Transcript Number Talks

Computational Fluency
What is
Computational Fluency?
Adding It Up
The National Academies Press
“Procedural Fluency- -skill in carrying
out procedures flexibly, accurately,
efficiently, and appropriately.”
Priorities in Mathematics
Grade
K–2
3–5
6
7
8
Priorities in Support of Rich Instruction and Expectations of
Fluency and Conceptual Understanding
Addition and subtraction, measurement using
whole number quantities
Multiplication and division of whole numbers and
fractions
Ratios and proportional reasoning; early
expressions and equations
Ratios and proportional reasoning; arithmetic of
rational numbers
Linear algebra
Key Fluencies
Grade
K
1
Required Fluency
Add/subtract within 5
Add/subtract within 10
Add/subtract within 20
(using mental strategies)
2
(by end of Grade 2, know from memory all sums of two one-digit numbers)
Add/subtract within 100 (pencil and paper)
(using strategies based on place value, properties of operations and/or the relationship between
addition and subtraction)
Multiply/divide within 100
(using strategies such as the relationship between multiplication and division (e.g., knowing that 8
× 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations)
3
(by the end of Grade 3, know from memory all products of two one-digit numbers)
Add/subtract within 1000
(using strategies and algorithms based on place value, properties of operations and/or the
relationship between addition and subtraction)
4
5
Add/subtract within 1,000,000
(using the standard algorithm)
Multi-digit multiplication
(using standard algorithm)
Key Fluencies (6-8)
6
Multi-digit division
(using standards algorithm)
Multi-digit decimal operations
(add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each
operation)
7
Solve px + q = r, p(x + q) = r
8
Solve simple 22 systems by inspection
Fourth Grade
• M.4.OA.4 fluently add and subtract
multi-digit whole numbers using the
standard algorithm.
Developing Fluency
1. Help children develop a strong
understanding of number
relationships within the operations.
2. Develop efficient strategies for fact
retrieval through practice.
3. Then provide drill in the use and
selection of those strategies once
they have been developed.
John A. Van de Walle & LouAnn H. Lovin
From Memory ≠ Memorize
Develop
Meaningful
Understanding
Practice
Fluency
M.2.OA.2 fluently add and subtract within 20 using mental
strategies and by end of Grade 2, know from memory all sums of
two one-digit numbers.
M.3.OA.7 fluently multiply and divide within 100, using
strategies such as the relationship between multiplication and
division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or
properties of operations and by the end of Grade 3, know from
memory all products of two one-digit numbers.
Fifth Grade
• M.5.NBT.5 fluently multiply multi-digit
whole numbers using the standard
algorithm.
Number Talks
http://books.google.com/books?id=p4B9F1u2T4kC&printsec=fro
ntcover&dq=number+talks&hl=en&sa=X&ei=6EPXT_v4Nsbx0
gGsx8CkAw&ved=0CDUQ6AEwAA#v=onepage&q=number%2
0talks&f=false
Number Talks
• Number talks are
short conversations
centered around
purposefully crafted
computation
problems.
Strategies
Addition
Subtraction
Multiplication
Division
Counting All/Counting
On
Adding Up
Repeated Addition or
Skip Counting
Repeated Subtraction or
Sharing/Dealing Out
Doubles/Near-doubles
Removal or counting
Back
Making Landmark or
Friendly Numbers
Partial Quotients
Making Tens
Place Value and
Negative Numbers
Partial Products
Multiplying Up
Making Landmark or
Friendly Numbers
Adjusting One Number
to Create an Easier
Problem
Doubling and Halving
Proportional Reasoning
Breaking Each Number
into Its Place Value
Keeping a Constant
Difference
Breaking Factors into
Smaller Factors
Compensation
Adding Up in Chunks
Key Components
Number Talks
•
•
•
•
•
Classroom environment and community
Classroom discussions
The teacher’s role
The role of mental math
Purposeful computation problems
Classroom Environment
Quiet Thumbs Up
Me Too
Strategy—Quiet Thumbs Up
Me Too!
Number Talks in Action
• Select several problems for the
participants complete as a number
talk.
Create Number Talks
• Create Number Talks for the first week
of school.
• Practice with a partner.
Teaching Basic Facts
What to do---
What NOT to do---
• Ask students to selfmonitor
• Focus on self-improvement
• Drill in short time
segments
• Work on facts over time
• Involve families
• Make drill enjoyable
• Use technology
• Emphasize the importance
of quick recall of facts
•
•
•
•
•
•
Don’t use lengthy timed
tests
Don’t use public
comparisons of mastery
Don’t proceed through all
facts all at once
Don’t move to
memorization to soon
Don’t use facts as a barrier
to good mathematics
Don’t use fact mastery as a
prerequisite for calculator
use