Rigor Breakdown

1. Rigor Breakdown Part 2: Procedural Skill and Fluency Grades 3–5

2. Session Objectives • 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.

3. 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)

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

5. AGENDA • 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

6. Lesson Engagement – White Board Exchange

7. 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?

8. 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.

9. AGENDA • 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

10. Required Fluencies

11. 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.

12. Lesson Engagement – Writing Counting Exercises and Exchanges • What surprised you about selecting and writing fluencies for a module?

13. Video – Choral / White Board Exchanges • Reflection: • Look for subtle details about the implementation of each fluency exercise. What do you notice?

14. Video Clip – Fraction Fluency in Grade 5

15. Video – Choral / White Board Exchanges • Reflection: • What details did you notice about the implementation of the fluency exercises?

16. AGENDA • 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. • Designing Sprints / Fluency Puzzles & Games

17. 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?

18. AGENDA • 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

19. 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 4th or 5th grade Sprint has 44 problems, younger students need fewer problems.

20. 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.

21. Fluency Puzzles and Games Use each digit 0 – 9 only once to complete the grid.

22. 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.

23. 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.

24. 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?

25. 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.

26. 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?