What are Number Talks?
Number Talks show us that there are many ways of thinking about and solving the same mathematical problem and that these differences are interesting and should be respected. Number Talks help grow our ability to think about numbers visually and flexibly and how to calculate without paper and pencil. With number talks, students have a chance to think through their understanding of numbers and explain their reasoning.
In this short routine, students might be shown an expression or equation, two numbers to compare, or a string of computations that hold a pattern. The students are encouraged to mentally solve the problem. There is no right or wrong way to solve the problem. It’s ok, if they don’t get the right answer at first, too. Making mistakes grows our brains. The most important thing for this routine, is to see different ways that we can solve a problem.
We love when there is more than one answer because making and discussing mistakes lead to much more learning, and it also allows us space to give mindset messages about mistakes. When we did the 12×15 number talk, there was a student who got 168, and as she was explaining her thinking, she stopped and said, “Oh, wait! I made a mistake.” Jo’s response was, “That’s great! That means you have synapses firing in your brain because you made that mistake.” Jo then invited her to explain her thinking when she made the mistake so that the class could understand what she did (see video here). This was an important moment because the student who was sharing, and the rest of the class, saw that her thinking was respected and her mistake was celebrated.
Remember to value mistakes and say things like “This is great we have three different answers; we will have a really good discussion.”
General Outline for a Number Talk
- Post the problem for all students to see.
- Allow wait time for students to mentally solve the problem. Encourage students to think of more than one way to solve the problem.
- Teacher records all possible answers generated by the students, without judgment.
- Select a student to share how they solved the problem.
- Have the student identify the answer they are defending, then explain their solution path.
- Record each step in the student's thinking as accurately as possible.
- Discuss the student's strategy, encouraging students to ask questions, revoice and rephrase in order to fully understand.
- Repeat, having multiple students share as time and interest allows.
- To close, ask students to look across the various strategies, make connections between them, and reflect on new learning.
Some questions you might ask are:
- What is your solution?
- How did you think through this problem?
- What did you do first? next? then?
- Why did you decide to ___?
- What is a different way to solve this problem?
- How are these strategies related?
Additional resources you might find helpful:
- Google Doc with Links: Optional - K-5 bank of Number Talks to get you started.
- Google Document: How to: Number Talks
- Google Document: Planning a Number or Dot Talk
- Videos from Inside Mathematics: Select from Grades 1-7
- Article: Number Talks (I'll convince you with ducks)
- Video from YouCubed: Jo Boaler discusses the importance of Number Talks
- Video from Mathematics Education Collaborative: MEC Number Talks 3rd Grade