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Map of Development - Counting (Models (Stable order (counting is always…
Map of Development - Counting
Scope of Development
verbally counts to 10
verbally counts to 20; knows that the last number states how many in all; tells what number comes next in order by counting (from 1-10
uses number names while counting to 100; tells what number comes before and after a specified number up to 20
uses skip counting by 2s, 5s, 10s; begins counting forward at any number between 1 and 120; counts backwards from 20
Big Ideas
Meaningful counting integrates different aspects of number and sets, such as sequence, order, one-to-one
correspondence, ordinality, and cardinality.
Numbers are abstract concepts.
A base-ten positional number system is an efficient way to represent numbers.
Models
Stable order
counting is always consistent - 1, 2, 3, 4, 5, 6 instead of 1, 2, 3, 4, 5, 9
Order Irrelevance
counting can begin with any object in a set and the total will still be the same
One to one correspondence
each object being counted must be given only one count (physically moving objects out of the way as students count them)
Conservation
the count for a group of objects stays the same no matter whether the objects are spread apart or close together
Abstraction
a quantity can be represented by different things
Cardinality
the last count of a group of objects represents the total number of objects in a group
Movement is magnitude
as one moves up the counting sequence, the quantity increases by 1, and as one moves down the counting sequence, the quantity decreases by 1
Unitizing
objects are grouped into tens once the count exceeds 9
Strategies
using one-to-one correspondence with counters on the light table to represent each student in their class photo
grouping objects with similarities, displaying them on wood blocks, and counting them using one-to-one correspondence
skip counting by 5s
co-creating number posters
counting the number of beads on the key rings and use one-to-one correspondence find the lock with the matching number
building and counting the blocks used: "Can you make something that is taller than 10 blocks?"
