number talks - curriculum
TRANSCRIPT
Number Talks
Helping Children Build
Mental Math
and
Computation Strategies
Sherry Parrish
The University of Alabama at Birmingham
Your Experiences
47 + 38
5 + 28 + 9 + 133
51 - 36
2 5 x 1 6
Number Sense
“. . . an awareness and understanding
about what numbers are, their
relationships, their magnitude, the
relative effect of operating on
numbers, including the use of mental
mathematics and estimation.”
Fennell and Landis (1994)
Standards for
Mathematical Practices
Make sense of problems and persevere
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for an express regularity in repeated reasoning
Common Core Content Standards
Counting and Cardinality
Operations and Algebraic Thinking
Number and Operations in Base Ten
Use strategies based upon place value and the properties of operations
Progression of Terminology
Strategies (student-invented)
Algorithms (generalized strategies)
Standard Algorithm
Computation
Progressions
Number Talks
A five to fifteen minute
classroom conversation
around purposefully crafted
computation problems that
are solved mentally
Computation Goals
Accuracy
Flexibility
Efficiency
Principles of Number Talks
Classroom Community
Accurate and Purposeful Recording
Logico-Mathematical Knowledge
Laying the Foundation
Conservation of Number
Subitizing
Composing/Decomposing numbers
Unitizing with 5 and 10
Efficient Counting
Computation as Efficient Counting
One-to-one correspondence
Counting for a purpose
Counting all
Counting on
Counting groups
Strategies with Number Relationships
Tools and Models
Dot Cards
Five and Ten Frames
Rekenreks
Dot Images
How many do you see?
How do you see it?
How many do you see?
How do you see it?
How many do you see?
How do you see it?
How many do you see?
How do you see it?
How many do you see?
How do you see it?
How many do you see?
How do you see it?
Number Talk Rehearsal
Create a “Dot Card.”
Lead a number talk with your small group using your Dot Card.
Focus on:
Listening
Recording
Questioning
Addition Number Talk
Purposeful Computation Problems
Landmark numbers: 99 + 99
Doubles: 16 + 15
Compensation: 16 + 39
Purposeful Number Talk Strings
50 + 50
49 + 49
60 + 60
59 + 59
15 + 15
15 + 16
18 + 18
18 + 17
Classroom Snapshot: 328 - 69
11
2 12 18
3 2 8
- 6 9
2 5 9
Subtraction Number Talk
70 – 34: Video Focal Points
Learning Community
Mathematical Practices
Teacher’s Role
Analyzing a Subtraction String
40 - 20
40 - 19
50 - 25
50 - 24
43 – 10
43 – 14
263-100
263-104
We are usually convinced more
easily by reasons we have found
ourselves than by those which have
occurred to others.
Blaise Pascal
Multiplication Number Talk
Stages for Fact Aquisition
Building conceptual understanding
Developing reasoning strategies
Moving toward automaticity
Purposeful Multiplication String
2 X 7
4 x 7
3 x 7
7 x 7
2
2
2
1
7
7 X 7
Open Array
7
2
2
2
1
7
4
3
7 X 7 = (4 x 7) + (3 x 7)
4 x 7
3 x 7
Multiplication String
4 x 25
6 x 25
12 x 25
12 x 25
(2 x 6) x 25 = 6 x (2 x 25)
(4 x 25) + (4 x 25) + (4 x 25)
(3 x 4) x 25 = 3 x (4 x 25)
(10 + 2) x 25
32 X 15
Video Focal Points: 32 x 15
Mathematical Practice Standards
Efficiency and Flexibility
Logico-Mathematical Knowledge
Will It Always Work?
12 x 25
45 x 16
24 x 35
Multiplication String
2 x 280
4 x 140
8 x 70
16 x 35
Consider . . .
What ideas related to teaching and
learning would you want your
teachers to notice after watching this
clip?
Number Talk Rehearsal
18 x 12 19 x 32
36 x 25 225 x 16
15 x 24 45 x 24
Multiplication
Division
9
7 7
?
? 63
Division Number Talk
Division String
16 ÷ 8
80 ÷ 8
400 ÷ 8
496 ÷ 8
Division String
600 ÷ 8
300 ÷ 4
150 ÷ 2
Role of Mental Math
Provides opportunities to
Consider place value
Build upon number relationships
Focus on magnitude of number
Think about reasonableness of
answer
Common Core Content Standards
Operations and Algebraic Thinking
Number and Operations in Base Ten
Use strategies based upon place value and the properties of operations
Fluency with Fractional Reasoning
Critical foundation for determining
success in higher mathematics
Siegler, et al, 2012
National Math Panel, 2008
Conventional Methods
Focus on memorization of procedures but
without achieving depth of understanding
National Research Council, 2001
Mueller, Yankelewitz, & Maher, 2010
1982 NAEP
Estimate the answer to
a) 1
b) 2
c) 19
d) 21
12 7.
13 8
1982 NAEP
Estimate the answer to
a) 1 7%
b) 2 24%
c) 19 28%
d) 21 27%
e) DK 14%
12 7.
13 8
NAEP - 2003
How many pieces, each 1/8 of a yard
long, can be made from a piece of
string 3/4 of a yard long?
55% of eighth-graders could correctly
solve this word problem.
NAEP - 2005
Only 65% of eighth-graders in 1996,
and 73% in 2005, could correctly
shade in 1/3 of a rectangle.
Multiple Identities
Fractions can sometimes represent:
a ratio
a proportion
a continuous quantity
a discrete quantity
Common Misconceptions
Partitioning
Whole number reasoning: 1/2, 1/3, 1/4
Density: 7/8 and 8/9
Defining the Whole
Fraction Number Talk
Strategies for Comparing Fractions
Benchmarks
Unit Fractions
Distance from the whole
Compare numerators
Compare denominators
Common Denominator
Comparing and Ordering Fractions
1/2 3/8 8/9 2/5
-2 0 2 -1 1
Fraction Number Talk
Using Relationships
for
Computation
Can You See?
Individual Reflection
Consider your current schools and
teachers. What philosophical and
instructional shifts are needed to focus on
student reasoning and the development of
the Standards for Mathematical Practice?
Mathematical Practices
Make sense of problems and persevere
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Reflecting and Planning
Where will you begin with Number Talks?
How will you help build a safe learning
environment?
What steps will help your teachers make
Number Talks a regular routine? Where
will it fit in their overall math lesson?
What barriers might you encounter with
teachers? Students? Administrators?
The best part of a teacher’s day
A five to fifteen minute classroom conversation
around purposefully crafted computation problems that
are solved mentally
Dr. Sherry Parrish
The University of Alabama at
Birmingham