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Number Sense

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Number Sense

Developed by Carrie Ann Floyd

Plainfield School District

During this workshop we will:

- Review the revised Preschool Math Standards that relate to number sense.
- Define number sense and its importance as a building block for all future mathematical learning.
- Review teaching strategies for number sense.

Write your favorite number from 1-20 that has personal significance to you on the post it.

For example: 4 - I have four children, 2 - I have two golden retrievers.

Mingle with each other, sharing your number and why you chose it.

Then, form groups based on the number you have.

After getting into your groups line up in order from

1-20.

- Number recognition: “We both have the number 3.”
- Writing numbers: “I wrote down the number 3.”
- Saying counting words in order: Getting into the order 1-10.
- Understanding that written numbers are symbols for number quantities.
- Understanding the relationship between numbers and quantities.
These skills all relate to number sense.

Number sense is defined as an intuitive feel for numbers and a common sense approach to using them. It is a comfort with what numbers represent, coming from investigating their characteristics and using them in diverse situations. Number sense is an attribute of all successful users of mathematics.

Preschoolers are beginning to develop number sense when they construct a notion of oneness, twoness, and so on… Young children also have a emerging concept of number when they see the relationship of one number to another.

Number Sense

*HighScopePreschool Mathematics Curriculum, 2012, p. 31”

Standard 4.1: Children begin to demonstrate an understanding of number and counting.

4.1.1 Count to 20 by ones with minimal prompting.

4.1.2 Recognize and name one digit written numbers up to ten with minimal prompting.

4.1.3 Know that written numbers are symbols for number quantities and, with support, begin to write numbers from 0 to 10.

4.1.4 Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”).

- Encourage and support individual attempts to learn to count to 20 or higher.
- Include and refer by name to written numbers in the classroom environment during daily routines and in the context of large and small group experiences.
- Intentionally refer to the symbol and number name when discussing numbers (quantities) of objects.
- Make materials and books that promote exploration of number quantities.

- Encourage children to compare numbers frequently through questions (e.g., “Are there more people riding in the bus or in the airplane?”) and graphing (e.g., favorite colors, pets).
- Provide manipulative and materials (e.g., print and digital material, sand molds, tactile numeral cards, puzzles, counting books, hand-held devices such as tablets, interactive whiteboards) and activities (e.g., tracing numbers in sand, forming numbers with clay, recording data) that feature number names and number quantities.
- Provide a wide variety of writing materials for children to informally explore writing numbers along with meaningful contexts for children to write numbers on charts and graphs.

1. Cardinality

Recognizing that things come in quantities begins around 2 years old.

Children grasp the association between numbers and quantities by connecting concrete objects with more abstract number words and symbols. (The idea of “oneness” and “twoness.”)

Preschoolers learn cardinal number words by rote and can count up to 20 by kindergarten.

At first they often say them in any order. They may omit some numbers and repeat others.

Preschoolers will become familiar with numerical order if exposed to numbers in counting songs, number books and natural opportunities.

2.Recognizing Number Symbols

Learning to read numbers symbols depends on how often children are exposed to them.

Children need adults to explicitly identify and name numerals when they are in the environment.

3. Writing Numerals

Writing numerals is a more difficult task then reading them.

Children begin with the numbers that are the easies to draw or write. (1,3,4,7) and then progress to more complex ones (2,5,6,8,9).

Perception and motor development may limit their ability.

Children may reverse numbers such as 2,3, 5.

When adults model standard numeral writing children will learn how to write them on their own. There is no need to correct such errors.

Scaffolding is a term developed by the theorist Lev Vygotsy.

It means to provide children with support on their current level of development while occasionally offering a gentle extension to the next level.

As you carry out these activities reflect on your experiences with children and the developmental range of these skills seen in preschoolers.

How might children, at varying levels of development, respond to the content and the materials?

* HighScopeScaffolding Group Times For Early Learners

Standard 4.1.1 Count to 20 by ones with minimal prompting

“Counting Song” Activity

At your table, you will be role playing this lesson as children while one or

two people will be the teacher.

After a few minutes, review the lesson plan that shows the basic three developmental levels for this activity: Earlier, Middle, and Later.

As a group come up with ideas for supporting each developmental level, and chart it on paper.

*HighScopeScaffolding Small Group Times for Early Learners

Standard 4.1.1 Count to 20 by ones with minimal prompting

Children sing a counting song to a familiar tune while tapping a body part a corresponding number of times during large group music and movement time.

*HighScopeNumbers Plus

“Counting Song ” Video Clip

Children may…

Earlier

Sing random number words or pat but do not do both at the same time

Middle

Recognize when numbers 1-5 are not said in the correct order

Sing numbers 1-5 in the correct order

Adults can… use these strategies

Encourage children to sing the number words with them

Slow down the singing and patting to help children hear

Count correctly and incorrectly, each time asking Is this the right order

Make a mistake in counting, (skip and number and see if children spot the error)

Children may…

Later

Say which numbers come next in sequence

Fill in a missed number

Say a number sequence up to 10

Adults can… use these strategies

While singing, stop counting and ask, What number comes next?

Extend the song up to 20

Ask a child to suggest a number to count to and to lead the next round using the next round

Count backwards, beginning with small numbers (e.g., 3, 2, 1, )

Math Standard 4.1.2 Recognize and name

one digit numbers up to ten with minimal prompting

“Numerals in Newspapers” Activity

At your table, you will be role playing the lesson as children while one or two people will be the teacher.

After a few minutes, review the lesson plan that shows the basic three developmental levels for this activity: Earlier, Middle, and Later.

As a group come up ideas for supporting each developmental level, and chart it

on paper.

* HighScopeScaffolding Small Group Times

Math Standard 4.1.2 Recognize and name one digit numbers up to ten with minimal prompting

Children search for large numbers in magazines and cut them out to make number collections during small group time.

*HighScope50 Small Group Times to Scaffold Early Learning

“Numerals in Newspapers” Video Clip

Children may…

Earlier

Point to a letter and call it a number

Look at or point to numerals and identify them as numerals

e.g.,“Here is a number.”

Middle

Identity numerals but make errors

Search for and finds a specific numeral

Relate numerals to familiar objects and events e.g., “That’s a four, I’m four years old.”

Adults can… use these strategies

Point out letters and numbers e.g.,

“This is the letter in your name, this is a number it says how many there are of something.”

Point to a number in the room and the same number in the magazine

Supply numeral names but not correct children

Cut out a specific numeral and ask children to find more of that numeral

Ask children to find specific numerals

Ask children to find numerals related to objects and events

Children may…

Later

Line up numerals in order

(example: I found a 1,2, and 3. I need a 4.)

Identify missing numerals

Say by how much one numeral is more or less than another (example: I found a 3. It’s one more than a 2.)

Adults can… use these strategies

Cut out numerals 0-9 and ask,

Can you help me glue mine in order?

Ask: What number comes after or before...?

Line up numerals with a space for a missing numeral and ask what else goes there (example:1,2,4,5, What number is missing?)

Ask many how many one numeral is bigger or smaller than another

- Standard 4.1.3 Know that written numbers are symbols for number quantities and, with support, begin to write numbers from 0 to 10.

- Standard 4.1.3 Know that written numbers are symbols for number quantities and, with support, begin to write numbers from 0 to 10.

Children may…

Earlier

Write squiggles to represent numerals

Middle

Write numeral like forms

(example: 1 and 0 backward 3)

Later

Write 3 or more recognizable numerals

Adults can… use these strategies

Acknowledge children’s interest in writing numerals

Provide materials for children to make numerals (example: play dough, sand crayons)

Ask children to read the numerals they write.

Write numerals during play

(example: Write a 2 and say, “I want 2 pieces of pizza”)

Encourage writing numerals in play.

Provide opportunities to write numerals. (example: As part of messages on message board)

- 4.1.4 Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”).
- (a)Accurately count quantities of objects up to 10, using one-to one-correspondence, and accurately count as many as 5 objects in a scattered configuration.
- (b)Arrange and count different kinds of objects to demonstrate understanding of the consistency of quantities (i.e., “5” is constant, whether it is a group of 5 people, 5 blocks or 5 pencils).
- (c)Instantly recognize, without counting, small quantities of up to 3 or 4 objects (i.e., subitize).

- 4.1.4 Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”).
- (a)Accurately count quantities of objects up to 10, using one-to one-correspondence, and accurately count as many as 5 objects in a scattered configuration.

- 4.1.4 Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”).
- (b)Arrange and count different kinds of objects to demonstrate understanding of the consistency of quantities (i.e., “5” is constant, whether it is a group of 5 people, 5 blocks or 5 pencils).

- Arranging and Counting Quantities
http://earlymath.erikson.edu/number-arrangements/

- 4.1.4 Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”).
- (c)Instantly recognize, without counting, small quantities of up to 3 or 4 objects (i.e., subitize).

http://earlymath.erikson.edu/matching-quantity-with-child-3/

Children may…

Earlier

Count objects by saying numbers in random order. (example: “2,8,3”)

Recount from beginning when asked “how many objects”

Use general quantity words (example: lots,wholelot, many) rather than words that compare quantity

Middle

Count up to 10 objects, may double count or skip numbers

Say a different number than the last one counted when saying “how many”

Count or eyeball two sets of objects and say which one has more, fewer, less

Adults can… use these strategies

Give children opportunities to count objects and model counting objects slowly

Acknowledge when children recount from the beginning

Introduce quantity words to compare (example: more, fewer less, same)

Recount with children by touching or moving objects while counting

Label the last number as how many (example: “You counted six. There are six bears.”)

Ask children how many more objects there are when they compare two sets of objects

Adults can… use these strategies

Acknowledge when children count objects correctly

Provide collections of more than 10 items for use in play

Ask genuine “how many” questions

Provide larger sets of objects to compare how many more or fewer a set has or if they are the same

Encourage children to explain how they figured out how many more or less when comparing sets

Children may…

Later

Count objects accurately using one to one correspondence

Say the last numbers of objects tells “how many”

Count or eye ball two sets of objects and say by how many one is more or fewer less than the other

* HighScope Numbers Plus Curriculum

- With your table, brain storm authentic opportunities for children to develop number sense throughout the daily routine.
- Write your ideas on index cards- include the activity and the part of the day.
- Post each index card by the sign that corresponds to your activity’s when, during the day, your activity would take place.

Standard 4.1: Children begin to demonstrate an understanding of number and counting.

4.1.1 Count to 20 by ones with minimal prompting.

4.1.2 Recognize and name one digit written numbers up to ten with minimal prompting.

4.1.3 Know that written numbers are symbols for number quantities and, with support, begin to write numbers from 0 to 10.

4.1.4 Understand the relationship between numbers and quantities (i.e., the last word stated when counting tells “how many”).

NJ DOE Preschool Math Standards

http://www.nj.gov/education/ece/guide/standards/math/master/standards.pdf

Number Sense Educational Leadership Article

http://www.ascd.org/ASCD/pdf/journals/ed_lead/el200402_griffin.pdf

Young Children and Math

http://membership.highscope.org/app/issues/54.pdf

NAEYC Math Position Statement

http://www.naeyc.org/store/files/store/TOC/167.pdf

Early Math the Next New Thing Article

http://highscope.org/file/NewsandInformation/ReSourceReprints/EarlyMath.pdf

50 Small Group Times to Scaffold Early Learning High/Scope Press

http://secure.highscope.org/productcart/pc/viewPrd.asp?idproduct=1026

Numbers Plus Math Curriculum High Scope Press

http://secure.highscope.org/productcart/pc/viewPrd.asp?idproduct=1066

Teaching Math to Young Children NCEE 2014-4005 U.S. Department of Education

http://ies.ed.gov/ncee/wwc/practiceguide.aspx?sid=18