How does Think Pair Share work in a mathematics classroom? It goes like this...

- Pose a question or task to the class, such as "Give an example of..." or "Which ones of these, if any, is an example of...?"
- (Think) Let students think about the question/task individually for about a minute (or whatever appropriate time)
- (Pair) Ask students to explain their solution/idea/thoughts to one person sitting next to them.
- (Share) Involve the entire class in a discussion of the question/task. A good way to start off is to walk around the class while the pairs are discussing and ask one or two pairs to share their ideas.
- (Recycle) If necessary, a class may not arrive at a consensus. In such cases the class can re-enter the pair phase and work with their partner to sort out the details.

Below are some examples chosen from elementary Number Theory. But these ideas can be easily adapted to any math course from Calculus to Math for Elementary Teaching to Real Analysis.

Example1: (Starter question)

Example1: (Starter question)

- State the definition of $n|k$, where $n,k$ are integers.
- Question: In your own words, interpret what $n|k$ means. Write a few sentences.
- Share with your neighbor your sentences and revise if necessary.
- Pick a few groups to share their work.

Example 2:

- Task: Determine which of the following statements is true.
- If $n$ is even, then $2|n$.
- If $n$ is even, then $n|2$.
- Think for yourself which one is correct.
- Convince your neighbor of your answer.
- Class discussion. Recycle if there is confusion or lack of consensus.

Example 3:

- Question: If $n|a$ and $n|b$, then $n|(a+b)$.
- Think of some strategies you could use to prove this theorem
- Discuss your strategies with your neighbor. Write questions, if you have any.
- Pick a few groups to share their strategies and/or questions
- Make a list of the ideas, and let students continue to ask questions. Then one can move on to the next task, leaving the proof as a homework problem that will be shared later. Another option is to let students come up with a sketch of a proof in class and clean it up at home to be turned in/presented the next time.