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Building Strategies for Whole-Number Comutation (DEVELOPMENT OF INVENTED…
Building Strategies for Whole-Number Comutation
A MOVE TO COMPUTATIONAL FLUENCY
addition and subtraction strategies that build on decomposing and composing numbers
Classrooms are doing number talks to let children solve problems and discuss how they did it.
CONNECTING ADDITION AND SUBTRACTION TO PLACE VALUE
Problems involving addition and subtraction is a good context for learning place value
THREE TYPES OF COMPUTATIONAL STRATEGIES
Direct modeling
Counting by ones
Use of Base-ten models
Invented strategies
Supported by written recordings
Mental methods when appropriat
children develop number sense
fewer errors
Standard Algorithms
Require guided development
use base-ten materials to model the steps
prove the algorithm produces the correct answer
DEVELOPMENT OF INVENTED STRATEGIES
Creating a supportive environment
have other students discuss if they think the answer is correct or not, before you say the answer
encourage student - student interactions and discussions
Models to support invented strategies
Split strategy
Shortcut strategy
numberlines
DEVELOPMENT OF INVENTED STRATEGIES FOR ADDITION
(+ -) single digits
extend basic facts to ten structures
Adding two digit numbers
years of models, drawings, and manipulatives
Subtraction as "think addition"
"how much do i add to
_
to get ___"
Take-away subtraction
What textbooks define subtraction as
Extensions and challenges
going higher then 100 (3 digit numbers
Crossing ten (or more)
challenges students
STANDARD ALGORITHMS FOR ADDITION AND SUBTRACTION
Standard Algorithm for Addition
Begin with models only
Place-value mats and Base-Ten Models
Develop the Written Record
Addition and Subtraction Recording Sheets
Standard algorithm for Subtracion
Begin with Models Only
Start by teaching as a "Take - away" situation.
Anticipate difficulties with zeros
regrouping across zero
Develop the written record
IINTRODUCING COMPUTATIONAL ESTIMATION
understanding
Measurement estimation: the approximate measurement
Quatity estimation: approximating the number of items
Computational estimation:
Suggestions to teach Computational Estimation
Use real examples
Use estimation language: EX about, close, just about, a little more than and between
Use context: Role play EX would a game cost 5 dollars or 50 dollars?
Accept a range of Estimates, offer a range as an option
Focus on flexible methods, not answers
Computational Estimation Strategies
Front-End Methods
when additiion or subtraction as the smae number of digits. after adding or subtracting the front digit just need to adjust the last digits
Rounding Methods
Round to same place value, or round one of the numbers before solving the problem
Compatible Numbers
Look for two or three compatible numbers that can be grouped to equal the same bench mark value
COMMON MISCONCEPTIONS WITH WHOLE-NUMBER COMPUTATION
mainly from students use of standard algorithms not invented strategies
EXAMPLES: -