rigor breakdown

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NYS COMMON CORE MATHE MATICS CURRI CULUM A Story of Units

Rigor BreakdownPart 2: Procedural Skill and Fluency

Grades PK–2

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Session Objectives

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• Examine the procedural skill and fluency component of rigor in GK—M5.

• Explore fluency activities for Grade 1 and Grade 2 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.

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Fluency Revisited

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“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)

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Fluency Revisited

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Accessible through:• Counting exercises• Choral & white board exchanges• Sprints• Fluency puzzles & games

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

AGENDA

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Counting Exercises / Choral & White Board Exchanges Examine examples from GK—M5. Select strategies for Grades 1 and 2. Consider ways to bridge gaps in prerequisite

knowledge.Sprints / Fluency Puzzles & Games

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Video – Choral Exchanges

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Reflection: • Look for subtle details about the

implementation of each fluency exercise. What do you notice?

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Video Clip – Double 10-Frames

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Module Study – Fluency

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• 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?

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Key Points

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• Counting exercises (and Sprints) are used for familiar fluencies.

• White board exchanges are used more for building new fluencies.

• Mastering 10 ones and some ones (K.NBT.1), decomposing numbers to 10 (K.OA.3), and how many to 10 (K.OA.4) are essential groundwork to mastery of sums and differences to 20.

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

AGENDA

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Counting Exercises / Choral & White Board Exchanges Examine examples from GK—M5. Select strategies for Grades 1 and 2. Consider ways to bridge gaps in prerequisite

knowledge.Sprints / Fluency Puzzles & Games

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Required Fluencies

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K K.OA.5 Add/subtract within 5

1 1.OA.6 Add/subtract within 10

2 2.OA.22.NBT.5

Add/subtract within 20 (know single-digit sums from memory)Add/subtract within 100

3 3.OA.73.NBT.2

Multiply/divide within 100 (know single-digit products from memory)Add/subtract within 1000

4 4.NBT.4 Add/subtract within 1,000,000

5 5.NBT.5 Multi-digit multiplication

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Lesson Engagement – Writing Counting Exercises and Exchanges

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• 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.

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Lesson Engagement – Writing Counting Exercises and Exchanges

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• What surprised you about selecting and writing fluencies for a module?

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

AGENDA

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Counting Exercises / Choral & White Board Exchanges Examine examples from GK—M5. Select strategies for Grades 1 and 2. Consider ways to bridge gaps in prerequisite

knowledge.Designing Sprints / Fluency Puzzles & Games

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Bridging Gaps in Prerequisite Knowledge

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• 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?

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

AGENDA

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Counting Exercises / Choral & White Board Exchanges Examine examples from GK—M5. Select strategies for Grades 1 and 2. Consider ways to bridge gaps in prerequisite

knowledge.Sprints / Fluency Puzzles & Games

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Sprint Design

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• 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 4th or 5th grade Sprint has 44 problems, younger

students need fewer problems.

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Sprint Design

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• 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.

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Fluency Puzzles and Games

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Use each digit 0 – 9 only once to complete the grid.

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Designing a Fluency Puzzle or Game

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• 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.

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Design a Sprint or Fluency Puzzle

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• 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.

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Lesson Engagement – Fluency

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• How do Sprints and fluency puzzles and games provide an opportunity to bridge gaps in prerequisite skills?

• How does coherence apply to fluency activities?

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Key Points

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• 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.

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N YS CO MM O N CO R E M AT H E MAT I C S C U R R I C ULU M A Story of Units

Next Steps

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• 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?