Number Sense
Developed by Carrie Ann Floyd
Plainfield School District
Objectives:
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.
Opening Activity
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.
What math skills did you use?
 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
*HighScope Preschool Mathematics Curriculum, 2012, p. 31”
New Jersey’s Preschool Math Standards and
Number Sense
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”).
Preschool Teaching Practices to Promote
Number Sense
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.
Preschool Teaching Practices to Promote Number
Sense (cont.)
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.
Thinking About Number Sense
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.
Thinking About Number Sense (cont.)
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.
Thinking About Number Sense (cont.)
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.
Recommended Materials for Number Sense
Books About Numbers
Puzzles and Manipulatives
Materials for Making and Writing Numerals
Using the Daily Routine
Taking A Closer Look
at the Parts of Standard 4.1
Scaffolding Number Sense
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?
* HighScope Scaffolding Group Times For Early Learners
Counting to Twenty by Ones
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.
*HighScope Scaffolding Small Group Times for Early Learners
“Counting Song”
Large Group Lesson
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.
*HighScope Numbers Plus
“Counting Song ” Video Clip
4.1.1 Count to 20 by Ones with Minimal Prompting
Developmental Range:
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)
4.1.1 Count to 20 by Ones with Minimal Prompting
Developmental Range: (cont.)
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, )
Standard 4.1.2 Recognizing and Naming Numbers
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.
* HighScope Scaffolding Small Group Times
“Numerals In Newspapers”
Small Group Lesson
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.
*HighScope 50 Small Group Times to Scaffold Early Learning
“Numerals in Newspapers” Video Clip
4.1.2. Recognize and Name One Digit Numbers
Developmental Range:
Children may…
Adults can… use these strategies
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.”
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
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.”
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
4.1.2. Recognize and Name One Digit Numbers
Developmental Range (cont.)
Children may…
Adults can… use these strategies
Later
Line up numerals in order
(example: I found a 1,2, and 3. I need
a 4.)
Cut out numerals 0-9 and ask,
Can you help me glue mine in order?
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.)
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 Writing Numbers from 0-10
 Standard 4.1.3 Know that written numbers are symbols for number
quantities and, with support, begin to write numbers from 0 to 10.
Standard 4.1.3 Written Numbers and
Number Quantities (cont.)
 Standard 4.1.3 Know that written numbers are symbols for
number quantities and, with support, begin to write numbers from 0
to 10.
4.1.3 . Writing Numbers from 0-10
Developmental Range:
Adults can… use these strategies
Children may…
Earlier
Acknowledge children’s interest in writing
Write squiggles to represent numerals
numerals
Provide materials for children to make numerals
(example: play dough, sand crayons)
Middle
Ask children to read the numerals they write.
Write numeral like forms
Write numerals during play
(example: 1 and 0 backward 3)
(example: Write a 2 and say, “I want 2 pieces of
pizza”)
Later
Write 3 or more recognizable
numerals
Encourage writing numerals in play.
Provide opportunities to write numerals.
(example: As part of messages on message board)
Standard 4.1.4: Numbers and Quantities
 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).
Standard 4.1.4(a)
Accurately Counting Quantities
 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.
Standard 4.1.4(b)
Consistency of Quantities
 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).
Standard 4.1.4(b)
Consistency of Quantities (cont.)
 Arranging and Counting Quantities
http://earlymath.erikson.edu/number-arrangements/
Standard 4.1.4(c)
Subitizing
 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).
Standard 4.1.4(c)
Subitizing (cont.)
http://earlymath.erikson.edu/matching-quantity-with-child-3/
4.1.4. Understand the relationship between numbers and quantities
Developmental Range
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,whole lot, 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
4.1.4. Understand the relationship between numbers and quantities
Developmental Range
Children may…
Adults can… use these strategies
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
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
Implementation Plan
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.
New Jersey’s Preschool Math Standards and
Number Sense
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”).
Resources
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