Number Talks Presented by: Kim Mott, Instructional Coach Beechgrove Andrea Krumpelman, Instructional Coach Summit View Elementary

Entrance Ticket How has your instruction in math changed this year as a result of the common core standards? Participants will complete the entrance ticket upon entering and begin reading the article.

“How to Get Students Talking “How to Get Students Talking! Generating Math Talk That Supports Math Learning” Article: “Number Talks Build Numerical Reasoning” by: Sherry Parrish www.nctm.org Show introductory video clip after reviewing this slide. Reference important points in the article. Jigsaw 5 key components in math. Kim introduction, Andrea jigsaw

Why Talk About Math “ 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.” Kim

What are Number Talks? Classroom conversations and discussions around purposefully crafted computation problems are at the very core of number talks. Number Talks incorporate: Accuracy: The ability to produce an accurate answer. Efficiency: The ability to choose an appropriate, expedient strategy for a specific computation problem. Flexibility: The ability to use number relationships with ease in computation. KIM

Number Talks in Action Before we watch the third grade number talk for 70-34, think about how you would mentally solve this problem. As you are viewing the video clip, consider the following: How are students using number relationships to solve the problem? How would you describe the classroom community and environment? Which strategies demonstrate accuracy, efficiency, and flexibility? How are the students’ strategies similar or different from your strategy? Show Classroom Clip 3.4 Copy PP. 347-350 for the reflections and observations for the strategies that the students use. Share out and discuss questions and observations from the video (Chart the strategies that demonstrate accuracy, efficiency and flexibility) KIM

The Key Components of Number Talks Classroom environment and community Classroom discussions The teacher’s role The role of mental math Purposeful computation problems Andrea: Recap

Classroom Environment and Community Safe, risk-free environment Students comfortable and offer responses for discussion Classroom exhibits a culture of acceptance based on the common goal of learning and understanding Community of learners based on mutual respect As we present this slide, ask participants what a Number Talks classroom environment looks like/feels like. Book PP. 10-15 Andrea

Classroom Discussions Develop system for students to respond to questions, while allowing for think time. What did we see in the video clip? Discuss the process of writing the problem on the board, students using their fist to indicate if they have an answer or not, raise their thumb with an answer, raise more fingers if they know more than one way/strategy to solve to problem. All answers, both correct and incorrect, are listed on the board. Students defend or justify their answers to prove their thinking. Teachers help students realize that mistakes are opportunities for learning. Change to the teacher being the learner is the criticial mind set change. ANDREA

The Teacher’s Role “Since the heart of number talks is classroom conversations, it is appropriate for the teacher to move into the role of facilitator.” Teachers must change their thinking from concentrating on the final correct answer, to listening and learning about students’ natural thinking through asking open ended questions. “What answer did you get?” “How did you get your answer?” P. 12 ANDREA

The Role of Mental Math Students need to approach problems without paper and pencil, and are encouraged to rely on what they know and understand about numbers and how they are related. Mental computation helps students strengthen their understanding of place value. Look at numbers as whole quantities and NOT JUST DIGITS! A problem such as, 199+199 written horizontally helps illustrate this reasoning. ANDREA

Purposeful Computation Problems Careful planning BEFORE the number talk is necessary to design “just right” problems for students. This planning is important because we want to have a purposeful number talk with a common focus/specific skill in mind. P. 15 book ANDREA

Establishing Procedures and Setting Expectations: The Four Essentials The number talk is designed to be only five to fifteen minutes of focused discussion. Select a designated location that allows you to maintain close proximity to your students for informal observations and interactions. Provide appropriate wait time for the majority of the students to access the problem. Accept, reject, and consider all answers. Encourage student communication throughout the number talk. Location of students is critical no matter if the students are in Kindergarten or 5th grade. KIM: talk about results, show Beechgrove video

Holding Students Accountable for their Learning Ask students to use finger signals to indicate the most efficient strategy. Keep records of problems posed in the corresponding student strategies. Hold small-group number talks every day. Create and post class strategy charts. (living document) Require students to solve an exit problem using the discussed strategies. (use an index card) Give a weekly computation assessment. ** When discussing #5, talk about index card using the purposeful strategy on the front and any other strategy the student wishes on the back. These exit cards are NEVER graded since they are used as a formative assessment only. This will help you direct the next day’s number talk.

Four Goals for K-2 Number Talks Developing number sense “Number sense is an awareness and understanding about what numbers are, their relationships, their magnitude, the relative effect of operating on numbers, including the use of mental mathematics and estimation.” Developing fluency with small numbers Subitizing (immediately recognizing a collection of objects as a single unit) Making tens P. 37 Conservation of Number: The understanding that the quantity of a given number of objects remains the same regardless of how it is spatially arranged. One to One Correspondence: Count a set of objectives while understanding how a given quantity correlates to a specific number. Fluency: Knowing how a number can be composed and decomposed and using that information to be flexible and efficient with solving problems. Subitizing: Immediately recognizing collection of objects as a single unit. (i.e. looking at dice and knowing the number immediately) Making Tens: Use ten frames, base ten blocks, unifix cubes, dot cards ANDREA

Classroom Link: Ten-Frames and Dot Cards Classroom Clip: Kindergarten Consider the following while viewing the clip: How does the teacher build student fluency with small numbers? What questions does the teacher pose to build understanding? How are the tools and models used to support the goals of K-2 number talks? What strategies are the students using to build meaning of the numbers? What examples of subitizing, conserving number, and one- to-one correspondence do you notice? What opportunities are created for the students to begin building an understanding of ten? How does the teacher support student communication during the number talk? Notice that in every instance the teacher never confirms the students’ solutions. She allows them to prove their answers and ask questions to help clarify their thinking. It is important to start this pedagogical perspective with kindergarteners. Developing a disposition that math should make sense and answers must be mathematically justified is an essential characteristic of becoming mathematically powerful. ANDREA

Classroom Link: Ten-Frames: 8+6 Classroom Clip 2nd grade Consider the following while viewing: How does the teacher build student fluency with small numbers using ten-frames? What questions does the teacher use to build understanding about decomposing and composing? How are the double ten-frames used to support the goals of K-2 number talks? What strategies are the students using to build meaning of the numbers? What opportunities are created for the students to understand and use 10 as a unit? How do the students demonstrate composing and decomposing numbers? Copy PP. 340-342 Andrea

Five Goals for Number Talks 3-5 Number sense Place value Fluency Properties Connecting mathematical ideas PP. 158-160 Number Sense: Estimation of a reasonable answer Applying Place Value to Computation Fluency: Knowing how a number can be composed and decomposed and using that information to be flexible and efficient with solving problems. Connections: Not just real-world word problems but the relationship between addition, subtraction, multiplication and division KIM

Classroom Link: Subtraction: 1000-674 Classroom Clip 5th Grade As you watch the video, consider the following: What evidence in the video supports student understanding of place value? How do the students’ strategies exhibit number sense? How does fluency with smaller numbers connect to the students’ strategies? Which strategies were most accessible to you? More challenging to follow? How are accuracy, flexibility, and efficiency interwoven in the students’ strategies? Copy PP. 366-367 KIM

Bringing It All Together: Number Talks from the Schoolwide Perspective “We have just taken a journey of number talks from kindergarten through the fifth grade by viewing video clips and group discussions. While teacher personalities and environments may change as students transition from grade level to grade level, essential number talk content and characteristics remain consistent from year to year. This consistency in teaching mathematically big ideas, instruction rooted in asking rather than telling, developing a safe learning community, and an unwavering quest for making sense are essential in building mathematically powerful students. The consistency from grade level to grade level does not occur by coincidence; it is purposefully orchestrated by the school learning community.” P. 305 It is our district’

Looking at Mathematics through a Common Core Lens Our goal as educators is to help students to become confident and competent in mathematics. We strive to create a classroom environment that encourages students to think critically about math in a variety of situations. As students explain their thinking to others, they self-correct and clarify their ideas leading to a deeper understanding of underlying mathematical concepts. Accuracy and the development of efficient problem-solving strategies are essential to student’s learning. The ability to solve problems many different ways and to understand the connections between mathematical ideas is equally important. As children learn to question, reconsider and justify solutions they become more confident in their own abilities as mathematicians.

Exit Slip: Taking a Look at your Own Practice What changes might you make in your math instruction based on the information you learned in today’s session on Number Talks? Things to think about: Learning community in your classroom Your role as the teacher Questioning techniques Use of models and tools to support student thinking Addressing student mistakes