# © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Rigor Breakdown Part 2: Procedural Skill and Fluency.

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© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Session Objectives 2 Understand the fluency component of rigor called for in the Standards, as defined by guiding documents Examine various activities that promote fluency in A Story of Units Compare and contrast fluency activities and analyze the impact and advantages of each Highlight Standards for Mathematical Practice in the fluency activities in A Story of Units Recognize the balance and intensity of all three components of rigor in A Story of Units

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Fluency Defined by the Instructional Shifts 3 “Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize through repetition, core functions.”

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Fluency Defined by the Publishers’ Criteria 4 “The word ‘fluently’ is used [in the standards] to set expectations for fluency.” (page 5) “Materials in grades K-6 help students make steady progress throughout the year toward fluent (accurate and reasonably fast) computation…. Progress toward these goals is interwoven with students’ developing conceptual understanding of the operations in question.” (page 10)

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Required Fluencies 5 K K.OA.5Add/subtract within 5 1 1.OA.6Add/subtract within 10 2 2.OA.2 2.NBT.5 Add/subtract within 20 (know single-digit sums from memory) Add/subtract within 100 3 3.OA.7 3.NBT.2 Multiply/divide within 100 (know single-digit products from memory) Add/subtract within 1000 4 4.NBT.4Add/subtract within 1,000,000 5 5.NBT.5Multi-digit multiplication

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Fluency Activities in A Story of Units 6 Promote automaticity – allows students to reserve their cognitive energy for higher-level thinking Daily, substantial, sustained, and supported by the lesson structure 10-20 minutes of easy-to-administer activities Energetic activities that allow students to see measureable progress Support conceptual understanding and application as well as the mathematical practices

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 7 Fluency Work – Counting Exercises Fluency Work – Choral and White Board Exchanges Fluency Work – Sprints

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Fluency – Counting Exercises 8 Appropriate for all grade levels, K-5 Counting forward and backwards supports addition and subtraction Skip-counting supports multiplication

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson Engagement – Skip-counting 9 Reflections: How could counting exercises have an impact or a benefit in your classes, school or district? How might counting exercises address trouble areas that your students experience?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Video Clip – Counting Exercises 10 Reflections: How could counting exercises have an impact or a benefit in your classes, school or district? How might counting exercises address trouble areas that your students experience?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Video Clip: Counting Exercises for K-1 11 This video is posted in the video library on EngageNY: http://engageny.org/video-library

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Video Clip: Counting with Bundles 12 This video is posted in the video library on EngageNY: http://engageny.org/video-library

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Counting Exercises 13 Reflections: How could counting exercises have an impact or a benefit in your classes, school or district? How might counting exercises address trouble areas that your students experience?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Counting Exercises Key Points 14 They are appropriate for all grade levels, PK-5. Counting forward and backwards supports addition and subtraction. Skip-counting supports multiplication. Counting exercises can be timed competitions, either as a class or as individuals.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Fluency – Choral and White Board Exchanges 16 Quick, efficient interactive drills and games Applies to a wide range of skills Making 10 using ten-frame cards for adding and subtracting Computing 1 less than, 2 more than, etc. Interpreting words with expressions

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Video Clip – Choral and White Board Exchanges 17 Reflections: How is conceptual understanding being reinforced in these examples of fluency work?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Video Clip: Ten-Frame Flash 18 This video is posted in the video library on EngageNY: http://engageny.org/video-library

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson Engagement – White Board Exchange 19 Take the challenge!

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Choral and White Board Exchanges 20 Reflections: How is conceptual understanding being reinforced in these examples of fluency work?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points 21 Exchanges can be used as a quick form of assessment. Exchanges allow for rapid completion of multiple practice problems. Exchanges create intensity in student practice. Exchanges give students immediate feedback.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Fluency – Sprints 23 Grade 2—Module 3 Fluency Progression A fast pace is essential. While administering Sprints, teachers assume the role of athletic coaches. A rousing routine fuels students’ motivation to do their personal best. Student recognition of increasing success is critical, and so every improvement is celebrated. One Sprint has two parts with closely related problems on each. Students complete the two parts of the Sprint in quick succession with the goal of improving on the second part, even if only by one more. With practice the routine takes about 8-10 minutes.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson Engagement – Sprints 24 Take the challenge! Sprint A: page 3.B.20 Sprint B: page 3.B.21

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Fluency – Sprints 25 Round B of the Sprint consolidates student progress, and builds confidence, especially for lower performing students. Intelligent design and sequence of delivery makes the Sprint superior to computer-generated worksheets. Sprints are aligned to individual lessons and topics and have been written to account for a large range of skill levels. Teachers are encouraged to study the sequence of problems in the Sprints from A Story of Units and create their own Sprints. Sprints do not have to be administered daily, but certainly can be done at least 2-3 times per week.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Sprints 26 Reflections: What evidence is there of the Standards for Mathematical Practice?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Video Clip - Sprints 27 Reflections: In what ways are Sprints advantageous in meeting the demands of fluency?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Video Clip: Sprints – Fluency in Action 28 This video is posted in the video library on EngageNY: http://engageny.org/video-library

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Sprints 29 Reflections: In what ways are Sprints advantageous in meeting the demands of fluency?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points 30 Sprints allow for rapid completion of multiple practice problems. Sprints create intensity in student practice. Sprints give students quick feedback. Sprints motivate students with a near-term goal for improvement.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Fluency Progressions in A Story of Units 31 Each module includes a Fluency Progression: Banks of activities that teachers may either select and use, or study as they create their own. Activities revisit previously learned material to develop automaticity, anticipate future concepts, and strategically preview or build skills for the day’s concept lesson. As teachers work with the materials, they should adjust them in consideration of their particular students’ needs.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points 32 Fluency standards exist for each grade. Fluency can be promoted in a variety of ways. Fluency work is usually included as a warm-up at the beginning of a lesson for approximately 10-20 minutes. A Story of Units provides frequent, rich opportunities for students to work toward achieving fluency. Fluency work often also provides opportunities to nurture the Standards of Mathematical Practice.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Next Steps 33 What type of fluency activity are you most eager to incorporate into your current teaching? How can you help your colleagues implement the fluency component of rigor?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Call for Equal Intensity and Balance 34 The Instructional Shifts: “Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity. Teachers create opportunities for students to participate in ‘drills’ and make use of those skills through extended application of math concepts...”

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Call for Equal Intensity and Balance 35 The Publishers’ Criteria: “To help students meet the expectations of the Standards, educators will need to pursue, with equal intensity, three aspects of rigor in the major work of each grade: conceptual understanding, procedural skill and fluency, and applications.” (page 5) “Materials and tools reflect the balances in the Standards…” (page 9)

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Intensity and Balance in A Story of Units 36

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Intensity and Balance in A Story of Units 37