# Introducing Number Talks

What is a Number Talk?

• A Number Talk is a short, powerful tool for helping students develop computational fluency and number sense.
• Number Talks are not necessarily directly related to the math curriculum. They are not intended to replace current curriculum or take up the majority of the time spent on mathematics (5-10 minutes).
• Number Talks allow students to make connections and find relationships and patterns.
• Number Talks also allow students to use the language of mathematics.

What is the focus of the Number Talk?

• The conversation is the focus of the Number Talks, and the teacher takes on the role of facilitator.
• Children develop computational fluency and number sense while thinking and reasoning like mathematicians.
• When they share their strategies with others, they learn to clarify and express their thinking, thereby developing mathematical language.
• Students share their mathematical thinking and develop efficient, flexible, and accurate computation strategies that build upon the key foundational ideas of mathematics such as composition and decomposition of numbers, our system of tens, and the application of properties.

For example, if a 1st grade student can only solve 13 -7 by using an algorithm, it means he/she has not been exposed to any other strategies to solve this kind of problem. During a number talk, one student might solve this by thinking of adding 3 to the 7 to make a 10, then adding 3 more to get to 13. Yes, this problem can be solved by adding 3 and 3 more. Students explain how they solved the problem, and the teacher makes a visual representation of these explanations.

Another student might solve this problem by decomposing the 7 into 3 and 4, so take away 3 from the 13 is 10, and then take away 4 more, it is 6. This strategy uses friendly tens as well.

When students are exposed to different ways to solve problems, and specially different ways to use numbers flexibly, they start making sense of numbers.

Algorithms are not always the most efficient strategy, and number talks provide students with a variety of strategies where other students use numbers flexibly to solve problems mentally.

How does Number Talks allow opportunities to make sense and persevere?

• Students look for number relationships to plan their strategies and seek alternate ways to verify their reasoning.
• Students develop flexibility in looking at problems from multiple perspectives!
• As students share their answers and strategies, they must evaluate other ideas and approaches, which further develops this mathematical disposition.

Do Number Talks help build fluency of basic facts?

• Yes, mental computation is a key component of number talks because it encourages students to build on number relationships to solve problems instead of relying on memorized procedures.
• Yes, mental computation causes them to be efficient with the numbers to avoid holding numerous quantities in their heads.
• Yes, repeated experiences with reasoning strategies are effective in committing facts to memory; memorizing is not. Multiplication problems can be solved by using numbers flexibly. All of these strategies are based on place value.

USING SIGNALS!

*Tell your students that you are going to be doing a Number Talk. They are to be thinking in their heads, and trying to figure out the answer.

*Tell them that they should be ready to share how they figured out the answer.

*You can use these signals for your Number Talks, or you can make your own signals with your class.

NUMBER TALK MOVES for teachers and students!

*You can introduce these Number Talk moves in one day, or a few each day.

WHAT DOES THE TEACHER SAY?

*After providing some wait time, ask students to share with their partner. When students explain to their peer first, they gain vocabulary and confidence to share with the class.

WHAT DOES THE STUDENT SAY?

*In order to help students use their mathematical language, show them these examples to share their thinking.

Your students can also come up with their own math language!

All number talks follow a basic six-step format.

1. Teacher presents the problem: Problems are presented in many different ways: a word problem, number problem, ten frames, dot cards, models. You can show problems on a document camera or write on the board. Present today’s problem on the board: “How many legs are there on 5 horses and 2 roosters?”
2.  Students figure out the answer. Give time to figure out the answer. To make sure the students have the time they need, ask them to give a “thumbs-up in front of chest” when they have determined their answer.
3. Students share their answers. Teacher collects different answers on the board. “Does anybody have a different answer?” Only answers on this step.
4. Then, students share their thinking. Have students share with a partner before they share out with class. This helps them be prepared to share. Have three or four students explain their thinking to the class. “Did anybody do it differently?” This is the most important part of the number talk, because it is here where students can visualize how other students solved the same problem.
5. The class agrees on the “real” answer for the problem. There might be different answers (Which one doesn’t belong?). Models and explanations are very helpful for students to see where their thinking went wrong, help them identify a step they left out, or clarify a point of confusion.
6. The steps are repeated for additional problems. Thank the students for their participation in the Number Talk.

Different examples of Number Talks

*Subitizing: How many do you see? How do you know?

*Different strategies to add, subtract, multiply and divide:

• Doubles/near doubles: 298 + 297
• Making Landmark or Friendly Numbers: 98 + 52
• Adding up in Chunks: 57 + 36
• Compensating: 37 – 18
• Partial Products: 14 x 16
• Doubling and Halving: 15 x 16

Repeated Subtraction: 100 ÷ 25

*Different types of images that promote discourse