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Building Number Sense in 4
Year Old Kindergarten
“Concepts embedded in number sense may be as important to early math
learning as concepts of phonemic awareness”- Gerslen and Chard 1999
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Activity: Stranger in the Woods
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Activity: Stranger in the Woods
Problem: Five animals investigated the stranger
in the woods. Which animals investigated the
stranger in the woods?
•How many visited the snowman in our
problem?
•How could you show the animals to share
your thinking with others?
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Teacher Reflections….
Who solved the problem accurately? Does the student understand the problem, does the student understand “five”?
What strategies did the students use- how do the examples compare and contrast?
If selecting a few pieces of student work to share with the whole class, what would you choose?
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The Components of Number Sense
Quantity- value
Magnitude- relative size
Numeration- names and naming systems that
are used in the spoken/written language for
numbers
Different forms of number
Equality- being quantitatively the same
Language- what we use to describe number
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What number is this?
3
What mathematical connections are being made that develops number sense in
your students?
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learn to decode words
learn to attack words
Learn that words never are the things they
describe – build background knowledge and
supplied context of the word
C-A-T is not a cat
? ?
?
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We must consider if we have worked to develop an understanding of
the concrete concept that this abstract orthographic symbol (3)
represents. We want to show a true representation of arbitrary
quantity.
Not „three”
Not the quantity
Not
Are we neglecting to teach the “threeness” of three?
3
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Point to remember….
Think about math symbols in the same way
as we think about letter symbols and words:
Helping children “break the code” with
numbers allows them to understand how
different forms of the number can come
together
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The Components of Number Sense
Quantity- value
Magnitude- relative size
Numeration- names and naming systems that
are used in the spoken/written language for
numbers
Different forms of that number
Equality- being quantitatively the same
Language- describe
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Counting and Cardinality
Several progressions originate in knowing
number names and the count sequence.
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Pre-Counting
The key focus in pre-counting is an understanding of
the concepts more, less and the same and an
appreciation of how these are related.
Children at this stage develop these concepts by
comparison and no counting is involved.
These concepts lay the foundation for children to
later develop an understanding of the many ways that
numbers are related to each other; for example five is
two more than three, and one less than six.
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From saying the counting words to counting
out objects- building 1-to-1 correspondence
Number sense begins with early counting to
telling how many in one group of objects.
Students usually know or can learn to say the
counting words up to a given number before
they can use these numbers to count objects
or to tell the number of objects.
1,2,3
To count a group of objects, they pair
each word said with one object.K.CC.4a Count to 100 by ones K.CC.1
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Before we can break the code at the symbolic level (3), we must first ascertain that students “see” number in
a way that will construct their understanding of compositions and decomposition of numbers.
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Playdough Stamping
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One-to-One Counting
Two skills are needed:
ability to say the standard list of counting
words in order
ability to match each spoken number with one
and only one object
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Counting objects arranged in a line is easiest;
- rectangular arrays (they need to ensure they
reach every row or column and do not repeat
rows or columns);
-circles (they need to stop just before the object
they started with); and
-scattered configurations (they need to make a
single path through all of the objects).K.CC.5
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Counting Sets
develops children‟s understanding of
cardinality.
This means that children understand when
you count the items in a set, the last number
counted tells the size of that set. They also
know that the number in a set will remain
constant as long as no items are added to the
set, or taken from the set.
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Remember:
Only the counting sequence is a rote procedure.
The meaning attached to counting is key
conceptual idea on which all other number
concepts are developed.
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Activities
Make Sets of More/Less/Same Provide students with cards with sets of 4-12 objects, a set of small
counters, and some word cards labeled More, Less, and Same. Next
to each card have students make three collections of counters: a set
that is more, one that is less, and one that is the same. The
appropriate labels then can be placed on the sets.
Have them show (Justify) how they know there are more in one group than
another.
Questions:
How do you know five is more than four?
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Video Clip- Pre Kindergarten Block
Play
http://youtu.be/gsDY6qftzQk http://youtu.be/gsDY6qftzQk
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Meaning Attached to Counting
Van de Walle makes it clear that an understanding of cardinality and the connection to counting is not a simple matter for 4 year olds
Child learn how to count before they understand that the last count word indicates the amount or set or the cardinality of the set. Cardinality Principle
VandeWalle states by age 4.5 students have/should made this connection.
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How many deer
are there?
1, 2, 3, 4, 5
Are there 5 deer?
5 because I
counted them! Student can use
counting to find a
matching set.
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Fosnot and Dolk discuss a class of 4 year
olds in which children who knew there were
17 children in the class however they were
unsure how many milk cartons they should
get so that each could have one.
To develop their understanding of counting,
engage children in any game or activity that
involves counts and comparisons.
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Games
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Activity: Counting Blocks
http://illuminations.nctm.org/ActivityDetail.asp
x?ID=27
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Relationships Among Numbers 1- 10
Once children acquire a concept of cardinality
and can meaningfully use their counting
skills, little is to be gained from counting
activities.
More relationships must be created for
children to develop number sense, a flexible
concept of number not completely tied to
counting.
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Subitizing- instantly seeing how many
Students come to quickly recognize the cardinalities of small groups without having to count the objects; this is called perceptual subitizing.
This develops into conceptual subitizing— recognizing that a collection of objects is composed of two collections and quickly combining their cardinalities to find the cardinality of the collection
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We read 7 in stages; Stage 1
Working on correspondence and counting skills- one by one
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Stage 2
Students will need to be presented small numbers that they can subitize and begin to see quickly.
Once students subitize up to 4-5 they develop the ability to combine numbers into larger numbers
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Stage 3
3+4=7 7=3+4
5+2
3+3+1
Student has developed number sense
through deeper understanding of quantity,
number composition, different forms of a
number and equality.
3+4=34 8-5=8
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Activities
Learning Patterns
Provide each student with about ten counters and a whiteboard as a mat. Hold up a “dot plate” for about 3 seconds. Say “Make the pattern/draw the pattern you saw using the counters or on the whiteboard. Spend time discussing the configuration of the pattern and how many dots. Do this with a few new patterns each day.
Questions:
How many dots did you see?
How did you see them?
What is a different way to see the total number of dots?
http://teachmath.openschoolnetwork.ca/documents/dotplatepatternsVDW.pdf
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Activities
Flash Cards
Show a student a flashcard with, for example, 7
things in groupings of 5 and 2.
Question:
How many things are there?
What helped you see how many there are?
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Activities
Dice combinations
Organize students into pairs. Give each pair two
dice. Have students take turns to roll the dice
and then say how many dots just by looking.
Ask: How many dots are on the first die? How
many dots on the second die? How many
dots all together?
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3 Some children develop the skill of “number
calling”- without understanding
Subitizing is a fun early step in ensuring that
our students are not “number calling” but
understanding what is underneath the
numeral.
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Think about 5
Teach quantity
Teach different forms of the number
Teach equality
Teach numeration
What is key? Make connections between
these components
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Activity: Stranger in the Woods
Problem: Five animals investigated the stranger
in the woods. Which animals investigated the
stranger in the woods?
•Which animals visited the snowman?
•How many visited the snowman in our
problem?
•How could you show the animals to share
your thinking with others?