Jefferson County Schools K-5 Math Back to School Conference Number Talks: Strengthen Students’ Mathematical Reasoning Jefferson County Schools K-5 Math Back to School Conference

K-5 Math Survey Depth of Knowledge Small Group Instruction Number Talks

Today’s Purpose To provide teachers with an instructional strategy that is grounded in developing students’ mathematical reasoning and conceptual understandings rather than just teaching rules and procedures without understanding of numerical relationships.

Outcomes Participants will deepen their understanding of mathematics discourse, including some background and rationale. Participants will experience Number Talks and consider how they might be used as part of a daily routine.

Focus Questions How can Number Talks develop students’ mathematical reasoning? How do Number Talks align to the Common Core Mathematical Practices and Content Standards?

Table Talk Have you implemented Number Talks as part of your daily routine? What were some of the benefits and challenges? When in your daily routine could you incorporate the use of Number Talks?

Number Talks A planned daily routine for whole‐class instruction Number Sense (efficiency, accuracy & flexibility) Generalized Arithmetic-conceptual understanding Reasoning and Problem Solving Mental Mathematics Preview-­Review-­Conceptual Understanding Cecilio

Curriculum Leadership Council 2011-2012 CLC December 6, 2011 Norms “No one is as smart as all of us are together.” Respect Individual think time Everyone participates Everyone helps Leave no one behind Be positive Technology courtesy

Four Goals for K-2 Number Talks Developing Number Sense Developing fluency with small numbers Subitizing Making Fives and Tens Number Conservation Number Talks -Sherry Parrish Cecilio

The Teacher’s Role Teacher as facilitator, questioner, listener and learner – NOT teller and explainer. Crafts purposeful problems. Supports discourse to deepen mathematical understanding and knowledge and keeps discussion focused on the important mathematics. Assists students to learn how to structure their comments and wonderings in a meaningful and natural manner. Asks open ended questions – from “What answer did you get” to “How did you get your answer?” and “Why did you choose your strategy?”

Hand Signals Solution Agree Strategy Question Comment Curriculum Leadership Council 2011-2012 CLC December 6, 2011 Hand Signals Solution Strategy Question Comment Agree *

Understanding Math Discourse Talk Moves Revoicing So you’re saying the top number in a fraction is called the numerator. Repeating Can you repeat what Miguel said in your own words? Classroom Discussions: Using Math Talk to Help Students Learn -S. Chapin, C. O’Connor, N Anderson (2003)

Understanding Math Discourse Talk Moves (continued) Reasoning Do you agree or disagree and why? Adding On Please add onto Jimena’s strategy. Waiting Please take some quite think time. Classroom Discussions: Using Math Talk to Help Students Learn -S. Chapin, C. O’Connor, N Anderson (2003)

WHAT the students are learning 1st Half Practice Standards: HOW the students are learning 2nd Half Content Standards: WHAT the students are learning

CCRS Mathematical Practices REASONING AND EXPLAINING 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others OVERARCHING HABITS OF MIND 1. Make sense of problems and persevere in solving them 6. Attend to precision MODELING AND USING TOOLS 4. Model with mathematics 5. Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

K-2 Number Talk in Jefferson County Watch the number talk. Refer back to the Key Components. What do you notice? - Classroom environment and community - Classroom discussions - The teacher’s role (facilitating vs. teaching) - The role of mental math - Purposeful computation problems (Think-Pair-Share)

Let’s View a K-2 Number Talk

Let’s View a K-2 Number Talk

Discuss the following… Classroom environment and community Classroom discussions The teacher’s role (facilitating vs. teaching) The role of mental math Purposeful computation problems

Various Number Talks

How many dots do you see? How did you see them? Dot Talk How many dots do you see? How did you see them? Intent: Participants will experience a Dot Talk. Talking Points: Explain to participants that we will now model a dot talk. Please note that this is an animated slide.

Mental Math After a 20% discount, the price is 80% of the original price. So 80% of the original price is $140. What is the original price?

Mental Math

Number String (Mental Math) 35 x 8 70 x 4 140 x 2

Number String (Mental Math) 3 x 50 3 x 100 3 x 149

True/False   Cecilio

True/False Number Talk  

Kirsten says that 10xy-5xy + 4xy equals xy Dilemma Number Talk Kirsten says that 10xy-5xy + 4xy equals xy David says that 10xy-5xy + 4xy equals 9xy Explain the mathematical reasoning that both David & Kirsten used to simplify the expression above. *Introduce Dilemmas as a type of number talk *What could come before and after this number talk. Give rationale. 28

How many cubes? How do you see them? What is the surface area? Spatial Reasoning How many cubes? How do you see them? What is the surface area?

Transformations Rotate the figure 90˚ clockwise. What are the new coordinates of point A?

What’s My Rule? In Out 1 5 3 2 21 13 9 4x+1

What’s My Rule? Input Output 1 5 3 2 25 9 8 X^2

What’s My Rule? X Y 1 5 3 2 26 10 X^2 +1

Number Talk Examples Dot Patterns Mental Math Number Strings True/False Statements Dilemmas Spatial Reasoning What’s My Rule? Error Analysis and Coaching Cecilio

Math Block •Balance procedural understanding and conceptual understanding •Balance whole group and small group •Balance teacher directed and student-focused Debrief Guided Math/ Learning Tasks Number Talks Mini-Lesson

Socio-mathematical Norms Errors are gifts, they promote discussion. Share a second sentence to connect your thoughts. The answer is important, but it is not the math. Build on the thinking of others. Ask questions until ideas make sense. Think with language and use language to think.

Questions Teachers Might Ask Who would like to share their thinking? Did someone solve it a different way? Who else used this strategy to solve the problem? How did you figure it out? Cecilio Intent: Participants will review possible questions teachers may ask of their students during a number talk. Talking Points: These questions are just a few questions a teacher would ask. The teacher could also have sentence stems that students use to share out their solutions and strategies. (Especially helpful for EL students.)

Questions Teachers Might Ask What did you do next? What did you need to know? Why did you do that? Tell me more. Which strategies do you see being used? Cecilio Intent: Participants will review possible questions teachers may ask of their students during a number talk. Talking Points: These questions are just a few questions a teacher would ask. The teacher could also have sentence stems that students use to share out their solutions and strategies. (Especially helpful for EL students.)

“ 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.” Why Talk About Math

3, 2, 1, Exit Ticket 3 Things you will do to prepare to implement Number Talks in your classroom 2 Things you discovered about Number Talks 1 Question you still have