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 3–5


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

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.



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)



Fluency Revisited

4

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



AGENDA

5

Counting Exercises / Choral & White Board Exchanges Examine examples from G3—M5. Select strategies for Grades 4 and 5. Consider ways to bridge gaps in prerequisite

knowledge.Sprints / Fluency Puzzles & Games



Lesson Engagement – White Board Exchange

6



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?



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.



AGENDA

9





Required Fluencies

10

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



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.



Lesson Engagement – Writing Counting Exercises and Exchanges

12

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



Video – Choral / White Board Exchanges

13

Reflection: • Look for subtle details about the

implementation of each fluency exercise. What do you notice?



Video Clip – Fraction Fluency in Grade 5

14



Video – Choral / White Board Exchanges

15

Reflection: • What details did you notice about

the implementation of the fluency exercises?



AGENDA

16


knowledge.Designing Sprints / Fluency Puzzles & Games



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?



AGENDA

18





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

students need fewer problems.



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.



Fluency Puzzles and Games

21

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



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.



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.



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?



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.



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?

rigor breakdown

Documents

fluency grades

fraction fluency

fluency work

fluency component of

examples of procedural

core functions

session objectives2examine

teachers time