Developing Whole-Number Place-Value Concepts
Role
of Counting
1.
Counting by ones.
2.
Counting by groups
and singles.
3.
Counting by tens
and ones.
Developing
Base-Ten Concepts
·
Grouping
Activities
·
The Strangeness of
Ones, Tens, & Hundreds
·
Grouping Tens to
Make 100
·
Equivalent
Representations
Oral
and Written Names for Numbers
·
Two-Digit Number
Names
·
Three-Digit Number
Names
·
Written Symbols
·
Assessing
Place-Value Concepts
Patterns
and Relationships with Multidigit Numbers
·
The Hundreds Chart
·
Relationship with
Landmark Numbers
·
Connecting Place
Value to Addition and Subtraction
·
Connections to
Real-World Ideas
Big
Ideas:
1.
Sets of 10 (and
tens of tens) can be perceived as single entities or units. For example, three
sets of 10 and two singles is a base-ten method of describing 32 single
objects. This is the major principle of base-ten numerations.
2.
The positon of
digits in numbers determine what they represent and which size group they
count. This is the major organization for developing number sense.
3.
There are patterns
to the way that numbers are formed. For example, each decade has a symbolic
pattern reflective of the 0-to-9 sequence
4.
The groupings of ones,
tens, and hundreds can be taken apart in different but equivalent ways. For
example, beyond the typical way to decompose 256 of 2 hundreds, 5 tens, and 6
ones, if can be represented as 1 hundred, 14 tens, and 16 ones but also 250 and
6. Decomposing and composing multidigit numbers in flexible ways is a necessary
foundation for computational estimation and exact computation.
5.
“Really big”
numbers are best understood in terms of familiar real-world references. I tis
difficult to conceptualize quantities as large as 1000 or more. However, the
number of people who will fill the local sport arena is, for example, a
meaningful referent for those who have experienced that crowd.
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