Chapter 11: Developing Whole-Number Place Value Concepts
Pre-Base-Ten Concepts
children tend to count by ones
many need to use an object or fingers to keep track
children don’t easily/quickly develop meaning to groups of ten
easy to attach words to materials & groups without knowing what they represent
Basic Ideas of Place Value
place value understanding requires new & difficult to construct concepts of grouping with
procedural knowledge of how groups are recorded in place values, how numbers are written & how
they are spoken
children who understand place value understanding groupings ie/ will know that 5 groups of 10
and 1 group of 3 is the same as 1 group of 53
children count in 3 different ways
o counting by ones begin with this method
o counting by groups and singles ie/ there are one, two, three, four, five groups of ten and
one, two, three singles; doesn’t directly say how many there are
o counting by tens and ones ie/ ten, twenty, thirty, fourty, fifty, fifty one, fifty two, fifty
three
objective: help children integrate grouping by tens concept with what they already know about
numbers from counting by ones
can’t tell them it will be the same, they must construct it themselves
way we say numbers is connected with groupings by ten concept
argued base-ten language (5 tens and 3) should be used throughout grade 2
way we write numbers should be coordinated with grouping scheme
Models for Place Value
children must construct the concept & impose it on the model
base-ten models should be proportional one to one ratio
o groupable models groups of ten can be made from singles; ie/ counters & cups;
interlocking cubes; bundles of sticks
o pregrouped/trading models groups that can’t be taken apart; efficient to model large
numbers; children may not understand what they are doing with them; ie/ strips & squares;
base-ten blocks; little ten-frame cards
no model guarantees children understand
non-proportional models used with children who already understand base-ten; use money to
represent $4.57
Developing Base-Ten Concepts
get students to count in groups other than tens “how could we count our shoes in some way that
would be easier than counting by ones?”
have students estimate groups of tens and ones
hard for children to understand that one individual objects is the same as one, singular ten
must

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