New York State Common Core
P-5
GRADE
Network Team Institute
Rigor Breakdown:
Procedural Skill and Fluency
Grades 3-5
Sequence of Sessions
Overarching Objectives of this November 2012 Network Team Institute
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Participants will understand the features of A Story of Units and how the curriculum is aligned with
the CCLS, Learning Progressions, Instructional Shifts, Publishers’ Criteria, PARCC, Major Content
Emphases, and the Pre-Post Math Standards.
Participants will understand how to use the How to Implement A Story of Units and A Story of Units:
A Curriculum Overview for Grades P-5 documents and be prepared to share these documents with
others.
Participants will explore G2—M3 and G5—M3 and be prepared to train others to teach these
modules.
Participants will extend understanding of the structure of these modules to other modules in A Story
of Units.
Participants will analyze assessment tasks associated with G2—M3 and G5—M3.
Participants will examine evidence of all three components of rigor in A Story of Units and be
prepared to promote balanced instruction.
High-Level Purpose of this Session
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
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Understand the fluency component of rigor called for in the Standards, as defined by the
Instructional Shifts and the Publishers’ Criteria
Examine various activities that promote fluency in A Story of Units
Compare and contrast fluency activities and analyze the impact and advantages of each
Highlight Standards for Mathematical Practice in fluency activities in A Story of Units
Recognize the balance and intensity of all three components of rigor in A Story of Units
Related Learning Experiences

This session was preceded by an overview of rigor and a breakdown session focusing on one
component of rigor – conceptual understanding. This session focuses on the fluency component of
rigor. The next session will focus on application.
Session Notes:
Date:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rigor Breakdown: Procedural Skill and Fluency Grades 3-5
3/23/16
1
Rigor Breakdown: Fluency
NYS COMMON CORE MATHEMATICS PD
Key Points
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
In each grade, students are expected to master certain fluencies over the course of the year.
Fluency can be promoted in a variety of ways.
Fluency work is usually done as a warm-up at the beginning of a lesson for approximately 10-20
minutes.
Fluency represents a major part of the instructional vision that shapes A Story of Units. Frequent, rich
opportunities to help students achieve fluency are woven throughout A Story of Units.
Fluency work also provides opportunities to nurture the Standards of Mathematical Practice. The
Standards for Mathematical Practice are embedded into all components of rigor and are not separate
from the content instruction.
Session Outcomes
What do we want participants to be able to do as a result of this session?
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
Identify key fluencies per grade as outlined by the CCSSM
Recognize and understand the different types of fluency activities in A Story of Units
How will we know that they are able to do this?
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
Participants will share their understanding of fluency requirements and fluency activities with
colleagues.
Participants and their colleagues will successfully implement fluency activities as described in A Story
of Units.
Session Overview
Section
Opening
Fluency Work –
Counting Exercises
Time
0:00-0:05
(5 min)
0:05-0:25
(20 min)
Overview
 Link to previous sessions; frame the
session, referencing the agenda
 Examine fluency as defined in the
Shifts and Publishers’ Criteria
 Examine how A Story of Units
implements fluency
 Review the flow and objectives of
this session
Prepared Resources
 Session PowerPoint
 Engage in examples of fluency as
 Video Clip: Skip-counting by
counting exercise
Fractions
 Watch a video clip of fluency as
counting exercises
 Analyze the impact and advantages
of counting exercises
Session Notes:
Date:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rigor Breakdown: Procedural Skill and Fluency Grades 3-5
3/23/16
Facilitator Preparation
 Review session notes and
PowerPoint presentation
 Download CCLS for easy reference
to Standards of Mathematical
Practice as needed
 Download Crosswalk of
Instructional Shifts for easy
reference as needed
 Download Publishers’ Criteria for
easy reference as needed
 Get a stopwatch
 Review and download video file as
a back-up in case there is a problem
with the embedded video
2
NYS COMMON CORE MATHEMATICS PD
Fluency Work –
Choral and White
Board Exchanges
0:25-0:35
(10 min)
Fluency Work –
Sprints
0:35-0:55
(20 min)
Closing
0:55-1:00
(5 min)
TOTAL TIME
60 min
 Learn about choral and white board
exchange fluency activities
 Engage in an example of choral and
white board exchange fluency work
 Watch a video clip of choral and
white board exchange fluency work
 Reflect upon how fluency can also
support conceptual understanding
 Engage in an example of Sprints
 Learn about Sprints
 Watch video clip of Sprints
 Look for evidence of mathematical
practices in Sprints
 Learn about banks of fluency
activities provided with A Story of
Units
 Summarize key points
 Reflect on next steps
 Reflect on the role of fluency in
balanced instruction
Rigor Breakdown: Fluency
 Video Clip: White Board Exchange
 Arrange for personal dry erase
boards and markers per participant
 Review and download video file as
a back-up in case there is a problem
with the embedded video
 G5—M3—B—L4 Sprints A and B:
Equivalent Fractions
 Fluency Progression
 Video Clip: Sprints – Fluency in
Action
 How to Implement A Story of Units
 Fluency Progression
 Get a stopwatch
 Review and download video file as
a back-up in case there is a problem
with the embedded Video
Session Roadmap
Opening
Time: 0:00-0:05
[5 minutes] In this section, you will…
 Link to previous sessions; frame the session, referencing the agenda
 Examine fluency as defined in the Shifts and Publishers’ Criteria
 Examine how A Story of Units implements fluency
 Review the flow and objectives of this session
Materials used include:

Session PowerPoint
(SLIDE 1) In the last session we looked at three approaches to developing conceptual understanding. Conceptual
understanding should be developed before related fluency work begins. In this session we will explore three different
forms of fluency work.
(SLIDE 2) The objectives of this session are to:
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
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Understand the fluency component of rigor called for in the Standards, as defined by the Instructional Shifts
and the Publishers’ Criteria
Examine various activities that promote fluency in A Story of Units
Compare and contrast fluency activities and analyze the impact and advantages of each
Session Notes:
Date:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rigor Breakdown: Procedural Skill and Fluency Grades 3-5
3/23/16
3
NYS COMMON CORE MATHEMATICS PD


Rigor Breakdown: Fluency
Highlight Standards for Mathematical Practice in the fluency activities in A Story of Units
Recognize the balance and intensity of all three components of rigor in A Story of Units
(SLIDE 3) Let’s begin with reviewing the definition of fluency given by the Instructional Shifts and the Publishers’
Criteria. The Crosswalk of Common Core Instructional Shifts: Mathematics states that, “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.”
(SLIDE 4) The Publishers’ Criteria specifies that, “the word ‘fluently’ is used [in the standards] to set expectations for
fluency.” (page 5) The document goes on to demand that, “Materials in grades K-6 help students make steady progress
throughout the year toward fluent (accurate and reasonably fast) computation…. Progress toward these goals is
interwoven with students’ developing conceptual understanding of the operations in question.” (page 10)
(SLIDE 5) This is an inventory of all the K-5 standards that call for fluency:
K
1
2
3
4
5
K.OA.5
1.OA.6
2.OA.2
2.NBT.5
3.OA.7
3.NBT.2
4.NBT.4
5.NBT.5
Add/subtract within 5
Add/subtract within 10
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
Add/subtract within 1,000,000
Multi-digit multiplication
(SLIDE 6) Fluency promotes automaticity, a critical capacity that allows students to reserve their cognitive resources for
higher-level thinking.
(CLICK TO ADVANCE SECOND BULLET ON SLIDE 6) Fluency represents a major part of the instructional vision that
shapes A Story of Units. In this curriculum, fluency is a daily, substantial, and sustained activity supported by the lesson
structure.
(CLICK TO ADVANCE THIRD BULLET ON SLIDE 6) A Story of Units includes 10 to 20 minutes of daily fluency work. A
variety of suggestions for fluency activities are offered. They are strategically designed for the teacher to easily
administer and assess. Note that the time spent each day will vary depending on the lesson and your students’ current
skill level.
(CLICK TO ADVANCE FOURTH BULLET ON SLIDE 6) The fluency activities in A Story of Units are generally high-paced and
energetic, getting students’ adrenaline flowing, and creating daily opportunities to celebrate improvement. From the
beginning of the year, students see their accuracy and speed measurably increase both as individuals and as a class.
Like opening a basketball practice with team drills and exercises, both personal and group improvements are exciting
and prepare the players for the application in the game setting.
(CLICK TO ADVANCE FIFTH BULLET ON SLIDE 6) By encouraging students to recognize patterns and make connections
within the lessons, the fluency exercises in A Story of Units support the other two components of rigor as well as the
Session Notes:
Date:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rigor Breakdown: Procedural Skill and Fluency Grades 3-5
3/23/16
4
NYS COMMON CORE MATHEMATICS PD
Rigor Breakdown: Fluency
Standards for Mathematical Practice.
(SLIDE 7) Fluency can be worked on in a variety of ways. In this session we will watch video clips and experience for
ourselves three general categories of the fluency activities that can be found in A Story of Units: counting exercises,
choral and white board exchanges, and Sprints.
Our goals for the session are to become familiar with the key fluency requirements per grade and to become familiar
with several examples of fluency exercises that can be used in your classrooms to promote fluency.
Fluency Work – Counting Exercises
Time: 0:05-0:25
[20 minutes] In this section, you will…
 Engage in examples of fluency as counting exercises
 Watch a video clip of fluency as counting exercises
 Analyze the impact and advantages of counting exercises
Materials used include:


Stopwatch
Video Clip: Skip-counting by Fractions
(CLICK TO ADVANCE ANIMATION ON SLIDE 7) We will begin with counting exercises.
(SLIDE 8) This is one category of fluency work that is appropriate for all grade levels. You may have heard of exercises
like ‘skip-counting’ or ‘happy counting.’ In a counting exercise, everyone might count chorally or individual students
might count taking turns one after the next competing in a whole-class timed challenge. A counting exercise might also
be individual timed challenges. In some cases, the students or the teacher may use a manipulative as the students
count.
(CLICK TO ADVANCE SECOND BULLET ON SLIDE 8) Counting exercises typically require counting both forward and
backwards. The fluency of being able to count backwards is often neglected, which is unfortunate, as it plays a vital role
in students’ ability to subtract.
(CLICK TO ADVANCE ANIMATION ON SLIDE 8) Thus, counting exercises that encourage going in both directions apply
directly to the addition and subtraction fluency standards of grades K-4.
(CLICK TO ADVANCE THIRD BULLET ON SLIDE 8) Skip-counting is a precursor to multiplication and thus also applies to
the 3rd grade standard 3.OA.7 for multiplying and dividing within 100. In both 4th and 5th grade, skip-counting can occur
in fractional amounts, counting by 1/3’s for example. In this case, the fluency activity also serves to solidify the
conceptual understanding of the number line.
(SLIDE 9) Let’s do a counting exercise together. While participating, reflect on these questions. We will discuss your
thoughts in response to these questions afterwards.
Session Notes:
Date:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rigor Breakdown: Procedural Skill and Fluency Grades 3-5
3/23/16
5
NYS COMMON CORE MATHEMATICS PD


Rigor Breakdown: Fluency
How could counting exercises have an impact or a benefit in your classes, school or district?
How might counting exercises address trouble areas that your students experience during concept
development and application work?
Let’s do an example of timed skip-counting as a class. (Form pseudo classes of 8 to 20 people per class,
give each class a name, e.g. Class A, Class B, Class C…)
If you coordinate with other teachers of your grade, you can get a bit of a class competition going to
see which class can count by 3’s up to 30 and back down to zero the fastest. We will simulate that
competition here amongst ourselves. Now that you have been divided into classes, stand up and form
a circle with your class. You’ll be Class A, (point throughout the room and continue naming the classes
as letters.)
Class A will demonstrate with me. I’ll start counting with ‘3’, then the next person says ‘6,’ (point
around the circle to indicate that the students take turns as the counting goes up by 3’s to 30), we only
say ‘30’ once, now we are headed back down, so that’s ’27’ (pointing to the next person), ‘24’, … and
we go all the way to 0, before I will click the timer to stop. OK, that took us a xx seconds. I will give
each group 1 min to practice before we hold the official competition.
I need silence as we begin. Class A will start. I will choose where it starts and I will start the timer when
that person says ‘3’. (Indicate who will start in Class A and time them as they count by 3’s up to 30 and
back down to 0.)
Continue to let each “class” have a turn and record the times for each class on the flip chart.
This took us several minutes because we let several classes have a try, but normally you could hold the
competition once each day for one week and then once a week you could hold it again, allowing your
class to try to improve their time. It is great fun to chart their progress, showing how their speed
improves from the beginning of the year. You can have similar charts and competitions for counting by
other numbers. Regardless of what number you are counting by, you will start with that number, go up
to a number 10 times that amount, and then backwards down to zero.
(SLIDE 10) Let’s watch a video clip of a skip-counting exercise practiced in grade 5. While watching the video, continue
to reflect on the questions. Later you will have an opportunity to discuss your thoughts.
This video shows Anita Meadows, a teacher at Saint Edward’s School in Vero Beach, Florida leading
students in skip-counting by eighths. You will notice that the pace in this video is a bit slow as students
are just beginning to gain fluency with this particular exercise.
(SLIDE 11 – Play Video Clip: Skip Counting by Fractions)
(SLIDE 12) Before discussing your thoughts on the video, let’s try one more counting exercise. This
time we will count in unison by sixths using mixed numbers as we go beyond 1.
Let’s start by skip-counting by 1/6’s with mixed numbers up to 2 wholes. (Participants will skip count
out lound as a whole group.) I’ll now draw out the number line to show the sixths.
Session Notes:
Date:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rigor Breakdown: Procedural Skill and Fluency Grades 3-5
3/23/16
6
Rigor Breakdown: Fluency
NYS COMMON CORE MATHEMATICS PD
(SWITCH TO DOCUMENT CAMERA and draw a number line from 0 to 2 with 1/6th intervals as shown.)
0
1
6
2
6
3
6
4
6
5
6
1
1
16
2
16
3
16
4
16
5
16
2
(Ask the following, filling in the equivalent fractions above or below the existing number line as
students give them.)
T: Raise your hand if you can say 2/6 as the largest unit? (1/3)
T: Raise your hand if you can say 3/6 as the largest unit? (1/2)
T: Raise your hand if you can say 4/6 as the largest unit? (2/3)
T: Raise your hand if you can say 1 2/6 as the largest unit? (1 1/3)
T: Raise your hand if you can say 1 3/6 as the largest unit? (1 1/2)
T: Raise your hand if you can say 1 4/6 as the largest unit? (1 2/3)
Now we will try skip-counting by sixths again, this time using the largest unit. I will give you a minute to
practice first; you may use the number line as you practice with a your partner at your table.
Let’s begin.
I will point up as we increase, then use this symbol (make a fist or a flat hand) to pause at the current
number; and I will point down when I want us to count backwards. Try not to look at the number line
as we count.
We will start with 0:
(Pointing upward and making a rhythmic motion to indicate the speed of the counting:) 0, 1/6, 1/3,
½, 2/3, 5/6, 1
(Make a fist or flat hand, then point downward with rhythmic motioning:) 5/6, 2/3, ½
(Make a fist or flat hand, then point upward with rhythmic motioning:) 2/3, 5/6, 1, 1 and 1/6, 1 and
1/3, 1 and ½, 1 and 2/3, 1 and 5/6, 2, 2 and 1/6, 2 and 1/3, 2 and 1/2
(Make a fist or flat hand, then point downward with rhythmic motioning) 2 and 1/3, 2 and 1/6, 2, 1 and
5/6. STOP. Well done.
(SWITCH BACK TO POWER POINT)
(SLIDE 13) Turn and talk with a partner at your table about your response to these questions.
(Allow 2 minutes for turn and talk, and then facilitate a discussion.)
Session Notes:
Date:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rigor Breakdown: Procedural Skill and Fluency Grades 3-5
3/23/16
7
NYS COMMON CORE MATHEMATICS PD
Rigor Breakdown: Fluency
(SLIDE 14) Let’s summarize some key points about counting exercises:
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They are appropriate for all grade levels, PK-5.
(CLICK TO ADVANCE SECOND BULLET ON SLIDE 14) Counting forward and backwards supports addition and
subtraction.
(CLICK TO ADVANCE THIRD BULLET ON SLIDE 14) Skip-counting supports multiplication.
(CLICK TO ADVANCE FOURTH BULLET ON SLIDE 14) Counting exercises can be untimed choral counting, or
timed competitions, either as a class moving from student to student allowing classes to compete against each
other by posting each class’ best time, or as individuals competing with both for their best personal time and
with one another.
Fluency Work – Choral and White Board Exchanges
Time: 0:25-0:35
[10 minutes] In this section, you will…
 Learn about choral and white board exchange fluency activities
 Engage in an example of choral and white board exchange fluency work
 Watch a video clip of choral and white board exchange fluency work
 Reflect upon how fluency can also support conceptual understanding
Materials used include:


Personal Dry Erase Boards and Markers
Video Clip: White Board Exchange
(SLIDE 15) In this next set of fluency examples, we’ll look at activities involving choral and white board exchanges.
(SLIDE 16) These are quick, efficient interactive drills and games. The teacher may use verbal call outs, flash-card style
manipulatives, or an overhead projector. Students respond either chorally or in writing on personal white boards or
use manipulatives displayed at their desks.
The personal white board has a number of benefits. During written fluency exercises the personal white board gives
the teacher instant feedback about student understanding and the boards are motivating to students. While students
do have to commit to writing something down, they can also erase quickly so that they do not have of suffer the
evidence of mistakes.
(CLICK TO ADVANCE SECOND BULLET AND SUB-BULLETS ON SLIDE 16) This type of choral or white board exchange can
be applied to a wide range of skills from how many to make 10 games to computing one less than, one more than (e.g.,
what is one less than 6, what is 2 more than 7), to writing expressions to represent words (e.g., show me an expression
for 2 less than the product of 4 and 5.) As we mentioned with skip-counting by fractional amounts, sometimes fluency
exercises can support and develop conceptual understanding as well.
(SLIDE 17) While you watch the video clips, notice how conceptual understanding is being reinforced. After the video,
you will have a chance to share your thoughts with your table.
Session Notes:
Date:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rigor Breakdown: Procedural Skill and Fluency Grades 3-5
3/23/16
8
NYS COMMON CORE MATHEMATICS PD
Rigor Breakdown: Fluency
This video shows Anita Meadows and her 5th grade students at Saint Edward’s School in Vero Beach,
Florida using a white board exchange.
(SLIDE 18 – Play Video Clip: White Board Exchange)
(SLIDE 19) Now let’s engage in a white board exchange. Get your white boards and markers ready.
Let’s begin.
Show me an expression for the product of 6 and 2. (As participants raise and show you a correct
answer of 12 acknowledge as many of them as is feasible saying, “Very Good,” “Yes,” or “Nice”, if a
participant writes an incorrect answer say to them, “Listen again, I want the product of 6 and 2.”)
T: Show me an expression for the product of 6 and 2.
T: Show me an expression for 1 more than the product of 6 and 2.
T: Show me an expression for the difference of 6 and 2.
T: Show me an expresssion for 1 more than the difference of 6 and 2.
T: Show me an expression for the quotient of 6 and 2.
T: Show me an expression for 1 more than the quotient of 6 and 2.
(SLIDE 20) Turn and talk with a partner at your table about how these activities reinforce conceptual
understanding.
(Allow 2 minutes for turn and talk, and then facilitate a discussion.)
(SLIDE 21) Let’s review some key points specific to choral and white board exchanges:




(CLICK TO ADVANCE FIRST BULLET ON SLIDE 21) Exchanges can be used as a quick form of assessment. Note
that white boards exchanges provide a better opportunity to assess students individually than do choral
responses, and that any choral exchange can be done as a white board exchange.
(CLICK TO ADVANCE TO SECOND BULLET ON SLIDE 21) Exchanges allow for rapid completion of multiple
practice problems.
(CLICK TO ADVANCE TO THIRD BULLET ON SLIDE 21) Exchanges create intensity in student practice.
(CLICK TO ADVANCE TO FOURTH BULLET ON SLIDE 21) Exchanges give students immediate feedback.
Session Notes:
Date:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rigor Breakdown: Procedural Skill and Fluency Grades 3-5
3/23/16
9
NYS COMMON CORE MATHEMATICS PD
Rigor Breakdown: Fluency
Fluency Work – Sprints
Time: 0:35-0:55
[20 minutes] In this section, you will…
 Engage in an example of Sprints
 Learn about Sprints
 Watch a video clip of Sprints
 Look for evidence of mathematical practices in Sprints
Materials used include:




Stopwatch
G5—M3—B—L4 Sprints A and B: Equivalent Fractions (provided in module)
Fluency Progression (provided in module)
Video Clip: Sprints – Fluency in Action
(SLIDE 22) Our next example of fluency work is the Sprint.
(SLIDE 23) These notes on Sprints are from the Fluency Progressions section of the Module Overview for Grade 5—
Module 3. Sprints are designed to develop fluency. A fast pace is essential. While administering Sprints, teachers
assume the role of athletic coaches. A rousing routine fuels students’ motivation to do their personal best.
(CLICK TO ADVANCE SECOND BULLET ON SLIDE 23) Student recognition of increasing success is critical, and so every
improvement is celebrated. Each Sprint has two parts with closely related problems on each. Students complete the
two parts of the Sprint in quick succession with the goal of improving on the second part, even if only by one more.
(CLICK TO ADVANCE THIRD BULLET ON SLIDE 23) With practice the entire routine takes only 8-10 minutes.
(SLIDE 24) The best way to learn about Sprints is to experience one. Let’s get started.
(Administer G5—M3—B—L4 Sprints A and B: Equivalent Fractions as described below.)
This Sprint involves equivalent fractions. Open your Grade 5—Module 3 and turn to page 3.B.12. Do
not look at the Sprint; cover it with your personal board and hold your pencil in the air to let me know
that you are ready. (Allow time for participants to locate the appropriate page.)
There are 44 problems on the Sprint. You will have 30 seconds. Do as many as you can. I do not
expect any of you to finish. If you do finish, count by 12s down the right hand side of the page. On your
mark, get set, GO! (Start stopwatch and time for 30 seconds.)
STOP. Put your pencils down. I will read the answers. You say ‘YES’ if you answer matches. Mark the
ones you have wrong, but don’t try to correct them. (Quickly call out the answers.) 2, 10, 4, 6, 8, 6, 4, 9,
6, 2, 6, 12, 12, 1, 3, 5, 2, 4, 1, 2, 4, 3, 4, 8, 2, 4, 15, 35, 4, 4, 42, 8, 9, 40, 54, 5, 56, 4, 7, 9, 9, 72, 84, 5, 6.
(If participants are still responding with ‘YES,’ begin counting by 12s until no more participants
respond.)
Session Notes:
Date:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rigor Breakdown: Procedural Skill and Fluency Grades 3-5
3/23/16
10
NYS COMMON CORE MATHEMATICS PD
Rigor Breakdown: Fluency
Count the number you have correct and write it on the top of the page. Raise your hand if you have 1
or more correct. 2 or more, 3 or more ... (Continue until all hands are down.) Let’s applaud our
winners.
You have a one minute to finish up the page and get ready for the next Sprint. (Allow 1 minute for
participants to finish. Encourage participants to work together if anyone needs help.)
Stop working. I will read the answers again so you can check your work. You say YES if your answer
matches. (Quickly call out the answers.) 2, 10, 4, 6, 8, 6, 4, 9, 6, 2, 6, 12, 12, 1, 3, 5, 2, 4, 1, 2, 4, 3, 4, 8,
2, 4, 15, 35, 4, 4, 42, 8, 9, 40, 54, 5, 56, 4, 7, 9, 9, 72, 84, 5, 6.
Turn and talk, for 1 minute, with a partner at your table about what patterns you notice in this Sprint.
Also talk about how those patterns could help you in the future. (Allow 1 minute for turn and talk, and
then facilitate a discussion.)
Stand up. Let’s march in place while counting by 6s. We’ll start at 0 and count up, by 6s, to 60. (Model
a fast, energetic march as participants do the same.) Now we’ll count back from 60, by 6s, to 0. This
time, instead of marching let’s do shoulder rolls. (Model slow, gentle shoulder rolls as participants do
the same.)
(CLICK TO ADVANCE SECOND BULLET ON SLIDE 24) Now let’s do Sprint B. Turn to page 3.B.13 in your
module. Do not look at the Sprint; cover it with your personal board and hold your pencil in the air to
let me know that you are ready. (Allow time for participants to locate the appropriate page.)
There are 44 problems on the Sprint. You will have 30 seconds. Do as many as you can. I do not
expect any of you to finish. If you do finish, count by 12s down the right hand side of the page. On your
mark, get set, GO! (Start stopwatch and time for 30 seconds.)
STOP. Put your pencils down. I will read the answers. You say ‘YES’ if your answer matches. Mark the
ones you have wrong, but don’t try to correct them. (Quickly call out the answers.) 10, 4, 6, 8, 4, 2, 6, 3,
9, 8, 8, 3, 9, 2, 1, 1, 5, 5, 3, 3, 3, 4, 12, 12, 3, 3, 25, 28, 3, 5, 35, 9, 8, 64, 45, 9, 48, 9, 1, 5, 12, 36, 4, 7 (If
participants are still responding with ‘YES,’ begin counting by 12s until no more participants respond.)
Count the number you have correct and write it on the top of the page. Raise your hand if you have 1
or more correct. 2 or more, 3 or more ... (Continue until all hands are down.) Let’s applaud our
winners!
Write the amount by which your score improved at the top of the page. Raise your hand if you
improved your score by 1 or more. 2 or more, 3 or more... (Continue until all hands are down.) Let’s all
applaud our winners for most improved!
Turn and talk with a partner at your table about this exercise. What about the Sprint routine do you
find most advantageous for students?
(Allow 2 minutes for turn and talk, and then facilitate a discussion.)
Each module ends with a Fluency Progression. Turn to the end of the Fluency Progression for this module, and take a
minute to read the Directions for Administering Sprints. When you are finished, turn and talk with a partner at your
Session Notes:
Date:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rigor Breakdown: Procedural Skill and Fluency Grades 3-5
3/23/16
11
NYS COMMON CORE MATHEMATICS PD
Rigor Breakdown: Fluency
table. (Allow 1 minute for independent reading and 1 minute for turn and talk. Then, facilitate a discussion.)
(SLIDE 25) It is important to note that round two of the Sprint is for the purpose of consolidating student progress, and
building confidence, especially for lower performing students, who often don’t feel successful in class. By recognizing
improvement, all students have an opportunity to be recognized by their classmates.
(CLICK TO ADVANCE SECOND BULLET ON SLIDE 25) The routine alone does not set the Sprint apart from other math
drills. It is in its intelligent design and sequence of delivery that the Sprint is superior to computer-generated
worksheets and other speed drills.
(CLICK TO ADVANCE THIRD BULLET ON SLIDE 25) Sprints are aligned to individual lessons and topics and have been
written to account for a large range of skill levels.
(CLICK TO ADVANCE FOURTH BULLET ON SLIDE 25) Teachers are encouraged to study the sequence of problems in the
Sprints provided in the modules in A Story of Units and create their own Sprints. Problems should progress from simple
to complex and include a pattern in the design. Students should be encouraged to look for the pattern and use it to
help them improve on Sprint B.
(CLICK TO ADVANCE FIFTH BULLET ON SLIDE 25) Sprints do not have to be administered daily, but certainly can be done
at least 2-3 times per week.
(SLIDE 26) Refer to the Standards of Mathematical Practice. As you read through the practices, reflect
on the exercise of taking a Sprint. Did you see evidence of one or more mathematical practices? Turn
and talk with your table about what mathematical practices you saw in action.
(Allow 2 minutes for turn and talk, and then facilitate a discussion.)
(SLIDE 27) While you watch the video, make note of any comments that resonate with you. After the video, you will
have an opportunity to discuss your thoughts.
This video, produced by Common Core Inc., is about fluency in general and about Sprints in particular.
In the video, you will see teachers talking about their experiences with administering Sprints. You will
also see some snapshots of students engaged in a Sprint.
(SLIDE 28 – Play Video Clip: Sprints – Fluency in Action)
(SLIDE 29) Turn and talk with a partner at your table about this video. In what ways are Sprints
advantageous in meeting the demands of fluency?
(Allow 2 minutes for turn and talk, and then facilitate a discussion.)
(SLIDE 30) Let’s review some key points related to sprints; use of Sprints:
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Sprints allow for rapid completion of multiple practice problems.
Sprints create intensity in student practice.
Sprints give students quick feedback.
Sprints motivate students with a near-term goal for improvement
Session Notes:
Date:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rigor Breakdown: Procedural Skill and Fluency Grades 3-5
3/23/16
12
NYS COMMON CORE MATHEMATICS PD
Rigor Breakdown: Fluency
Closing
Time: 0:55-1:00
[5 minutes] In this section, you will…
 Learn about banks of fluency activities provided with A Story of Units
 Summarize key points
 Reflect on next steps
 Reflect on the role of fluency in balanced instruction
Materials used include:


Fluency Progression (provided in module)
How to Implement A Story of Units
(SLIDE 31) Fluency Progressions are included in each module to assist with planning this work. These materials are
banks of activities that teachers may either select and use, or study as they create their own.
Turn, again, to the Fluency Progression located at the end of the Module. Take a minute to look through the
information. (Allow 1 minute for independent reading and 1 minute for turn and talk. Then, facilitate a discussion.)
The bank of fluency activities for each lesson is intentionally organized so that activities revisit previously learned
material to develop automaticity, anticipate future concepts, and strategically preview or build skills for the day’s
concept lesson. It is important to provide ample opportunities to review familiar fluencies as needed, as well as to
begin developing automaticity with new ones. The suggestions may or may not be ideal for the students in a given
class. As teachers work with the materials, they should adjust them in consideration of their particular students’ needs.
(SLIDE 32) Let’s review the key points of this session:
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
In each grade, students are expected to master certain fluencies over the course of the year.
Fluency can be promoted in a variety of ways.
Fluency work is usually done as a warm-up at the beginning of a lesson for approximately 10-20 minutes.
Fluency represents a major part of the instructional vision that shapes A Story of Units. Frequent, rich
opportunities to help students achieve fluency are woven throughout A Story of Units.
Fluency work also provides opportunities to nurture the Standards of Mathematical Practice. The Standards for
Mathematical Practice are embedded into all components of rigor and are not separate from the content
instruction.
(SLIDE 33) Take a moment to reflect on these next steps:


What type of fluency activity are you most eager to incorporate into your current teaching?
How can you help your colleagues implement the fluency component of rigor?
Turn and talk with a partner at your table about how you will to begin to implement fluency work.
(Allow 2 minutes for turn and talk, and then facilitate a discussion.)
Session Notes:
Date:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rigor Breakdown: Procedural Skill and Fluency Grades 3-5
3/23/16
13
NYS COMMON CORE MATHEMATICS PD
Rigor Breakdown: Fluency
(SLIDE 34) Recall that procedural skill and fluency is but one of three components of rigor. The Instructional Shifts
require that, “Students are practicing and understanding. There is more than a balance between these two things in
the classroom – both are occurring with intensity. Teachers create opportunities for students to participate in ‘drills’
and make use of those skills through extended application of math concepts…”
(SLIDE 35) So we see that the standards call for equal intensity and balance among the three components. On page 5
of the Publishers’ Criteria we are told that, “To help students meet the expectations of the Standards, educators will
need to pursue, with equal intensity, three aspects of rigor in the major work of each grade: conceptual understanding,
procedural skill and fluency, and applications.” On page 9, the Publishers’ Criteria tells us that, in respect to rigor,
“Materials and tools reflect the balances in the Standards…” The variety of fluency work that we have explored is an
important part of balanced, rigorous instruction.
(SLIDE 36) The time spent on each component of rigor in daily lessons varies and is guided by the rigor emphasized in
the standard(s) addressed in any given lesson. To clearly communicate the carefully balanced and rigorous instruction
of A Story of Units, the overview of each module includes a Distribution of Instructional Minutes diagram. This is an
example. It shows, at a glance, the time devoted to each component of rigor in the module as a whole, as well as in any
given lesson of the module. Look at Lesson 4 of this example module. Note that this lesson begins with 15 minutes of
fluency work, followed by 20 minutes of concept development and 15 minutes of problem-solving applications. As is
usual, the lesson ends with a 10 minute student debrief.
(SLIDE 37) To further promote balanced rigorous instruction, every lesson begins with a pie graph illustrating the
Suggested Lesson Structure. Note that this information is from Lesson 4 of the Distribution of Instructional Minutes
diagram that we just discussed. The actual order of Fluency Practice, Concept Development, Application Problems, and
Student Debrief in each lesson is determined by the content and pedagogy of the lesson. Fluency is usually first—by
beginning class with animated, adrenaline-rich fluency work, students are more alert when presented with the Concept
Development and Application Problems.
In closing, let’s look at where this information can be found in the How to Implement A Story of Units document. Turn
to the section explaining The Common Core Approach to Lesson Structure on page 21. Note that information about the
Distribution of Instructional Minutes and the Suggested Lesson Structure is provided.
Turn to page 22 and read the section on Fluency Practice. (Allow 2 minutes for participants to read independently, and
then facilitate a discussion.)
Turnkey Materials Provided
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PowerPoint Presentation
How to Implement A Story of Units
G5—M3—B—L4 Sprints A and B: Equivalent Fractions (provided in module)
Fluency Progressions (provided in module)
Video Clip: Skip-counting by Fractions
Video Clip: White Board Exchange
Video Clip: Sprints – Fluency in Action
Session Notes:
Date:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rigor Breakdown: Procedural Skill and Fluency Grades 3-5
3/23/16
14
NYS COMMON CORE MATHEMATICS PD
Rigor Breakdown: Fluency
Additional Suggested Resources
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CCLS – http://www.p12.nysed.gov/ciai/common_core_standards/pdfdocs/nysp12cclsmath.pdf
Instructional Shifts – http://schools.nyc.gov/NR/rdonlyres/9375E046-3913-4AF5-9FE3D21BAE8FEE8D/0/CommonCoreInstructionalShifts_Mathematics.pdf
Publishers’ Criteria – http://www.corestandards.org/assets/Math_Publishers_Criteria_K8_Summer%202012_FINAL.pdf
Session Notes:
Date:
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Rigor Breakdown: Procedural Skill and Fluency Grades 3-5
3/23/16
15