NYS COMMON CORE MATHEMATICS CURRICULUM A Story of

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 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 • Examine the procedural skill and fluency component of rigor in G 3—M 5. • 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. 2 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Fluency Revisited “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) 3 © 2012 Common Core, Inc. All rights reserved. commoncore. org

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

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA Counting Exercises / Choral & White Board Exchanges Ø Examine examples from G 3—M 5. Ø Select strategies for Grades 4 and 5. Ø Consider ways to bridge gaps in prerequisite knowledge. Sprints / Fluency Puzzles & Games 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 • 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? 7 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points • 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. 8 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA Counting Exercises / Choral & White Board Exchanges Ø Examine examples from G 3—M 5. Ø Select strategies for Grades 4 and 5. Ø Consider ways to bridge gaps in prerequisite knowledge. Sprints / Fluency Puzzles & Games 9 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Required Fluencies K K. OA. 5 Add/subtract within 5 1 1. OA. 6 Add/subtract within 10 2 3 2. OA. 2 2. NBT. 5 3. OA. 7 3. NBT. 2 Add/subtract within 20 (know single-digit sums from memory) Add/subtract within 100 Multiply/divide within 100 (know single-digit products from memory) Add/subtract within 1000 4 4. NBT. 4 Add/subtract within 1, 000 5 5. NBT. 5 Multi-digit multiplication 10 © 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 • 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. 11 © 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 • What surprised you about selecting and writing fluencies for a module? 12 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Video – Choral / White Board Exchanges Reflection: • Look for subtle details about the implementation of each fluency exercise. What do you notice? 13 © 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 Reflection: • What details did you notice about the implementation of the fluency exercises? 15 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA Counting Exercises / Choral & White Board Exchanges Ø Examine examples from G 3—M 5. Ø Select strategies for Grades 4 and 5. Ø Consider ways to bridge gaps in prerequisite knowledge. Designing Sprints / Fluency Puzzles & Games 16 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Bridging Gaps in Prerequisite Knowledge • 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? 17 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA Counting Exercises / Choral & White Board Exchanges Ø Examine examples from G 3—M 5. Ø Select strategies for Grades 4 and 5. Ø Consider ways to bridge gaps in prerequisite knowledge. Sprints / Fluency Puzzles & Games 18 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Sprint Design • 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. 19 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Sprint Design • 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. 20 © 2012 Common Core, Inc. All rights reserved. commoncore. org

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

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Designing a Fluency Puzzle or Game • 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. 22 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Design a Sprint or Fluency Puzzle • 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. 23 © 2012 Common Core, Inc. All rights reserved. commoncore. org

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

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points • 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. 25 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Next Steps • 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? 26 © 2012 Common Core, Inc. All rights reserved. commoncore. org