Number Talks TK - 2nd Grades

“Teaching math well calls for increasing our understanding of the math we teach, seeking deeper insights into how students learn mathematics, and refining our lessons to best promote students’ learning.” A Message from Math Solutions Founded by Marilyn Burns

“Teaching math well calls for increasing our understanding of the math we teach, seeking deeper insights into how students learn mathematics, and refining our lessons to best promote students’ learning.” A Message from Math Solutions Founded by Marilyn Burns

How many do you see?

How do you see them?

How do you see them? 5 + 3

How do you see them? 3 + 3 + 2

How do you see them? 2 + 2 + 2 +2

How do you see them? 3 + 3 + 2

How do you see them?

How many do you see?

How do you see them?

How do you see them? 18 As 3 groups of 6 6 + 6 + 6 = 18 or 6 x 3 = 18

18 As 6 groups of 3 How do you see them? 3 + 3 + 3 + 3 + 3 + 3 = 18 or 3 x 6 = 18

How do you see them? 18 As 3 groups of 6 6 + 6 + 6 = 18 or 6 x 3 = 18

How do you see them? 18 As 2 groups of 9 9 + 9 = 18 or 9 x 2 = 18

How do you see them?

A sample of what students would hear during Number Talks 3 + 3 + 3 + 3 + 3 + 3 = 18 3 x 6 = 18 6 + 6 + 6 = 18 6 x 3 = 18 9 + 9 = 18 9 x 2 = 18 Array Dice Subitizing Repeated Addition Multiplied Sets Groups

What is a Number Talks? A Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing practice with mental computations and the development of conceptual understanding.

What is the Goal of a Number Talk? The primary goal of a Number Talk is computational fluency. Mental mathematics is a key component of Number Talks because it encourages students to construct numerical relationships and to develop their own strategies instead of relying on solely memorized procedures.

In order for children to become conceptually fluent, they need to know particular concepts that go beyond what is required to memorize basic facts and procedures. Numbers are composed of smaller numbers. Numbers can be taken apart and combined with other numbers to make new numbers. What we know about one number can help us figure out other numbers. What we know about parts of smaller numbers can helps us with parts of larger numbers. Numbers are organized into groups of tens and ones (and hundreds, tens, and ones, and so forth). What we know about numbers to 10 helps with numbers to 100 and beyond.

What is a Number Talks? Intentional and Planned Math Moments Short 10-15 minute sessions Daily Routines Practice with Mental Computations Development of Conceptual Understanding and Fluency

Identify the Key Components of Number Talks Classroom environment and community Classroom discussions and discourse The teacher’s role The role of mental math

What is the format for Number Talks? Basic steps of Number Talks Teacher present the problem. Students figure out the answer. Students share their answer. Students share their thinking. The class agrees on the “real” answer for the problem. The steps are repeated for additional problems.

Classroom Discussions During a Number Talk, the teacher will present the class with a problem. This can be accomplished in a variety of ways: On the Board Holding Up an Index Card Through a Power Point Using the Document Camera Teachers provide the students with time to think and formulate solutions mentally. Using the Number Talk Hand Signals, students indicate when they are have a solution(s). When most students have indicated they have solutions the teacher will begin the discussion by calling on students.

Presenting a Problem 12 + 69  

Symbols Meanings Thumb Up Thumb Up and Forefinger Out Place Thumb Up against Chest This signifies that you are thinking Thumb Up and Forefinger Out Hand remains on chest, fingers extended as ideas are thought of I am willing to share Thumb and Pinky Finger Hand Motion “I agree” Thinking Have an Idea I Agree

163 + 147 How many do you see? I am thinking I am thinking and I have a solution I agree with …

163 + 147 How do you see them? I am thinking I am thinking and I have a solution I agree with …

Class Discussions Students are now given the opportunity to share their strategies and justifications with their peers. There are many benefits of sharing and discussing computation strategies: Clarify their own thinking. Consider and test other strategies to see if they are mathematically logical. Investigate and apply mathematical relationships. Build a repertoire of efficient strategies. Make decisions about choosing efficient strategies for specific problems.

Response Prompts My strategy is ... My strategy is similar / different because... I can prove my thinking by... I would like to revise my thinking... I heard you say that... I know my answer is correct because... I agree / disagree with your answer because... I would like to add... Can you explain... I can connect to this because...

Class Discussions Wrong answers are used as opportunities to unearth misconceptions and for students to investigate their thinking.

Teacher’s Role In the past we as teachers have had the role of “teaching by telling.” Our role must shift with Number Talks to help students make sense of mathematics by building upon mathematical relationships. Our role must shift from being the sole authority in imparting information and confirming correct answers to assuming the interrelated roles of facilitator, questioner, listener, and learner. Our role is to help our students ponder and discuss the problems by posing questions that lead to conversations that build on meaningful mathematics.

The Role of Mental Math Mental computation is a key component of Number Talks because it encourages students to build on number relationships to solve problems instead of rely on memorizing procedures. One of the focuses of Number talks is for students to focus on number relationships and use these relationships to develop efficient, flexible strategies with accuracy. Mental computations causes them to be efficient with the numbers to avoid holding numerous quantities in their heads. Mental computations help strengthen students’ understanding of place value.

Rationale for Number Talks Our classrooms are filled with students and adults who think of mathematics as rules and procedures to memorize without understanding the numerical relationships that provide the foundation for these rules. Accuracy denotes the ability to produce an accurate answer. Efficiency refers to the ability to choose the appropriate, expedient strategy for a specific computation problem. Flexibility means the ability to use number relationships with ease in computation.

How to begin... Focus on building number sense Progress through age related concepts and skills

Developing Specific Strategies in a K-2 Classroom Four Goals for K-2 Number Talks Developing Number Sense Developing fluency with small numbers Subitizing Making tens Kindergarten Fluency Number Talks 1st Grade Addition Number Talks 2nd Grade Addition and Subtraction Number Talks

Developing Specific Strategies in a K-2 Classroom Dot Images Counting On by Ones Counting On in Chunks Making Tens Five Frames / Ten Frames Doubles / Near-Doubles Breaking Each Number into Its Place Value and Combining Adding Up Counting Back Removal

Number Talk Activity Gather your supplies 10 Index Cards Dots Marker Using your grade level “String Sheets” create at least two strings you can use with your students on Monday. Practice your Number Talks with others at your table.

Questions to Help Guide Conversations How many do you see? Who would like to share their thinking? How do you see them? Why did you do that? Tell me more. Who else started the problem this way? How did you think about that? Did anyone else see this in a different way? What strategies do you see being used?

Charting Our Student’s Thinking As our students communicate their thinking it is important that we chart their thinking. Just as in the opening example, model what students are communicating. Asking clarifying questions. Allow the student enough time to answer the question. Be slow to provide them too much assistance.

Elementary Number Talks Resources https://elementarynumbertalks.wordpress.com/ Humphreys, C., & Parker, R. E. (2015). Making number talks matter: developing mathematical practices and deepening understanding, grades 4-10. Portland, ME: Stenhouse . Parrish, S. (2014). Number talks: helping children build mental math and computation strategies, grades K-5. Sausalito, CA, USA: Math Solutions

Thank You for your participation today! Catherine Vittorio San Bernardino County Superintendent of Schools Catherine.Vittorio@sbcss.net