Strategies for Whole-Number Computation
Computational Strategies
Direct modeling
–
–Use of base-ten models
Invented strategies
–Using written recordings
–
Traditional algorithms
–
–May influence use of invented strategies
More on Invented Strategies
Compared
to traditional algorithms
–Numbers vs. digits
–Left handed vs. right handed
–
Benefits
–Helps with base ten concepts
–
–Less re-teaching is required
–
–Faster than traditional algorithms
Developing Invented Strategies
Use story problems
Discuss student’s solutions
Choosing numbers
Integrate place value development
Move away from direct modeling
Invented Strategies
Addition and subtraction
–Single digits
–Tens and hundreds
Adding two digit numbers
–Add tens, ones, then combine
–
–Move some to make tens
–
Subtraction
–Counting up
Add
tens to get close, then ones
Add
tens to overshoot, then come back
Add
ones to make a ten, then tens and ones
–Take-away subtraction
Take
tens from the tens, then subtract ones

Take
extra tens, then add back

Traditional Algorithms
Addition
–Begin with models
–Written record
Subtraction
–Begin with models
–Zeros
–Written record
Multiplication
Invented strategies
–Useful representation
–Single digit multiplier
Complete-Number
Strategies

Compensation
Strategies
–Using multiples of 10 and 100
Traditional Algorithms
–Written record
One digits
–
–
Two digits
–
Division
Invented strategies
–Sharing and measurement problems
–
Traditional Algorithms
–Use of models
–Written record

Early Fraction Concepts
Fractional Parts
Sharing
–Story problems

Fraction language
–Number of parts
–
Models
–Area
–Length
–Sets
Fraction Symbols
Fractional-parts counting
Top and bottom numbers
–What is the bottom number?
–What is the top number?
Mixed numbers
–
Parts and whole tasks
–Given the whole and the fraction, find the part
–Given the part and the fraction, find the whole
–Given the whole and the part, find the fraction
Fraction Number Sense
Understanding of zero, one-half, and one
Which is more?
–Focus on concepts
–Conceptual thought patterns for comparisons
More
of the same size parts
Same
number of parts but parts of different sizes
More
and less than one-half or one whole
Distance
from one-half or one whole
–Fractions tell us about relationship between part and whole
Estimation
–
Equivalent-fraction concepts
–
–Use of models