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CHAPTER 11 BUILDING STRATEGIES FOR WHOLE-NUMBER COMPUTATION (DEVELOPMENT…
CHAPTER 11 BUILDING STRATEGIES FOR WHOLE-NUMBER COMPUTATION
TOWARD COMPUTATIONAL FLUENCY GRADES 3-5
Emphisis on multiplication and division
Procedural Fluency:
Teacher create a rewarding flexible environment for solving problems
1) Direct modeling
Manipulatives or drawings, counting
Direct representation of the story problem
ask for written numeric records of how problems solved
2) Invented Strategies
Develop, discuss and use efficient, accurate and generalizable methods to compute
Best way to learn is by listening to peers
Environments for inventing
feel safe and nuturing
avoid identifying the right answer
encourage talking
Promot curiosity
Show samples
Select numbers with care
Contrasts with standard algorithms
Algorithms digit orientated vs stratagies number orientated
Invented are flexible
Benefits of Invented Strategies
Fewer Errors
Less reteaching is required
Students develop number sense
Basis of mental computation and estimation
Flexible
Invention is important process of doing math
Serve well on standardized tests
Mental Computation
invented strategy that is done mentally
Different for everyone
Standard algoritms
Making sense of the procedure as a process
Must be understood
"the right way"
IF YOU USE IT YOU MUST UNDERSTAND IT
DELAY
DEVELOPMENT OF INVITED STRATEGIES IN ADDTION AND SUBTRACTION
Models to support invented strategies
Fluently add and subtract within 100
Empty Number Line
sequential jump strategy
model students thinking
Bar Diagrams
Subtraction comparison situations and part part whole
Short cut strategy
Adding Multidigit Numbers
Subtration as "Think-addition"
Change is unknown
Take-Away Subtraction
STANDARD ALGORITHMS FOR ADDITION AND SUBTRACTION
Digit orientated
INVENTED STRATEGIES FOR MULTIPLICATION
Useful Representaion
Choice of model based on story problem
Students should be shown every model for multi digit
Multipilication by a One- Digit Multiplier
Complete-number strategies
Set of single groups
long columns of the same number and add them up
Partitioning strategies
By decades
Multiplication of Multidigit Numbers
STANDARD ALGORITHMS FOR MULTIPLICATION
Begin with Models
Area Models
Example: Garden Problems
Open Array
Blank Rectangle
Written Record
Partial Products
Lattice Multiplication
Grid method
INVENTED STRATEGIES FOR DIVISION
missing-factor strategies
cluster problems
STANDAD ALGORITHMS FOR DIVISION
Partition or fair share model
Partial quotients using a visual model
Develop the written record
Explicit-trade method
Repeated Sbtraction
Two digit Divisors
COMPUTATIONAL ESTIMATION
Use real examples
estimation language
use a context