier to comprehend manipulative. They can also be encouraged to look at the problem in other ways or possibly use a different method to solve the problem.

AFTER: This is the time to discuss the problem with the class. Let the students tell or show how they reached their solutions. Give everyone an opportunity and enough time to explain and justify their answers. Identify what worked and have the students use that as a reference for future problems. There are multiple ways to solve this problem, and the students can make a list of all viable solutions to help them think about this type of problem.

Once the class has an understanding on how this type of problem is worked out, the students can be assigned a few more similar problems to work out on their own to assess how well they are comprehending the material.

Source

The Franklin Institute - Resources for Science Learning