Place Value - Development for age 5 - 9+ Concepts, Activities, Assessment, and Evaluation

Place value concepts build upon concepts described for prenumber sense ( age 0 - 6) counting, and number sense ( age 6 - age 8).

Ten is a big number

No place value understanding. Children see ten as the same kind of number as 1,2,3, ... 9, only bigger. Can count to ten and say they have ten fingers or ten toes. Most likely do not conserve or have cardinality.

Grouping by ten

Children can use one-to-one relationships and systematically count objects accurately to at least twenty. They can also skip count by tens and understand skip counting as repeated addition. Not multiples of ten. There is no place value understanding. Students understand numbers can be grouped with different combinations and ten is just one of several groupings. Students are easily confused by the one in teens and two in twenties as one and two rather than ten or twenty.

When asked they will represent numbers greater than ten with a one-to-one relationship For example: showing how many students in their class by drawing designs so one design represents one student. Not groups of tens and ones. They are working toward unitizing (counting groups of objects in equivalent groups using a one-to-one strategy; like counting five groups of ten by 1, 2, 3, 4, 5 and recognizing it as five equal groups of ten or 50) but have not achieved unitizing.

Place value models should be actual objects put into groups of ten.

Students can inventory books in the classroom by creating stacks of ten books and can recognize the groups of ten as units as well as a group of ten, but not simultaneously. Total books as groups of ten and extras.

Pre place value

Place value models need to be proportional for children.

At his level students understand Number value - cardinality to 100, can order and sequence numbers to 100, know zero is the absence of objects, understand hierarchical use of numbers in a counting sequence, and more than one addition fact relate to a number's value (but not hierarchical inclusion of addtion related to number sense), and those facts can be used to compose and decompose numbers.

While students can group objects by tens, they consider it as an additive process the same as putting objects into other groupings (pairs, fives, eight, four...) together.

Solves addition and subtraction problems mentally by decomposing into groups of tens and ones, composing the tens, then the ones, and adding the tens and ones.

May or may not know how zero is used to mark positions with no value.

Unitize

Students can count each group as one unit (1 of 10, 2 of 10, 3 of 10 ...) and realize that each unit has and must have an equivalent number of objects in it.

Students know that five groups of ten is fifty. They don't need to count by tens five times to know five groups is 50.

Students understand that groups can be regrouped as other equivalent groups (One group of ten is also two groups of five, and other combinations to make ten.).

Place value relationships

Before students develop place value relationships they must unitize and usually have number value to at least 1000. Can round numbers to multiples of ten and can count forward and backward by tens and hundreds starting with any number. Knows multiples of ten including 10 X 10, and maybe 10 X 100.

Students who understand place value relationships know:

Place value and decimals

Unitizing place values of decimal numbers less than one: tenths, hundredths, thousandths ...

Place value as exponential

 

Dr. Robert Sweetland's notes
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