Overview & Rationale

The “explore” phase of the lesson is crucial for making the lesson student- centered – the onus of mathematical thinking and work shifts from the teacher to the students. This is the time when students actually do the work of solving the mathematics tasks (usually in small groups or in pairs). Your role is to move among groups as students work, but you want to avoid mini-lecturing! Instead, you want to allow students to struggle and make mistakes. Listen closely and see what solutions students are coming up with. If students get stuck or are ready to move forward, you can stimulate their thinking, mainly by asking questions. To support students’ in problem solving and to make productive use of student solutions, you will need to anticipate student responses to the task and have a plan for monitoring their work to prepare for the whole class discussion.

1. Solve the task at least 3 different ways.

These strategies/solutions should be ways that students are likely to respond to the mathematics task. Along with these different solution paths, make note of any specific strategies that are not shown by the solution itself, possible confusions or misconceptions that might arise, etc. Figure 4.3 (p. 43) in the Five Practices book provides an example of what it looks like to anticipate different solution paths for a task. If you are having trouble, there is a wealth of research on students' mathematical thinking and mathematics teaching that can help you anticipate likely solution paths and possible confusions for your selected mathematics topic.

2. Plan questions or actions to respond to student thinking.

For each solution path that you anticipated, you’ll plan a few questions or actions to respond to the specific solution strategy. You should refer to Chapter 4 in the 5 practices book as you think about both assessing questions and advancing questions.

3. Compile the anticipated strategies and responses to student thinking

Make a monitoring chart for the task (see Figure 4.5, p. 45-46 & Appendices B & C in the Five Practices book). This monitoring chart will come at the end of the lesson plan. There is already a template for you to use.