Characteristics of Rich Math Tasks

• Rich math tasks are open to encourage multiple methods, representations, and pathways.

• Rich math tasks are inquiry based.

• Rich math tasks allow students to experience the mathematics conceptually before procedures.

• Rich math tasks have a visual component.

• Rich math tasks are "low floor" and "high ceiling".

• Rich math tasks require students to convince, reason, or justify.

Five Principles of Effective Questioning 

1. Plan questions ahead of time that encourage thinking and reasoning. 

2. Ask questions in ways that include all students. 

3. Give students time to think. 

4. Avoid judging students' responses. 

5. Follow up students' responses in ways that encourage deeper thinking.

Five Practices for Orchestrating Productive Mathematics Discussions

1. Anticipating likely student responses to challenging mathematical tasks

2. Monitoring students' actual responses to the tasks (while students work in pairs or small groups)

3. Selecting particular students to present their mathematical work during whole-class discussion

4. Sequencing the student responses that will be displayed in a specific order

5. Connecting different students' repsonses and connecting the responses to key mathematical ideas