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

Activity: Stranger in the Woods

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?

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?

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

What number is this?

3

What mathematical connections are being made that develops number sense in

your students?

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

? ?

?

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

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

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

Counting and Cardinality

Several progressions originate in knowing

number names and the count sequence.

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.

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

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.

Playdough Stamping

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

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

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.

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.

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?

Video Clip- Pre Kindergarten Block

Play

http://youtu.be/gsDY6qftzQk http://youtu.be/gsDY6qftzQk

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.

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.

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.

Games

Activity: Counting Blocks

http://illuminations.nctm.org/ActivityDetail.asp

x?ID=27

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.

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

We read 7 in stages; Stage 1

Working on correspondence and counting skills- one by one

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

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

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

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?

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?

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.

Think about 5

Teach quantity

Teach different forms of the number

Teach equality

Teach numeration

What is key? Make connections between

these components

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?