5/30/13 Book Study:
Number Talks
by Sherry Parrish
HELPING CHILDREN
BUILD MENTAL MATH
AND COMPUTATION
STRATEGIES
Grades 2 – 5
Wednesday, June 5th
Facilitated by: Christine Roberts
[email protected]
Goals/Agenda
—  Welcome
—  Overview
—  Sample Number Talks
—  Videos
—  Routine
¡  Teacher’s role
¡  Student expectations
—  Supporting the Common Core State Standards
—  Next Steps
—  Wrap Up
Norms
1 5/30/13 Number Talks
—  Calculate the following mentally.
—  Be prepared to share strategies aloud.
8+6
Number Talks by Sherry Parrish
Number Talks: Video
Classroom Clip: 2.1
—  Watch the video showing a Second Grade
addition Number Talk.
Discuss (with your elbow partner):
—  What is the teacher’s role in the number talk?
—  What features of this video would you like to
see in your classroom?
5
Number Talks by Sherry Parrish
Why Number
Talks?
The practice of number talks is one of the most
powerful vehicles I know for helping students learn to
reason with numbers and make mathematically
convincing arguments, for building a solid foundation
for algebraic reasoning, and for teaching mathematics
as a sensemaking process. If all teachers make this shift
in their practice, it would represent a profound
advancement in mathematics education.
- Ruth Parker
Number Talks by Sherry Parrish
2 5/30/13 What are Number Talks?
u Classroom conversations around purposefully crafted
computation problems that are solved mentally.
u The problems are designed to elicit specific strategies
that focus on number relationships and number theory.
u Students are given problems in either whole- or small-
group settings and are expected to mentally solve them
accurately, efficiently, and flexibly.
u By sharing and defending their solutions and strategies,
students have the opportunity to collectively reason
about numbers while building connections to key
conceptual ideas in mathematics.
Number Talks by Sherry Parrish
Rationale for Number Talks
—  “Our classrooms are filled with students and
adults who think of mathematics as rules
and procedures to memorize without
understanding the numerical relationships
that provide the foundation for these rules.”
Number Talks by Sherry Parrish
Accuracy, Efficiency, and Flexibility
—  “Accuracy denotes the ability to produce an
accurate answer; efficiency refers to the
ability to choose an appropriate, expedient
strategy for a specific computation problem;
and flexibility means the ability to use
number relationships with ease in
computation.”
Number Talks by Sherry Parrish
3 5/30/13 Focusing on the Mathematical Process,
NOT Answer Getting
—  Students are asked to defend or justify their answers to
prove their thinking
—  Students have a sense of shared authority in determining
whether an answer is accurate
—  Teacher is not ultimate authority
—  Wrong answers are used as opportunities to unearth
misconceptions
—  Students investigate their thinking and learn from
mistakes
—  Mistakes play an important role in learning and provide
opportunities to question and analyze thinking, bring
misconceptions to forefront, and solidify understanding
Number Talks by Sherry Parrish, pages 11-12
My Favorite No
—  The Teaching Channel:
—  https://www.teachingchannel.org/videos/class-
warm-up-routine
The Teaching Channel, https://www.teachingchannel.org/videos/class-warm-up-routine
Number Talks: Video
Teacher Interview
—  Watch the video showing a Teacher Interview.
Discuss (with your face partner):
—  How does the teacher feel about Number Talks?
—  How have Number Talks influenced her
classroom and her teaching?
12
Number Talks by Sherry Parrish
4 5/30/13 Number Talks Articles
—  Choose one of the articles to
read.
¡ Stand-Up,
Hand-Up, Pair-Up
¡ Share
your thoughts and
questions after reading the
article.
13
Tulare County Office of Education
Number Talks
—  Calculate the following mentally.
1000 - 674
Number Talks by Sherry Parrish
Classroom Clip: 3.1
As you watch the video, consider:
—  What evidence in the video supports student
understanding of place value?
—  How do the student’s strategies exhibit number
sense?
—  Which strategies were more accessible to you: More
challenging to follow?
—  How are accuracy, flexibility, and efficiency
interwoven in the students’ strategies?
Number Talks by Sherry Parrish
5 5/30/13 What Are
Number Talks?
Key Components of Number Talks
1)  Classroom environment and community
2)  Classroom discussions
3)  The teacher’s role
4)  The role of mental math
5)  Purposeful computation problems
Number Talks by Sherry Parrish
Overview
—  Mental math problems posed
—  Students are given think time and indicate a solution
and multiple strategies
—  Students share solutions and explain their thinking
—  Encourages students to communicate about math
—  The teacher acts as a facilitator and his/her primary
function is to question students in order to guide the
discussion
Number Talks by Sherry Parrish
6 5/30/13 Routine
—  Daily, 5-15 minutes
—  Consistent location
—  Students in close proximity, seated on the floor or in
chairs
—  Easy visibility for teacher and students
—  Teacher records student thinking on the whiteboard
and/or chart paper
—  Problem or string of problems are posed
—  Students are given think time
—  Teacher facilitates a conversation around
the problem(s) posed that day
Number Talks by Sherry Parrish
Number Talks Hand Signals
o 
Teach the Hand Signals
o  I have an answer
(Thumb up in front of chest)
o  I agree
(“hang ten” back and forth)
o  I disagree
(hands back and forth by
ears or in front of body)
Number Talks by Sherry Parrish
Classroom Discussions
—  Teacher writes problem on board and give students
time to solve the problem mentally.
—  Once students find an answer, they are encouraged
to continue finding efficient strategies while others
are thinking.
—  Students indicate when they are ready with a
solution by quietly raising a thumb against their
chest. They indicate they have other approaches by
raising another finger for each solution.
Number Talks by Sherry Parrish
7 5/30/13 Classroom Discussions Continued
—  The quiet form of acknowledgement allows for more
student think time at the same time as challenging
students that already have an answer.
—  All answers- correct and incorrect- are recorded.
—  Students share strategies and justifications with
peers.
Number Talks by Sherry Parrish
Benefits of Sharing and Discussing
Computation Strategies
Students have the opportunity to:
1.  Clarify their own thinking.
2.  Consider and test other strategies to see if they are
mathematically logical.
3.  Investigate and apply mathematical relationships.
4.  Build a repertoire of efficient strategies.
5.  Make decisions about choosing efficient strategies
for specific problems.
Number Talks by Sherry Parrish
Sample Number Talk
—  Calculate the following mentally.
—  Be prepared to share strategies aloud.
59 + 13
Number Talks by Sherry Parrish
8 5/30/13 Classroom Clip: 32
As you watch the video, consider:
—  What evidence in the video supports student
understanding of place value?
—  How does each strategy foster number sense and the
use of number relationships?
—  Which strategies were most accessible to you? More
difficult to follow?
—  Choose one of the strategies to model with the open
number line. How could this be an effective tool for
your students?
Number Talks by Sherry Parrish
Teacher and Student Roles
in Number Talks
Roles and Participation
—  Teacher’s role
—  Student participation
¡  Planning - be purposeful in
¡  All students work to find an
the selection of problems
answer
¡  Facilitating
¡  Signal that they have an
answer and if they have
¡  Questioning
multiple strategies
¡  Recording answers/student
¡  Share and explain their
thinking
thinking
¡  Accepting – accept and
¡  Defend their thinking
record answers/explanations
without confirming or
¡  Inquire about the thinking
denying
of others
Number Talks by Sherry Parrish
9 5/30/13 The Teacher’s Role
—  Teacher's role shifts from being sole authority in
giving information and confirming correct answers
—  Teacher is facilitator, questioner, listener, and
learner
—  Guide students to ponder and discuss examples that
build upon teacher’s purposes.
—  “How did you get your answer?”
—  “By changing my question from “What answer did
you get” to “How did you solve this problem?” I was
able to understand how they were making sense of
mathematics.”
Number Talks by Sherry Parrish
Teacher Responsibilities
—  Plan problems with a purpose/goal in mind
—  Pose the problem(s) for the day
—  Record student responses to reflect how they were
explained (not the teacher’s interpretation)
—  Practice notation to represent student thinking
accurately
—  Provide the structure and procedures to facilitate the
Number Talks
—  Post sample prompts to helps students structure their
explanations or questions in front of the class
—  Be aware of the equal sign and use it
properly
Number Talks by Sherry Parrish
Choosing Purposeful Problems
—  Craft problems that guide students to focus on
mathematical relationships.
—  Teacher’s goal and purpose should determine the
numbers and operations that are chosen.
Discuss:
—  How might you work together to select and plan for
number talks?
Number Talks by Sherry Parrish
10 5/30/13 Number Talks are a Purposeful Vehicle to:
—  Make sense of mathematics
—  Develop efficient computation strategies
—  Communicating mathematically
—  Reasoning and proving solutions
Number Talks by Sherry Parrish
Sample Number Talk and Video
—  Classroom Clip 5.3:
16 x 35
Number Talks by Sherry Parrish
As you watch the Number Talk, consider:
1)  What procedures are in place that allow students to
share their thinking?
2)  What opportunities exist for the teacher to
informally assess student understanding?
3)  How is student communication encouraged and
valued?
4)  How would you describe the teacher’s role during
the number talk?
Number Talks by Sherry Parrish
11 5/30/13 Developing Student Strategies
and Supporting all Learners
Developing Accountability with Students
1)  Ask students to use finger signals to indicate the most
efficient strategy.
2)  Keep records of problems posed and the corresponding
student strategies.
3)  Hold small-group number talks throughout each week.
4)  Create and post class strategy charts.
5)  Require students to solve an exit problem using the
discussed strategies.
6)  Give a periodic computation assessments to monitor
growth.
Number Talks by Sherry Parrish
Supporting Students
—  Use this time to make informal observations and
interactions.
—  Provide appropriate wait time to ensure that the
majority of the students have accessed the problem.
—  Validate student thinking by accepting all answers.
—  Encourage student communication throughout the
number talk.
Number Talks by Sherry Parrish
12 5/30/13 Developing Strategies
—  Discuss with your partner at least four different
strategies to solve 28 + 29.
—  How will you teach alternate strategies to students?
Sample Number Talk
—  Calculate the following mentally.
—  Be prepared to share strategies aloud.
28 + 29
Number Talks by Sherry Parrish
Number Talks: Video
Classroom Clip: 3.1
Discuss:
—  How does the teacher’s recording of each strategy
provide access for all students?
—  Which strategies are easiest for you to understand?
—  Which strategies are more challenging to follow?
—  What mathematical concepts are being addressed during
the number talk.
—  How did the teacher bring these ideas to the forefront for
the class?
Number Talks by Sherry Parrish
13 5/30/13 Supporting English Learners
—  According to David Foster, mathematics director,
founder of the Silicon Valley Mathematics Initiative
for the Noyce Foundation,
“Number Talks are one of the most
important routines you can implement
in order for EL students to be
successful in mathematics. The key is
in how you record student responses.”
Tulare County Office of Education
Come se suma?/How do we add?
—  A Number Talk in Spanish from Inside Mathematics:
—  http://www.insidemathematics.org/index.php/2nd-
grade-icomo-se-suma-how-do-we-add
Inside Mathematics, insidemathematics.org
OA
Progression
“K, Counting and Cardinality; K-5, Operations and Algebraic Thinking,” page 6, www.commoncoretools.wordpress.com
14 5/30/13 8 Common Addition Strategies
1.  Counting All
2.  Counting on
3.  Doubles/Near-Doubles
4.  Making Tens
5.  Making Landmark or Friendly Numbers
6.  Compensation
7.  Breaking Each number into its Place Value
8.  Adding Up in Chunks
43
Number Talks by Sherry Parrish
Number Talks
—  Calculate the following mentally.
—  Try to use multiplication strategies.
12 x 15
Number Talks by Sherry Parrish
Multiplication and Division Strategies
—  Repeated addition or
skip counting
—  Repeated subtraction
or sharing/dealing out
—  Partial products
—  Multiplying up
—  Breaking factors into
—  Partial quotients
smaller factors
—  Making a landmark or
—  Proportional
reasoning
friendly number
—  Doubling and halving
Number Talks by Sherry Parrish
15 5/30/13 Number Talks
—  Calculate the following mentally.
—  Be prepared to share strategies aloud.
150÷15
Number Talks by Sherry Parrish
Number Talks
—  Calculate the following mentally.
—  Be prepared to share strategies aloud.
300÷15
Number Talks by Sherry Parrish
Number Talks Video
Classroom Clip: 5.4
Discuss:
—  How did this particular sequence of problems help
students use number relationships to solve the
problems?
—  What student confusions and misunderstandings
surfaced with the array model?
—  How did the teacher navigate the discussion to build
understanding about multiplication, division, and array
model?
Number Talks by Sherry Parrish
16 5/30/13 Number Talks
—  Anticipate possible student strategies and how they
might be recorded.
496 ÷ 8
Supporting the CCSS
for Mathematics
True/False
with
Justification
?
7=4+3
?
4+3=3+5
?
9 = 16 - 7
Teacher
Learning
Content
Student
Math Assessment Collaborative
?
16 - 7 = 7 - 16
The Silicon Valley Mathematics Initiative
1.OA.7 Understand the meaning of the equal sign,
and determine if equations involving addition and
subtraction are true or false. For example, which of
the following equations are true and which are
false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2
51
The Silicone Valley Mathematics Project
17 5/30/13 NUMBER TALKS:
RELATIONAL THINKING
7+6=
+ 5
43 + 28 =
+ 42
28 + 32 =27 +
12 + 9 = 10 + 8 +
52
The Silicone Valley Mathematics Project
The Standards for Mathematical Practice
Mathematically proficient students:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Tulare County Office of Education
Mathematical Practices - Discuss
—  What are some of the ways that the Mathematical
Practices Standards are demonstrated through
Number Talks?
Talking Chips
1.  The teacher provides a discussion topic and think time.
2.  Any student begins the discussion, placing one of his/her chips in
the center of the table.
3.  Any student with a chip continues discussing, using his/her chip.
4.  When all chips are used, teammates each collect their chips and
continue the discussion using their talking chips (until the
teacher stops the discussion).
Tulare County Office of Education
18 5/30/13 Guess My Rule
—  Extending Number Talks
to Other Math Concepts
from Inside Mathematics:
—  http://
www.insidemathematics.
org/index.php/5th6thgrade-guess-my-rule
Inside Mathematics, insidemathematics.org
Planning for Number Talks
—  Identify grade level standards that require the type
of mathematical thinking that Number Talks
Promotes.
—  Write several problems with your table group for
your selected standards.
Tulare County Office of Education
Getting Started and
Next Steps
19 5/30/13 Tips for Getting Started
1.  Start with smaller problems to elicit thinking from
multiple perspectives
2.  Be prepared to offer a strategy from a previous
student
3.  It is okay to put a student strategy on the back
burner
4.  As a rule, limit to 5-15 minutes
5.  Be patient with yourself and students as you
incorporate Number Talks into your regular math
time
Number Talks by Sherry Parrish
Next Steps
—  What are your next steps in preparing
Number Talks for next school year?
—  What did you learn from today’s session?
—  What do you still need to learn?
Tulare County Office of Education
Resources
20 5/30/13 commoncore.tcoe.org
Tulare County Office of Education
Resources
—  Questions/comments
—  Resources:
¡  http://mathperspectives.com/num_talks.html
¡  http://www.insidemathematics.org/index.php/classroomvideo-visits/number-talks
¡  http://sdcounts.tie.wikispaces.net/file/view/
Numbertalks.pdf
¡  http://www.sandi.net/cms/lib/CA01001235/Centricity/
Domain/101/Math%20Documents/Routines/
mid_level_routinebank.pdf
Tulare County Office of Education
Resources
¢ TCOE Instructional Services
— 
www.tcoe.org/ERS/CCSS
¢ TCOE Common Core Repository
— 
www.commoncore.tcoe.org
—  E-mail:
Christine Roberts
[email protected]
Tulare County Office of Education
21 5/30/13 Feedback
—  Please complete
the feedback form
and leave it on the
back table.
—  Have a great day!
Tulare County Office of Education
22