PSSD Math:
Open Middle Problems

What is an Open Middle Problem?
An Open Middle problem is a specific type of task where the beginning of the task is “closed” or the same for everyone, and the end is also “closed” or same answer for everyone. The middle of the problem is “open”; this means that there are many ways to complete/solve the problem. As Open Middle problems have evolved, some have turned into task that have both “open” middles and “open” ends.

How Can I Use Open Middle Problem?
Open Middle questions are a type of problem and can be used for a variety of purposes and different formats. These types of problems lend themselves to collaborative group work. In addition, students are expected attempt a problem multiple time before reaching a conclusion. An additional benefit is that these problems can be used formatively to determine students’ abilities and understandings because they can highlight the processes that students use to solve these problems.

Depending on the what topic is being explored, these problems may require different materials and resources. As well, there are a number of different ways to facilitate students who are working through these problems. What follows are some ways considerations to help teachers determine how to use Open Middle problems.

Inquiry/Discovery in a Collaborative Setting

If the goal is to have students come to understand a topic at a deeper level, having students work together to develop a solution/strategy to solve the problem is a good choice. The goal is to have students attempt problems and try out a variety of ways to solve the problems so that they arrive at a deeper understanding of the concepts. In these situations, students are given the problem in small groups and asked to share possible methods and solutions with their group members. The group works together to try to find a strategy that works and then refine it.

Inquiry/Discovery in an Individual Setting

Another way to get students to understand a topic at a deeper level is to introduce an Open Middle problem to a  student give them a sheet/scaffold that has 6-8 attempt boxes on it (linked below!). The purpose of having the attempt boxes is so that student try to find multiple different ways to solve the Open Middle problem - in this way we are asking students to look for the best solution/strategy. The goal here is not to be correct on the first attempt but to continue to develop a better strategy/process every attempt.

Knowledge Demonstration in a Collaborative Setting

In this structure students are looking to utilize their knowledge of the concepts to demonstrate effective strategies to solve these problems. Teachers observe their students and look for the strategies used. The goal is to move students past the "guess and check" stage into strategies where they can provide explanations around how they know they have the most correct/efficient answer.

Knowledge Demonstration in an Individual Setting

Again the goal here is to see what students know and can do, and is therefore similar to what is noted above. In this scenario though students are provided with the attempt worksheet to share their thinking. The portion that we care about the most is the explanation they provide to share their thinking, as well as the "what to try next" box - with the goal that students can provide a deeper understanding then simply guess and check.

Where Can I Find Open Middle Problems? 

The most comprehensive place to find Open Middle problems is on the Open Middle Website. This includes questions at different grade levels and on different topics (though it is organized according to Common Core standards and not Saskatchewan Curriculum). 

You Mentioned Something About "Attempt Sheets?"

We did! You can find these below.