Number talks
What is a Number Talk? ■ Purposely crafted numeric discussions designed to build flexibility, accuracy, and efficiency in mathematical thinking. ■ About 5-15 minute discussions where students look for patterns, try multiple strategies to solve a problem, discuss their strategies with a partner, and share with the whole group. ■ Help teachers understand and follow their students’ thought process, identify misconceptions, and foster the development of the Standards for Mathematical Practice.
Goals of Number Talks ■ Provide a safe environment to propose and evaluate strategies for solving problems and reasoning about numbers ■ Develop more efficient strategies to solve problems ■ Serve as a scaffold to traditional algorithms ■ Develop conceptual understating and procedural fluency ■ Help students judge the reasonableness of answers
Developing Accountability During Number Talks ■ Have students use hand signals ■ Hold small group number talks ■ Require students to solve an exit slip using one of the strategies from the number talk ■ Give a weekly computation assessment that requires students to show or describe the strategy they used to solve each problem.
Supports ■ Sentence starters – “My strategy is different than ___’s because…” “My strategy is similar to ___’s, but…” “I have a question about how ___ solved…” “I noticed…” “What would happen if…” ■ Create and post class strategy charts
The school is having a Box Top competition. Mrs. Muth’s 2nd grade class collected 28 Box Tops today and Mrs. Kremer’s class collected 29 Box Tops. How many did the 2nd grade classes collect? ■ What strategies might students use to solve this problem? Try to think of more than one strategy. How could you represent these strategies visually? Numerically? ■ Put a thumbs-up when you think of one strategy and a way to visualize it. Add an additional finger for each new strategy you think of. ■ Discuss your strategies with a partner(s).
Benefits to Using Real-World Contexts ■ Makes the problem relevant to the students ■ Provides a purpose for learning the concept ■ Adds meaning to the numbers ■ Provides a mental image of the mathematics concept in the problem ■ Provides a framework to help students determine if an answer is reasonable
Now you try ■ Use the example problems to try a number talks with your peers. ■ Grade level groups of about 4 ■ Take turns being the teacher/recorder of the strategies
Variations ■ Small group – student led; each person has a role; facilitator – records strategies, interruption police - “___, please stop interrupting; conversation leaders – take turns sharing strategies; paraphraser ■ 2 minute paper or time to write/draw on individual white boards– then share with a peer; share a few examples and record the strategies
Variations – “My Favorite No” Eight students had a car wash to earn money for their class field trip to Chicago. They earned $816. If they equally share the money, how much will each student get to pay for the cost of the field trip to Chicago?
“Let the Chalk (or markers) Do the Talk” Show the sum of 581 + 397 as many ways as you can. Each person in your group will have a different color. Each color should appear on the paper (the colors should be represented as equally as possible). You may not talk, but can write questions to each other and can draw pictures to show your thinking. We will then do a gallery walk to compare each groups' work and pose questions to each other.
References ■ Humphreys, C., & Parker, R. (2015). Making number talks matter: Developing Mathematical Practices and deepening understanding, grades 4-10. Portland, ME: Stenhouse Publishers. ■ Kazemi, E., & Hintz, A. (2014). Intentional talk: How to structure and lead productive mathematical discussions. Portland, ME: Stenhouse Publishers. ■ Parrish, S. (2014). Number talks: Helping children build mental math and computational strategies. Sausalito, CA: Math Solutions. ■ Parrish, S. (October, 2011). Number talks build numerical reasoning: Strengthen accuracy, efficiency, and fluency with these mental math and computation strategies. Teaching Children Mathematics, 18(3), 198-206.
Additional Examples of Number Talks ■ Inside Mathematics - Number Talks from real math classrooms – One example for each grade – grades 1-7 - http://www.insidemathematics.org/classroom-videos/number-talks ■ Kindergarten – Ten Frames and Dot Cards https://www.youtube.com/watch?v=62epCIFdRa0 ■ First Grade – Adding and Subtracting Within 20 https://www.teachingchannel.org/videos/addition-math-lesson-ousd ■ First Grade – Tens Frame - https://www.youtube.com/watch?v=ssfT0GMM7Oo ■ Second Grade – Regrouping – Small group, student facilitated number talk https://www.teachingchannel.org/videos/subtraction-math-lesson-ousd ■ Second Grade – Using Compensation for Adding - https://www.youtube.com/watch?v=jnVcmVc6Z4 ■ Third Grade – Number Patterns https://www.teachingchannel.org/videos/teaching-numberpatterns ■ Third Grade – Strategies to Put Together and Break Apart Two Digit Numbers https://www.teachingchannel.org/videos/third-grade-mental-math
Additional Examples of Number Talks ■ Third Grade – Apply Properties of Multiplication and Use the Structure of Number Patterns https://www.teachingchannel.org/videos/multiplication-division-in-the-core ■ Fourth Grade - Preparation for Fraction Multiplication https://www.teachingchannel.org/videos/fraction-multiplication-intro-sbac ■ Fourth Grade – Reasoning About Division https://www.teachingchannel.org/videos/common-core-teaching-division ■ Fifth Grade – Adding Fractions Without Common Denominators https://www.youtube.com/watch?v=7l7WfEOi12w ■ Fifth Grade – Division Strategies - https://www.youtube.com/watch?v=DQtgFaVqv7c ■ Sixth Grade - Math Talk – Discovering How to Find the Surface Area of Rectangular Prisms - https://www.teachingchannel.org/videos/teaching-surface-area ■ Sixth Grade – Finding the Percent of a Number https://www.youtube.com/watch?v=mRV-26fEq-s
Goals of Number Talks ■ Provide a safe environment to propose and evaluate strategies for solving problems and reasoning about numbers ■ Develop more efficient strategies to solve problems ■ Serve as a scaffold to traditional algorithms ■ Develop conceptual understating and procedural fluency ■ Help students judge the reasonableness of answers
Developing Accountability During Number Talks ■ Have students use hand signals ■ Hold small group number talks ■ Require students to solve an exit slip using one of the strategies from the number talk ■ Give a weekly computation assessment that requires students to show or describe the strategy they used to solve each problem.
Supports ■ Sentence starters – “My strategy is different than ___’s because…” “My strategy is similar to ___’s, but…” “I have a question about how ___ solved…” “I noticed…” “What would happen if…” ■ Create and post class strategy charts
The school is having a Box Top competition. Mrs. Muth’s 2nd grade class collected 28 Box Tops today and Mrs. Kremer’s class collected 29 Box Tops. How many did the 2nd grade classes collect? ■ What strategies might students use to solve this problem? Try to think of more than one strategy. How could you represent these strategies visually? Numerically? ■ Put a thumbs-up when you think of one strategy and a way to visualize it. Add an additional finger for each new strategy you think of. ■ Discuss your strategies with a partner(s).
Benefits to Using Real-World Contexts ■ Makes the problem relevant to the students ■ Provides a purpose for learning the concept ■ Adds meaning to the numbers ■ Provides a mental image of the mathematics concept in the problem ■ Provides a framework to help students determine if an answer is reasonable
Now you try ■ Use the example problems to try a number talks with your peers. ■ Grade level groups of about 4 ■ Take turns being the teacher/recorder of the strategies
Variations ■ Small group – student led; each person has a role; facilitator – records strategies, interruption police - “___, please stop interrupting; conversation leaders – take turns sharing strategies; paraphraser ■ 2 minute paper or time to write/draw on individual white boards– then share with a peer; share a few examples and record the strategies
Variations – “My Favorite No” Eight students had a car wash to earn money for their class field trip to Chicago. They earned $816. If they equally share the money, how much will each student get to pay for the cost of the field trip to Chicago?
“Let the Chalk (or markers) Do the Talk” Show the sum of 581 + 397 as many ways as you can. Each person in your group will have a different color. Each color should appear on the paper (the colors should be represented as equally as possible). You may not talk, but can write questions to each other and can draw pictures to show your thinking. We will then do a gallery walk to compare each groups' work and pose questions to each other.
References ■ Humphreys, C., & Parker, R. (2015). Making number talks matter: Developing Mathematical Practices and deepening understanding, grades 4-10. Portland, ME: Stenhouse Publishers. ■ Kazemi, E., & Hintz, A. (2014). Intentional talk: How to structure and lead productive mathematical discussions. Portland, ME: Stenhouse Publishers. ■ Parrish, S. (2014). Number talks: Helping children build mental math and computational strategies. Sausalito, CA: Math Solutions. ■ Parrish, S. (October, 2011). Number talks build numerical reasoning: Strengthen accuracy, efficiency, and fluency with these mental math and computation strategies. Teaching Children Mathematics, 18(3), 198-206.
Additional Examples of Number Talks ■ Inside Mathematics - Number Talks from real math classrooms – One example for each grade – grades 1-7 - http://www.insidemathematics.org/classroom-videos/number-talks ■ Kindergarten – Ten Frames and Dot Cards https://www.youtube.com/watch?v=62epCIFdRa0 ■ First Grade – Adding and Subtracting Within 20 https://www.teachingchannel.org/videos/addition-math-lesson-ousd ■ First Grade – Tens Frame - https://www.youtube.com/watch?v=ssfT0GMM7Oo ■ Second Grade – Regrouping – Small group, student facilitated number talk https://www.teachingchannel.org/videos/subtraction-math-lesson-ousd ■ Second Grade – Using Compensation for Adding - https://www.youtube.com/watch?v=jnVcmVc6Z4 ■ Third Grade – Number Patterns https://www.teachingchannel.org/videos/teaching-numberpatterns ■ Third Grade – Strategies to Put Together and Break Apart Two Digit Numbers https://www.teachingchannel.org/videos/third-grade-mental-math
Additional Examples of Number Talks ■ Third Grade – Apply Properties of Multiplication and Use the Structure of Number Patterns https://www.teachingchannel.org/videos/multiplication-division-in-the-core ■ Fourth Grade - Preparation for Fraction Multiplication https://www.teachingchannel.org/videos/fraction-multiplication-intro-sbac ■ Fourth Grade – Reasoning About Division https://www.teachingchannel.org/videos/common-core-teaching-division ■ Fifth Grade – Adding Fractions Without Common Denominators https://www.youtube.com/watch?v=7l7WfEOi12w ■ Fifth Grade – Division Strategies - https://www.youtube.com/watch?v=DQtgFaVqv7c ■ Sixth Grade - Math Talk – Discovering How to Find the Surface Area of Rectangular Prisms - https://www.teachingchannel.org/videos/teaching-surface-area ■ Sixth Grade – Finding the Percent of a Number https://www.youtube.com/watch?v=mRV-26fEq-s
