© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Rigor Breakdown Part 2: Procedural Skill and Fluency Grades 3–5

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Session Objectives 2 Examine the procedural skill and fluency component of rigor in G3—M5. Explore fluency activities for Grade 4 and Grade 5 lessons related to the development of fractions. Explore how cross-grade coherence is accessible through the fluency component of rigor. Recognize opportunities to emphasize the Standards of Mathematical Practice during activities that promote fluency.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Fluency Revisited 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.” (excerpt from the Shifts)

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Fluency Revisited 4 Accessible through: Counting exercises Choral & white board exchanges Sprints Fluency puzzles & games

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 5

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson Engagement – White Board Exchange 6

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Module Study – Fluency 7 How does the module use counting exercises differently from choral and white board exchanges? What themes are present in the fluency activities for this module? How does each activity relate to the purpose of the lesson / module?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points 8 Counting exercises (and Sprints) are used for familiar fluencies. White board exchanges are used more for building new fluencies. Studying multiples of 6, 7, 8, and 9 works toward the required fluency for the grade (3.OA.7), and prepares students for recognizing when a fraction is equal to a whole number.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 9

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

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson Engagement – Writing Counting Exercises and Exchanges 11 Consider the entire module and discuss with your partner what fluencies would be most appropriate for your lessons. Each of you pick a choral or white board exchange to write. Share what you’ve written with your partner.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson Engagement – Writing Counting Exercises and Exchanges 12 What surprised you about selecting and writing fluencies for a module?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Video – Choral / White Board Exchanges 13 Reflection: Look for subtle details about the implementation of each fluency exercise. What do you notice?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Video Clip – Fraction Fluency in Grade 5 14

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Video – Choral / White Board Exchanges 15 Reflection: What details did you notice about the implementation of the fluency exercises?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 16

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Bridging Gaps in Prerequisite Knowledge 17 What prerequisite fluency is important for success in this lesson? Can gaps in prerequisite skills be both assessed and remediated through fluency? Do any other fluency exercises seem appropriate to add to the fluency plan for the module?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA 18

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Sprint Design 19 A Sprint has two parts (Sprint A and Sprint B) with closely related problems on each. Students are given 60 seconds for each Sprint. Every student should get at least 25% right. Ideally, no student will finish within the 60 seconds. A typical 4 th or 5 th grade Sprint has 44 problems, younger students need fewer problems.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Sprint Design 20 Problems on the Sprint start easy and get progressively more complex (perhaps in quadrants). Problems should be patterned in such a way as to encourage MP.8, “Look for and express regularity in repeated reasoning.” Intelligent design and delivery makes the Sprint superior to computer-generated worksheets.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Fluency Puzzles and Games 21 Use each digit 0 – 9 only once to complete the grid.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Designing a Fluency Puzzle or Game 22 Fluency puzzles and games should both have students working loads of problems in a relatively short amount of time. Puzzles (and sometimes games) build students observation and reasoning skills (MP.2, MP.7, MP.8) as well as their perseverance in problem solving (MP.1). Games add the aspect of competition, motivating an improvement in speed and accuracy.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Design a Sprint or Fluency Puzzle 23 Take time now to design your own Sprint or fluency puzzle or game. Share your Sprint or puzzle with a partner. Give your partner one suggestion for improvement.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson Engagement – Fluency 24 How do Sprints and fluency puzzles and games provide an opportunity to bridge gaps in prerequisite skills? How does coherence apply to fluency activities?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points 25 Fluency is designed with the entire module, year, and previous years in mind. Schools are encouraged to use a familiar set of fluency styles across the grades. White board exchanges are best applied for building fluency in a new skill. Sprints and counting exercises are best applied for gaining additional speed and accuracy with previously learned skills.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Next Steps 26 In what ways are your schools / districts already implementing fluency and cross-grade coherence in the classroom? How can you help your colleagues use fluency to promote coherence in the curriculum?