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DOCUMENT RESUME
ED 482 298 PS 031 672
TITLE Missouri Pre-K Mathematics Standards, Teacher's Guide, [and]Parent Handbook: Early Mathematics.
INSTITUTION Missouri State Dept. of Elementary and Secondary Education,Jefferson City.
PUB DATE 2003-09-00NOTE 57p.; For full text of Teacher's Guide:
http://dese.mo.gov/divimprove/fedprog/earlychild/Pre-K%20Standards/mathteacher.pdf. For full text of Parent Guide:http://dese.mo.gov/divimprove/fedprog/earlychild/Pre-K%20Standards/mathparent.pdf.
AVAILABLE FROM Missouri Department of Elementary and Secondary Education,205 Jefferson Street, P.O. Box 480, Jefferson City, MO 65102-0480. Tel: 573-751-4446; Fax: 573-751-1179; Web site:http://dese.mo.gov. For full text of standards:http://dese.mo.gov/divimprove/fedprog/earlychild/ Pre-KStandards/mathstandards.pdf.
PUB TYPE Guides Classroom Teacher (052) Guides Non-Classroom(055)
EDRS PRICE EDRS Price MF01/PC03 Plus Postage.DESCRIPTORS Academic Standards; Developmentally Appropriate Practices;
Educational Objectives; *Mathematics Education; ParentMaterials; Parent Student Relationship; Parents as Teachers;*Preschool Children; *Preschool Education; *State Standards;Student Educational Objectives; Teacher Student Relationship;Teaching Guides
IDENTIFIERS Indicators; Mathematical Thinking; *Missouri
ABSTRACT
This document is comprised of three publications of the earlychildhood section of the Missouri Department of Elementary and SecondaryEducation: (1) prekindergarten mathematics standards; (2) a teacher's guidefor early mathematics; and (3) a parent's handbook for early mathematics. Thestandards, developed by a broad-based group of individuals whose backgroundsrepresent the many facets of the Missouri early childhood community, providebroad descriptions of what most children should know and be able to do by thetime they enter kindergarten and represent a shared set of expectations forpreschoolers in the field of mathematics. The standards publicationdelineates the Missouri prekindergarten guiding principles and presentsprocess standards, indicators of competency development, and examples ofbehaviors children may exhibit in their mathematical development in thefollowing areas: (1) number and operations; (2) geometry and spatial sense;(3) patterns and relationship; (4) measurement; and (5) exploring data. Theteacher's guide explains the standards and offers practical suggestions forcreating engaging, developmentally appropriate learning communities thatfoster each child's mathematical thinking. The guide includes definitions ofthe mathematical concepts used in the standards, suggested teachingstrategies for each standard area, suggestions for involving parents andfamilies, and a 62-item resource list of books, websites, magazines, andother materials. The parent handbook introduces the mathematics standards,defines mathematical terms, provides information on how a child may exhibit
Reproductions supplied by EDRS are the best that can be madefrom the original document.
progress toward a particular standard or goal, and offers suggestions forparental support of mathematical development. The handbook closes with a listof general tips for parents, an 11-item bibliography, and a list of 63 booksfor young children incorporating mathematical concepts. (KB)
Reproductions supplied by EDRS are the best that can be madefrom the original document.
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Missouri Pre-K MathematicsStandards, Teacher's Guide, [and]
Parent Handbook: Early Mathematics.
Missouri Department of Elementary andSecondary Education
Early Childhood Section
BEST COPY AVAILABLE
November 2002
U.S. DEPARTMENT OF EDUCATIONOffice of Educational Research and Improvement
EDUCATIONAL RESOURCES INFORMATIONCENTER (ERIC)
)(This document has been reproduced asreceived from the person or organizationoriginating it.
0 Minor changes have heen made toimprove reproduction quality.
Points of view or opinions stated in thisdocument do not necessarily representofficial OERI position or policy.
1
PERMISSION TO REPRODUCE ANDDISSEMINATE THIS MATERIAL HAS
BEEN GRANTED BY
J,11 11'1/40
TO THE EDUCATIONAL RESOURCESINFORMATION CENTER (ERIC)
1,
MI6
L
_
Missouri Department of Elementary and Secondary Education Early Childhood Section
3 BEST COPY AVAILABLE
s
The standards are broad descriptions of what most children should know and be able to do by the time
they enter kindergarten. They are not a curriculum but are a framework for communicating a shared set
of expectations for preschool children in the field of mathematics.
We realize some children will far exceed these standards; others will not enter kindergarten with the
knowledge and experiences suggested in this document. Just as we recognize that different people bring different
things to our society, we also recognize that variability in children is normal. The standards are not intended to be
used to determine whether a child "is ready" to enter kindergarten. The standards are, however, goals for adults to
use in supporting the mathematical development of preschool children. Available evidence indicates that the
standards are appropriate for most children.
The standards were developed by a broad-based group of individuals whose backgrounds are
representative of many facets of the early childhood community in Missouri. The standards are intended to be
used in a variety of early childhood settings by a variety of people parents, parent educators, child-care
providers, Head Start and public/private school teachers, etc. They are consistent with current research and
recommendations from other state and national initiatives.
It is our hope that the ultimate beneficiaries of this work will be our children, resulting in all children
entering school ready to succeed.
ist\;550uT; PTek6Vicrivn P`Cloc:ptes
1. All children actively seek to comprehend the world in which they live. Given the opportunity to make
choices concerning their activities, they acquire knowledge, skills and the ability to solve problems.
2. Children construct knowledge and values through interactions with peers, parents and other adults and
through active exploration of the physical and social environment.
3. Young children's thinking contains predictable errors.
4. Early learning and areas of development interact and influence each other.
5. Families (parents) are the child's first and most important teachers.
6. Children exhibit individual differences in their development of competencies.
4
Content Component Process Standards
Number and operations Uses number to show quantityUses language to represent number of objectsSolves problems using numberUses numerical representation
Geometry and spatial sense Investigates positions and locationsExplores shapes in the environment
Patterns and relationships Recognizes relationships in the environmentUses patterns in the environment
Measurement Makes comparisonsUses measurement
Exploring data Collects, organizes and uses information
Process Standards Competencies in the process of mathematical development.
Indicators Milestones toward the development of competencies.
Examples Observable behaviors children may exhibit in their mathematical development.
Guiding Principles Principles of child development that guide Missouri early childhood practices.
Page 3Missouri Pre-K Mathematics Standards
5
Uses number to show quantity.Number and operations: understanding of numbers, ways of representingnumbers, relationships among numbers and number systems
Number: a unit belonging to a mathematical system used for counting,measuring, ordering and labeling; the meaning of a number word or numeral
Number sense: the ability to understand numbers, ways of representingnumbers and relationships among numbers (Number sense is much morethan counting it involves the ability to think and work with numberseasily and to understand their uses (i.e., counting, measuring, orderingand labeling) and relationships.)
Numerals: conventional symbols that represent numbers (e.g., "1" is the numeral for "one")
Rote count: recite the names of the numerals in order or sequence (e.g., singing a counting song)
Count with understanding: attach a number name to a series of objects; to understand that the numberspoken when tagging or touching the last object also identifies the total number in the group
Ordinal numbers: numbers that indicate the position of an object in a sequence (i.e., first, second, third)
Operations on numbers: basic number combinations and strategies for computing such as addition and subtraction
Quantity: how many units are in a set (i.e., an amount or the result of counting)
Everyday fractions: numbers that represent parts of whole objects in the child's environment (e.g., half a sandwich)
One-to-one correspondence: linking a single number name with one object, and only one, at a time
Estimate: make an educated guess as to the amount or size of something
Indicator Examples1. Shows interest in counting
and quantity.
,
The childuses fingers to indicate the number (e.g., holds up five fingers toshow age).
repeats counting rhymes and singing games with numbers.counts familiar objects (e.g., family members, friends, toys)although not always accurately.
asks how many.
2. Develops increasing abilityto rote count in sequence.
The childcounts from one to 10 or beyond.
3. Counts objects withunderstanding.
The childcounts five items (e.g., blocks, crayons, cars) accurately.hands one to five objects upon request (e.g., hands you threepotatoes when you say, "Joe, hand me three potatoes.")
Page 4Missouri Pre-K Mathematics Standards
6
Uses language to representnumber of objects.
Indicator Examples
1. Uses language to comparenumber (e.g., more/less,greater/fewer, equal to).
The childlooks at his or her own and another child's blocks and determines
who has more blocks.compares raisins with a friend's and decides they have the sameamount.
asks, "How many more do you have?"
2. Combines and names howmany.
The childputs the red, yellow and blue crayons together and counts how
many crayons there are.recognizes that three cars and two trucks is a total of five vehicles.
3. Separates and names howmany.
The childparticipates in finger plays, songs or stories such as "Five Little
Monkeys" or "Five Little Ducks" that use backward counting.plays with a plastic ball and bowling pins and can tell how many
fell down and how many are left standing.
4.
/
Explores everyday fractions.The child
says (although not always accurately), "I have a whole orange," or"I have half an apple."
Page 5Missouri Pre-K Mathematics Standards
7
Numbe conci orXaVoris
Solves problems using number.
Indicator Examples1. Names how many there are
in a group (up to fiveobjects) without counting.
The childrecognizes that there are two or three crayons in a box.rolls a number cube and tells how many dots are on it withoutcounting.
2. Uses one-to-onecorrespondence whencounting objects.
The childcan count five blocks in a row, saying the number as each block istouched.
gets a carton of milk for each child at the table.puts a cup with each napkin when setting the table.holds an additional ringer up for each number when counting orally.
3. Uses one-to-onecorrespondence to comparethe size of a group of objects.
The childcompares two rows of blocks, two in one line and four in another,
and can tell which one has more or less.matches number of cars to a friend's and says, "I have more."
4.
/
Estimates, then counts toverify the number ofobjects.
The childwhile playing in the sand guesses how many cups it would take to
fill a bucket and counts the cups of sand put in the bucket.guesses how many pennies are on the table, then counts the pennies.
Page 6Missouri Pre-K Mathematics Standards
8
Uses numerical representation.
Indicator Examples1. Uses drawings to represent
number.The child
draws pictures showing size (e.g., short/tall) and quantity of familymembers.
creates a way to keep score during a game.draws a picture to indicate number of objects or snacks.
2. Identifies numerals ineveryday situations.
The childselects numerals on the telephone, calculator or computer.finds and names numerals in books or on signs.
3. Uses ordinal numbers (first,second, last).
The childcan identify position in a line of children (e.g., who is first, second,
last).can put three objects in a line and tell which object is first, middle
or last.tells the position of objects (i.e., first, second, last).
4. Writes some numerals. The childdraws numerals in sand.creates numerals with rolled clay or pipe cleaners.tries to write how old he or she is.tries to copy a telephone number.
5. Matches numeral withquantity.
The childwhen playing a game with a spinner or number cube, correctly counts
the spaces on the game board that match the numeral or symbol.uses magnetic or flannel numerals to show how many marbles there
are.
Page 7Missouri Pre-K Mathematics Standards
9
6eomet`Cy avIci sckt;at svose
Investigates positionsand locations.
Geometry: the area of mathematics that involves shape, size,position, direction and movement and describes and classifiesthe physical world we live in
Location: where an object is in space
Orientation: the position or arrangement of an objectPosition: the place where an object or person is in relation to others
Attribute: a characteristic or feature of an object such as color, size, shape, weight and number of sides
Spatial sense: children's awareness of themselves in relation to the people and objects around them; includesknowing boundaries, arrangements and positions
Shape: the form of an objectThree-dimensional: objects that have length, width and depth; solid figures such as cubes, spheres and cylinders
Two-dimensional: objects that have length and width but not depth; shapes such as squares, triangles and circles
Indicator Examples
1. Takes objects apart and putsthem together.
The childbuilds with interlocking blocks.puts lids on containers.completes simple puzzles.
2. Uses actions and words toindicate position andlocation,
The childmoves self to show positions during play (e.g., under a table, in thetent, between friends).
uses objects to show position (e.g., puts the bears on/off/on top of/above/below/beside the box).
talks about objects that are on/off/under/in front of/behind/inside/outside/next to/between/etc.
says when reading The Three Billy Goats Gruff "The big billy goatis on the bridge, and the troll is under the bridge."
3. Uses actions and words toindicate movement andorientation,
The childmoves self to show positions (e.g., up, down, forward, backward,around, through, to, from, sideways, across, back and forth, in astraight or curved path).
explains where objects in a room have been moved.describes how to get to a location using landmarks.follows a path or moves through an obstacle course.draws paths or beginnings of a map to show location during play.
Page 8Missouri Pre-K Mathematics Standards
ti
Explores shapesin the environment.
Indicator Examples
1. Investigates and talks aboutthe characteristics of shapes.
The childsays, "A circle is round."discovers some blocks stack and some blocks roll.says that squares and triangles have corners and straight sides.
2. Creates and duplicatesthree-dimensional and two-dimensional shapes using avariety of materials.
The childuses blocks to make other shapes or objects.makes shapes with Play-Doh, pipe cleaners, string or yarn.attempts to draw shapes and make pictures using shapes.says after cutting the sandwich, "Look, I made a triangle (or
rectangle) with my sandwich."
3. Identifies and names someshapes.
The childpoints to or names simple shapes (e.g., box shape, ball shape, circle,
triangle, square).says, "The pizza is round. My piece is triangle-shaped."says, "The flag is the shape of a rectangle."
4.
_
/
Indicates if shapes are alikeor different using one ormore characteristics.
The childThree-dimensional shapes
says, "A bubble and an orange are both like balls (spheres)."says, "A block (cube) is shaped like a box."says, "This ball rolls, but this block does not."
Two-dimensional shapessays, "A triangle has three sides," or "A square has four sides."says, "A circle is curved (round) like a hula hoop."
Page 9Missouri Pre-K Mathematics Standards
11
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Recognizes relationshipsin the environment.
Patterns and relationships (algebra): the primary objective is for young children to be able to identify andanalyze simple patterns, extend them and make predictions about them
Match: find two objects that have at least one characteristic in common
Sort: place or assign objects in two or more groups on a basis of at least one characteristic
Regroup: place or assign objects in two or more groups using a different characteristic than was used the firsttime the objects were grouped
Order: arrange objects or numbers to show a progressive increase or decrease of a specific characteristic
Relative difference: the specific characteristic that differs among a group of objects (e.g., size)
Pattern: a sequence of colors, shapes, objects, sounds or movements that repeats again and again in a regulararrangement; patterns are a way for young students to recognize order and to organize their world
Extend: continue a pattern beyond what is shown
Indicator Examples1. Matches, sorts and regroups
objects according to one ormore characteristic.
The childsorts plastic foods by size, color, shape or category.matches objects that are alike (e.g., puts all of the two-hole buttons
in one pile and four-hole buttons in another).matches adult animals to their babies.when playing Go Fish, matches all the cards with threes.
2. Orders things according torelative differences.
The childsorts stuffed animals from smallest to largest.talks about who is tall, taller, tallest.arranges a group of blocks from longest to shortest.
Page 10Missouri Pre-K Mathematics Standards
12
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Uses patternsin the environment.
Indicator Examples
1. Recognizes patterns. The childtalks about color or pattern in clothing (e.g., says, "I have red andblue stripes on my shirt.").
identifies color patterns that repeat (e.g., red, blue, red, blue).
2. Duplicates and extendspatterns.
The childimitates a pattern of sounds and physical movements (e.g., clap,stomp, clap, stomp, ...).
continues rhythmic patterns.completes the patterns in a story (e.g., says, "Brown Bear, Brown
Bear, what do you seer).repeats a pattern according to size, color, shape, etc. while stringing
beads.predicts what comes next when an adult "reads" the pattern usingsimple vocabulary (e.g., car, car, boat, car, car, ).
3. Creates patterns. The childcreates simple patterns with beads or blocks according to color, sizeor shape.
creates simple patterns when drawing, coloring orpainting.
13
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Makes comparisons.Measurement: young children's intuitive notions of comparingvolume, area, length and other attributes that they will eventuallylearn to measure; involves decisions about how much or how longCompare: think about same and different; describe the relationship betweentwo or more objects
Measurable features: characteristic or attribute of an object that can be quantified(represented with a number) such as size, shape, weight and number of sides
Sequence: an arrangement of events or actions in a progressive order over time
Indicator Examples1. Compares objects using
measurable features.
,
The childuses words to describe opposites (e.g., big/little, long/short, heavy/light).chooses the largest snack.says, "My bucket is heavier."says, "This crayon is shorter."
2. Describes measurement. The childtalks about an object being longer than another object.uses a variety of language to describe measurement (e.g., shorter,
taller, wider, bigger, heavier, lighter, holds more, hot, cold).
3. Orders three or more objectsaccording to length or sizedifferences.
The childplaces ribbons in order by length.puts cars in a row according to size.puts pans (or measuring cups) inside each other.
4. Uses language associatedwith time in everydaysituations.
The childsays, "Snack time comes after rest time.says, "It's nighttime because it is dark."says, "I eat breakfast in the morning."says, "My birthday comes in the summer."
1
5. Anticipates, remembers andpredicts a sequence ofevents.
The childsays, "I brush my teeth before I go to bed."says, "We went to the library and then the grocery store."recalls recent events and talks about them (e.g., says, "Yesterday we
went to the zoo.").describes the sequence of activities when going to the grocery store.tells stories such as "The Three Little Pigs" with events in order.points out when a familiar story is not told in the correct order.
14
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Uses measurement.
Indicator Examples1. Explores ways to measure. The child
fills a container with solids or liquid (e.g., sand, ice cubes, water).pours liquid from one container to another container.sees how many blocks it takes to cover a sheet of paper.
2. Measures using objects. The childplaces a string next to an object to measure length.uses the toy thermometer to measure the "patient's" temperature.imitates using a ruler when helping dad.
Page 13Missouri Pre-K Mathematics Standards
15
clata
Collects, organizesand uses information. _Amok
Exploring data: informal experience with data by collecting, organizing, representing and comparing theinformation
Data: information gathered to answer a question
Classify: sort or form groups by similar characteristics
Organize: arrange information in order to see relationships, often using graphs and charts
Indicator Examples
1. Asks questions to gatherinformation.
The childasks, "What is your favorite color?"asks, "What month is your birthday?"asks, "What do you like to play outside?"asks, "How many brothers and sisters do you have?"
2. Sorts and classifies objectsinto groups and sometimesexplains how the groupingwas done .
The childputs objects together that have the same use (e.g., blocks, dishes,vehicles, clothes).
explains how the buttons were sorted (e.g., says, "I put the redbuttons together.").
3.
z
Evaluates information toanswer questions.
The childsays two kids have birthdays in July.says, "I have five trucks and four cars."says, "More buttons are red."
Page 14Missouri Pre-K Mathematics Standards
16
Margaret Albrecht, Parents as Teachers National Center
Diane Bauer, OACAC Head Start
Dee Beck, DESE
Karen Berding, Moberly School DistrictGretchen Berhorst, DESE
Linda Biederman, Rockwood School District
Lana Brooks, DESE
Ruth Carmichael, Springfield School DistrictJulie Cowell, DESE
Ruby CrenshawHarriman, Daruby Early LearningCenter
Jeannie Edwards, St. Louis Community College at
Florissant Valley
Ruth Flynn, DESE
Terrie Foltz, Project Construct National Center
Sheri Griffin, Central Methodist CollegeAngie Koetting, DESE
Jane Kostelc, Parents as Teachers National Center
Val Lane, Children's Therapy Center
Peg Lee, Francis Howell School District
Amy Light le, New Bloomfield School District
Bianca Love, Kansas City School District
Freda Markley, Consultant
Maurita McCarthy, Project Construct National CenterTwanna McDaniel, Asia's Learn and Play House
Becky Myers, Project Reach
Darin Preis, Head Start Collaboration Office
Kellie Quinn, LIFT
JoAnne Ralston, Department of Health and SeniorServices
Tammy Randolph, Southeast Missouri State
UniversityCindy Reese, Division of Family Services
Sharon Schneeberger, Project Construct National
CenterCindy Segalhorst, Francis Howell School District
Jodi Trautwein, Southeast Missouri State UniversityTheresa Villmer, DESE
Susan Whiting, DESE
Lisa Willoughby, Cole Camp School District
Kathi Winkler, Hickman Mills School DistrictMaureen Zupanec, Lee's Summit School District
Mathematical Concepts Defined for Early ChildhoodDefinitions for mathematical concepts found in each of the Missouri Preschool Mathematical ContentComponents can be found on the page where the first process standard of each content component isdescribed. The definitions were gleaned from the following resources.
Copley, J.V. (2000). The young child and mathematics. Washington, DC: National Association for the Educationof Young Children.
Fromboluti, C.S., and Rinck, N. (1999). Early childhood: Where learning begins: mathematics. Jessup, MD: U.S.Department of Education.
Irons, R.R. (2002). Growing with Mathematics: Pre-K. Bothell, WA: Wright Group/McGraw Hill.National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston,
VA: Author.Waite-Stupiansky, S., Church, E.B., Feeney, L., Karnes, M., Katz, LG., and Ward, C. (1992). Learning through
play: Math, a practical guide for teaching young children. New York: Scholastic.Wolf, D.P., and Neugebauer, B. (Eds.). (1996). More than numbers: Mathematical thinking in the early years.
Redmond, WA: Child Care Information Exchange.
Page 15Missouri Pre-K Mathematics Standards
17
II '
Department of Elementary and Secondary Education (DESE)
Department of Health and Senior Services
Department of Social Services
Missouri Head Start Collaboration Office
Parents as Teachers National Center
Project Construct National Center
t Missouri Department of Elementary and Secondary EducationEarly Childhood SectionP.O. Box 480Jefferson City, MO 65101(573) 751-2095dese.mo.gov"Making a positive difference through education and service"
18
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ren
lear
n. I
t is
impo
rtan
t to
keep
inm
ind,
how
ever
, tha
t chi
ldre
n le
arn
and
deve
lop
in th
eir
own
uniq
ue w
ays.
Whi
le r
esea
rch
dem
onst
rate
s th
at th
ese
stan
dard
s ar
e ap
prop
riat
e fo
rm
ost c
hild
ren
who
are
abo
ut to
ent
er k
inde
rgar
ten,
our
res
pons
ibili
ty a
sed
ucat
ors
is to
ass
ess
whe
re e
ach
child
is o
n th
e co
ntin
uum
of
mat
hem
atic
alth
inki
ng a
nd b
uild
on
wha
t tha
t chi
ld k
now
s an
d ca
n do
.O
ngoi
ng o
bser
vatio
nal a
sses
smen
t is
a ke
y el
emen
t in
supp
ortin
gch
ildre
n's
earl
y m
athe
mat
ical
dev
elop
men
t. T
his
guid
e w
ill il
lust
rate
som
ein
dica
tors
that
teac
hers
can
rel
iabl
y as
sess
to s
how
eac
h ch
ild's
pro
gres
sov
er ti
me.
Thi
s da
ta c
an b
e us
ed to
pla
n m
eani
ngfu
l, en
gagi
ng le
arni
ngex
peri
ence
s th
at p
rom
ote
both
mat
hem
atic
al d
evel
opm
ent a
nd a
love
for
solv
ing
prob
lem
s. I
n ad
ditio
n, y
ou w
ill f
ind
info
rmat
ion
abou
t cre
atin
gm
athe
mat
ical
ly r
ich
envi
ronm
ents
and
par
tner
ing
with
par
ents
and
fam
ilies
to p
rom
ote
mat
hem
atic
al th
inki
ng a
nd a
n en
thus
iasm
for
lear
ning
. Lis
tsde
fmin
g th
e m
athe
mat
ical
term
s re
ferr
ed to
in th
e st
anda
rds
and
outli
ning
help
ful r
esou
rces
are
als
o in
clud
ed.
Tea
cher
% G
Wile
; Ear
lyM
athe
mat
ics
3
Gui
ding
Pri
ncip
les
IEis
sour
i ear
ly c
hild
hood
pra
ctic
es a
re b
ased
on
the
follo
win
gpr
inci
ples
. The
y pr
ovid
e a
stru
ctur
e to
sup
port
our
wor
k w
ithyo
ung
child
ren
and
rem
ind
us o
f th
e "b
ig p
ictu
re"
the
theo
retic
al f
ram
ewor
k fo
r ou
r te
achi
ng.
1. A
ll ch
ildre
n ac
tivel
y se
ek to
com
preh
end
the
wor
ld in
whi
ch th
eyliv
e. G
iven
the
oppo
rtun
ity to
mak
e ch
oice
s co
ncer
ning
thei
r ac
tiviti
es,
they
acq
uire
kno
wle
dge,
ski
lls a
nd th
e ab
ility
to s
olve
pro
blem
s. C
hild
ren
are
born
with
a d
esir
e to
lear
n ab
out a
nd m
ake
sens
e of
thei
r w
orld
.R
esea
rch
has
show
n us
that
if c
hild
ren
are
able
to c
hoos
e w
hat t
hey
wou
ld li
ke to
fm
d ou
t abo
ut, t
hey
not o
nly
gain
kno
wle
dge
and
skill
s bu
tar
e hi
ghly
mot
ivat
ed to
do
so. W
e ca
n fo
ster
this
ear
ly lo
ve f
or le
arni
ngby
allo
win
g ch
ildre
n ch
oice
s in
thei
r ac
tiviti
es a
nd b
y su
ppor
ting
thei
rat
tem
pts
to s
olve
thei
r ow
n pr
oble
ms.
2. C
hild
ren
cons
truc
t kno
wle
dge
and
valu
es th
roug
h in
tera
ctio
ns w
ithpe
ers,
par
ents
and
oth
er a
dults
and
thro
ugh
activ
e ex
plor
atio
n of
the
phys
ical
and
soc
ial e
nvir
onm
ents
. Chi
ldre
n fl
ouri
sh in
a le
arni
ngco
mm
unity
whe
re th
ey c
an d
irec
tly a
ct o
n ob
ject
s an
d in
tera
ct w
ithpe
ople
. Thi
s is
bec
ause
, for
you
ng c
hild
ren,
thou
ghts
and
act
ions
are
ver
ycl
osel
y re
late
d. W
hen
we
prov
ide
child
ren
with
opp
ortu
nitie
s to
exp
lore
,ex
peri
men
t, m
ake
pred
ictio
ns, c
olla
bora
te a
nd s
hare
thei
r th
inki
ng w
ithot
hers
, we
supp
ort b
oth
thei
r co
gniti
ve a
nd s
ocia
l dev
elop
men
t.
3. Y
oung
chi
ldre
n's
thin
king
con
tain
s pr
edic
tabl
e er
rors
. As
child
ren
deve
lop,
they
con
stru
ct k
now
ledg
e by
inte
grat
ing
new
info
rmat
ion
with
wha
t the
y al
read
y kn
ow I
n do
ing
so, c
hild
ren
will
oft
en m
ake
erro
rs o
rm
ista
ken
assu
mpt
ions
. Thi
s is
a n
eces
sary
par
t of
the
lear
ning
pro
cess
.W
hen
we
give
chi
ldre
n en
ough
tim
e an
d ap
prop
riat
e gu
idan
ce to
reco
gniz
e an
d co
rrec
t the
ir e
rror
s, w
e no
t onl
y te
ach
them
how
to th
ink
for
them
selv
es, b
ut w
e sh
ow th
em th
at w
e ha
ve c
onfi
denc
e th
at th
ey c
anfi
gure
thin
gs o
ut. C
hild
ren
with
con
fide
nce
in th
eir
own
abili
ty to
wor
kth
roug
h pr
oble
ms
are
activ
e th
inke
rs?
4. E
arly
lear
ning
and
are
as o
f de
velo
pmen
t int
erac
t and
infl
uenc
e ea
chot
her.
Whi
le a
dults
are
acc
usto
med
to c
ateg
oriz
ing
lear
ning
by
subj
ect
area
s (s
cien
ce, m
ath,
etc
.), t
his
is n
ot h
ow y
oung
chi
ldre
n or
gani
ze th
eir
thou
ghts
. The
ir e
mot
iona
l and
soc
ial d
evel
opm
ent g
oes
hand
in h
and
with
thei
r le
arni
ng in
oth
er a
reas
. In
fact
, a c
hild
's a
bilit
y to
bui
ld a
know
ledg
e ba
se d
epen
ds u
pon
his
or h
er s
ocia
l, em
otio
nal a
nd p
hysi
cal
deve
lopm
ent a
nd is
clo
sely
link
ed to
it. A
s ed
ucat
ors,
we
serv
e ch
ildre
nbe
st b
y de
sign
ing
lear
ning
exp
erie
nces
that
are
bot
h m
eani
ngfu
l to
them
and
that
spa
n va
riou
s ar
eas
of d
evel
opm
ent.
LiT
each
er's
Gui
de: E
arly
Mai
hem
atic
s
5. F
amili
es (
pare
nts)
are
the
child
's f
irst
and
mos
t im
port
ant t
each
ers.
Fam
ilies
(pa
rent
s), a
s ch
ildre
n's
earl
iest
and
mos
t inf
luen
tial t
each
ers,
are
our
mos
t hel
pful
par
tner
s in
edu
catin
g yo
ung
child
ren.
We
are
all d
eepl
yin
vest
ed in
the
child
's s
ucce
ss a
nd s
hare
a c
omm
on g
oal:
to p
rovi
deth
e be
st e
duca
tion
poss
ible
in a
saf
e, n
urtu
ring
env
iron
men
t tha
t is
rich
with
opp
ortu
nitie
s fo
r le
arni
ng. B
uild
ing
open
, res
pect
ful a
nd tr
ustin
gre
latio
nshi
ps w
ith th
e pa
rent
s an
d fa
mili
es o
f th
e ch
ildre
n in
our
car
ehe
lps
child
ren
deve
lop
a se
nse
of s
ecur
ity a
nd c
ontin
uity
bet
wee
n ho
me
and
scho
oL
6. C
hild
ren
exhi
bit i
ndiv
idua
l dif
fere
nces
in th
eir
deve
lopm
ent o
fco
mpe
tenc
ies.
Alth
ough
res
earc
h (a
nd o
ur o
wn
expe
rien
ce)
has
show
nus
that
chi
ldre
n ge
nera
lly g
o th
roug
h id
entif
iabl
e st
ages
as
they
gro
w a
ndde
velo
p, it
is a
lso
true
that
ther
e ca
n be
gre
at in
divi
dual
dif
fere
nces
inth
e ra
te a
nd m
anne
r in
whi
ch c
hild
ren
pass
thro
ugh
thes
e st
ages
. Thi
sva
riat
ion
is n
orm
al. W
e ca
n be
st s
uppo
rt e
ach
child
's p
rogr
ess
by m
eetin
gch
ildre
n w
here
they
are
and
bui
ldin
g on
thei
r st
reng
ths.
child
ren
flour
ish
in a
team
ing
com
mun
ity w
here
they
can
dire
ctly
act
on
obje
cts
and
inte
ract
with
peo
pte
I.
Org
aniz
atio
nhe
sta
ndar
ds c
over
the
broa
d sc
ope
of c
hild
dev
elop
men
t and
are
orga
nize
d by
:
Con
tent
Com
pone
ntth
e sp
ecif
ic c
onte
nt a
rea
to b
e ad
dres
sed
(e.g
,nu
mbe
r an
d op
erat
ions
or
mea
sure
men
t).
II.
Proc
ess
Stan
dard
sid
entif
iabl
e co
mpe
tenc
ies
or c
apab
ilitie
s in
the
proc
ess
of m
athe
mat
ical
dev
elop
men
t, su
ch a
s so
lvin
g pr
oble
ms
usin
gnu
mbe
r or
usi
ng n
umer
ical
rep
rese
ntat
ion.
III.
Ind
icat
ors
obse
rvab
le m
ilest
ones
in th
e de
velo
pmen
t of
com
pete
ncie
s, s
uch
as w
ritin
g so
me
num
eral
s or
taki
ng o
bjec
ts a
part
and
putti
ng th
em to
geth
er a
gain
.
IV. E
xam
ples
spec
ific
beh
avio
rs c
hild
ren
may
exh
ibit
in th
eir
mat
hem
atic
al d
evel
opm
ent
Thi
s st
ruct
ure
prov
ides
us
with
an
acce
ssib
le w
ay to
see
how
the
stan
dard
sfi
t int
o ou
r cu
rric
ulum
and
teac
hing
pra
ctic
es. D
efin
ition
s of
the
term
s an
dco
ncep
ts u
sed
in th
e st
anda
rds
are
liste
d on
pag
es 6
thro
ugh
8.
Tea
cher
's G
uide
: Ear
y M
athe
mat
ic-5
5
Mat
hem
atic
sS
tand
ards
(G
oals
)fo
r th
e P
resc
hool
Yea
rsel
ow a
re th
e St
anda
rds
(Goa
ls)
for
Pre-
K M
athe
mat
ics
asid
entif
ied
by th
e M
isso
uri D
epar
tmen
t of
Ele
men
tary
and
Seco
ndar
y E
duca
tion,
Ear
ly C
hild
hood
Sec
tion.
Num
ber
and
oper
atio
nsU
ses
num
ber
to s
how
qua
ntity
.U
ses
lang
uage
to r
epre
sent
num
ber
of o
bjec
ts.
Solv
es p
robl
ems
usin
g nu
mbe
r.U
ses
num
eric
al r
epre
sent
atio
n.
Geo
met
ry a
nd s
patia
l sen
seIn
vest
igat
es p
ositi
ons
and
loca
tions
.E
xplo
res
shap
es in
the
envi
ronm
ent.
Pat
tern
s an
d re
latio
nshi
psR
ecog
nize
s re
latio
nshi
ps in
the
envi
ronm
ent.
Use
s pa
ttern
s in
the
envi
ronm
ent
Mea
sure
men
tM
akes
com
pari
sons
.U
ses
mea
sure
men
t
Exp
lorin
g da
taII
Col
lect
s, o
rgan
izes
and
use
s in
form
atio
n.
Mat
hem
otic
at C
once
pts
Def
ined
Con
tent
com
pone
nt: N
umbe
r an
d op
erat
ions
Num
ber
and
oper
atio
ns: u
nder
stan
ding
of
num
bers
, way
s of
rep
rese
ntin
gnu
mbe
rs, r
elat
ions
hips
am
ong
num
bers
and
num
ber
syst
ems
Num
ber:
a u
nit b
elon
ging
to a
mat
hem
atic
al s
yste
m u
sed
for
coun
ting,
mea
suri
ng, o
rder
ing
and
labe
ling;
the
mea
ning
of
a nu
mbe
r w
ord
ornu
mer
alN
umbe
r se
nse:
the
abili
ty to
und
erst
and
num
bers
, way
s of
rep
rese
ntin
gnu
mbe
rs a
nd r
elat
ions
hips
am
ong
num
bers
(N
umbe
r se
nse
is m
uch
mor
eth
an c
ount
ing;
it in
volv
es th
e ab
ility
to th
ink
and
wor
k w
ith n
umbe
rs e
asily
and
to u
nder
stan
d th
eir
uses
(co
untin
g, m
easu
ring
, ord
erin
g an
d la
belin
g)an
d re
latio
nshi
ps.)
Num
eral
s: c
onve
ntio
nal s
ymbo
ls th
at r
epre
sent
num
bers
(e.
g., "
1" is
the
num
eral
for
"on
e")
6T
each
er's
Ear
ly M
athe
mat
ics
Rot
e co
unt:
reci
te th
e na
mes
of
the
num
eral
s in
ord
er o
r se
quen
ce (
e.g,
sing
ing
a co
untin
g so
ng)
Cou
nt w
ith u
nder
stan
ding
: atta
ch a
num
ber
nam
e to
a s
erie
s of
obj
ects
;to
und
erst
and
that
the
num
ber
spok
en w
hen
tagg
ing
or to
uchi
ng th
e la
stob
ject
als
o id
entif
ies
the
tota
l num
ber
in th
e gr
oup
Ord
inal
num
bers
: num
bers
that
indi
cate
the
posi
tion
of a
n ob
ject
in a
sequ
ence
(i.e
., fi
rst,
seco
nd, t
hird
)O
pera
tions
on
num
bers
: bas
ic n
umbe
r co
mbi
natio
ns a
nd s
trat
egie
s fo
rco
mpu
ting
such
as
addi
tion
and
subt
ract
ion
Qua
ntity
: how
man
y un
its a
re in
a s
et (
i.e.,
an a
mou
nt o
r th
e re
sult
ofco
untin
g)E
very
day
frac
tions
: num
bers
that
rep
rese
nt p
arts
of
who
le o
bjec
ts in
the
child
's e
nvir
onm
ent (
e.g.
, hal
f a
sand
wic
h)O
ne-t
o-on
e co
rres
pond
ence
: lin
king
a s
ingl
e nu
mbe
r na
me
with
one
obje
ct, a
nd o
nly
one,
at a
tim
eE
stim
ate:
mak
ing
an e
duca
ted
gues
s as
to th
e am
ount
or
size
of
som
ethi
ng
Con
tent
com
pone
nt: G
eom
etry
and
spa
tial s
ense
Geo
met
ry: t
he a
rea
of m
athe
mat
ics
that
invo
lves
sha
pe, s
ize,
pos
ition
,di
rect
ion
and
mov
emen
t and
des
crib
es a
nd c
lass
ifie
s th
e ph
ysic
al w
orld
we
live
inL
ocat
ion:
whe
re a
n ob
ject
is in
spa
ceO
rien
tatio
n: th
e po
sitio
n or
arr
ange
men
t of
an o
bjec
tPo
sitio
n: th
e pl
ace
whe
re a
n ob
ject
or
pers
on is
in r
elat
ion
to o
ther
sA
ttrib
ute:
a c
hara
cter
istic
or
feat
ure
of a
n ob
ject
suc
h as
col
or, s
ize,
sha
pe,
wei
ght a
nd n
umbe
r of
sid
esSp
atia
l sen
se: c
hild
ren'
s aw
aren
ess
of th
emse
lves
in r
elat
ion
to th
e pe
ople
and
obje
cts
arou
nd th
em; i
t inc
lude
s kn
owin
g bo
unda
ries
, arr
ange
men
tsan
d po
sitio
nsSh
ape:
the
form
of
an o
bjec
tT
hree
-dim
ensi
onal
: obj
ects
that
hav
e le
ngth
, wid
th a
nd d
epth
; sol
idfi
gure
s su
ch a
s cu
bes,
sph
eres
and
cyl
inde
rsT
wo-
dim
ensi
onal
: obj
ects
that
hav
e le
ngth
and
wid
th b
ut n
ot d
epth
;sh
apes
suc
h as
squ
ares
, tri
angl
es a
nd c
ircl
es
Con
tent
com
pone
nt: P
atte
rns
and
rela
tions
hips
Patte
rns
and
rela
tions
hips
(al
gebr
a): t
he p
rim
ary
obje
ctiv
e is
for
you
ngch
ildre
n to
be
able
to id
entif
y an
d an
alyz
e si
mpl
e pa
ttern
s, e
xten
d th
em a
ndm
ake
pred
ictio
ns a
bout
them
Mat
ch: t
o fi
nd tw
o ob
ject
s th
at h
ave
at le
ast o
ne c
hara
cter
istic
in c
omm
onSo
rt: t
o pl
ace
or a
ssig
n ob
ject
s in
two
or m
ore
grou
ps o
n a
basi
s of
at l
east
one
char
acte
rist
icR
egro
up: t
o pl
ace
or a
ssig
n ob
ject
s in
two
or m
ore
grou
ps u
sing
a d
iffe
rent
char
acte
rist
ic th
an w
as u
sed
the
firs
t tim
e th
e ob
ject
s w
ere
grou
ped
Tea
cher
's G
Ode
: Ear
ly M
athe
mat
ics
7
Ord
er: a
rran
ge o
bjec
ts o
r nu
mbe
rs to
sho
w a
pro
gres
sive
incr
ease
or
decr
ease
of
a sp
ecif
ic c
hara
cter
istic
Rel
ativ
e di
ffer
ence
: the
spe
cifi
c ch
arac
teri
stic
that
dif
fers
am
ong
a gr
oup
of o
bjec
ts (
e.g,
siz
e)Pa
ttern
: a s
eque
nce
of c
olor
s, s
hape
s, o
bjec
ts, s
ound
s or
mov
emen
ts th
atre
peat
s ag
ain
and
agai
n in
a r
egul
ar a
rran
gem
ent;
patte
rns
are
a w
ay f
oryo
ung
stud
ents
to r
ecog
nize
ord
er a
nd to
org
aniz
e th
eir
wor
ldE
xten
d: c
ontin
ue a
pat
tern
bey
ond
wha
t is
show
n
Con
tent
com
pone
nt: M
easu
rem
ent
Mea
sure
men
t: yo
ung
child
ren'
s in
tuiti
ve n
otio
ns o
f co
mpa
ring
vol
ume,
area
, len
gth
and
othe
r at
trib
utes
that
they
will
eve
ntua
lly le
arn
to m
easu
re;
invo
lves
dec
isio
ns a
bout
how
muc
h or
how
long
Com
pare
: thi
nk a
bout
sam
e an
d di
ffer
ent;
desc
ribe
the
rela
tions
hip
betw
een
two
or m
ore
obje
cts
Mea
sura
ble
feat
ures
: a c
hara
cter
istic
or
attr
ibut
e of
an
obje
ct th
at c
anbe
qua
ntif
ied
(rep
rese
nted
with
a n
umbe
r) s
uch
as s
ize,
sha
pe, w
eigh
t and
num
ber
of s
ides
Sequ
ence
: an
arra
ngem
ent o
f ev
ents
or
actio
ns in
a p
rogr
essi
ve o
rder
ove
rtim
e
Con
tent
com
pone
nt: E
xplo
ring
data
Exp
lori
ng d
ata:
info
rmal
exp
erie
nce
with
dat
a by
col
lect
ing,
org
aniz
ing,
repr
esen
ting
and
com
pari
ng th
e in
form
atio
nD
ata:
info
rmat
ion
gath
ered
to a
nsw
er a
que
stio
nC
lass
ify:
sor
t or
form
gro
ups
by s
imila
r ch
arac
teri
stic
sO
rgan
ize:
to a
rran
ge in
form
atio
n in
ord
er to
see
rel
atio
nshi
ps, o
ften
usi
nggr
aphs
and
cha
rts
Sou
rces
of d
efin
ition
sC
ople
y, J
.V. (
2000
). T
he y
oung
chi
ld a
nd m
athe
mat
ics.
Was
hing
ton,
DC
: Nat
iona
lA
ssoc
iatio
n fo
r th
e E
duca
tion
of Y
oung
Chi
ldre
n.Fr
ombo
luti,
C.S
., an
d R
inck
, N. (
1999
). E
arly
chi
ldho
od. W
here
lear
ning
beg
ins:
mat
hem
adcs
. Jes
sup,
MD
: U.S
. Dep
artm
ent o
f E
duca
tion.
Iron
s, R
R. (
2002
). G
row
ing
with
Mat
hem
atic
s: P
re-K
Bot
hell,
WA
: Wri
ght
Gro
up/M
cGra
w H
ill.
Nat
iona
l Cou
ncil
of T
each
ers
of M
athe
mat
ics.
(20
00).
Pri
naPl
es a
nd s
tand
ards
for
scho
ol m
athe
mat
ics.
Res
ton,
VA
: Aut
hor.
Wai
te-S
tupi
ansk
y, S
., C
hurc
h, E
.B.,
Feen
ey, L
., K
arne
s, M
., K
atz,
L.G
., an
dW
ard,
C. (
1992
). L
earn
ing
thro
ugh
plg:
Mat
h, a
pra
ctic
al g
uide
for
teac
hing
youn
gch
ildre
n. N
ew Y
ork:
Sch
olas
tic.
Wol
f, D
.P, a
nd N
euge
baue
r, B
. (E
ds.)
. (19
96).
Mor
e th
an n
umbe
rs: M
athe
mad
cal
thin
king
in th
e ea
rlyy
ears
. Red
mon
d, W
A: C
hild
Car
e In
form
atio
nE
xcha
nge.
8T
each
er's
Giri
de: E
arly
Mat
hem
atic
s
Ack
now
ledg
men
tsA
he M
isso
uri P
re-K
Mat
hem
atic
s St
anda
rds
are
the
colla
bora
tive
effo
rt o
f a
broa
d-ba
sed
grou
p of
indi
vidu
als
who
rep
rese
nt th
em
any
face
ts o
f th
e ea
rly
child
hood
com
mun
ity in
Mis
sour
i. T
his
com
mitt
ee d
rew
upo
n cu
rren
t res
earc
h an
d co
nsul
ted
othe
r na
tiona
l and
stat
e in
itiat
ives
for
rec
omm
enda
tions
. In
addi
tion,
the
Mis
sour
i Dep
artm
ent
of E
lem
enta
ry a
nd S
econ
dary
Edu
catio
n, M
isso
uri D
epar
tmen
t of
Hea
lth,
Mis
sour
i Dep
artm
ent o
f So
cial
and
Sen
ior
Serv
ices
, the
Mis
sour
i Sta
teH
ead
Star
t Col
labo
ratio
n O
ffic
e, th
e Pa
rent
s as
Tea
cher
s N
atio
nal C
ente
r,an
d th
e Pr
ojec
t Con
stru
ct N
atio
nal C
ente
r co
ntri
bute
d to
this
wor
k un
der
the
lead
ersh
ip o
f th
e E
arly
Chi
ldho
od S
ectio
n of
the
Dep
artm
ent o
fE
lem
enta
ry a
nd S
econ
dary
Edu
catio
n. T
he c
ompl
ete
list o
f co
mm
ittee
mem
bers
app
ears
bel
ow.
Com
mitt
ee M
embe
rs
Mar
gare
t Alb
rech
t, P
aren
ts a
s T
each
ers
Nat
iona
l Cen
ter
Dia
ne B
auer
, OA
CA
C H
ead
Sta
rt
Dee
Bec
k, D
ES
E
Kar
en B
erdi
ng, M
ober
ly S
choo
l Dis
tric
t
Gre
tche
n B
erho
rst,
DE
SE
Lind
a B
iede
rman
, Roc
kwoo
d S
choo
l Dis
tric
t
Lana
Bro
oks,
DE
SE
Rut
h C
arm
icha
el S
prin
gfie
ld S
choo
l Dis
tric
t
Julie
Cow
ell D
ES
E
Rub
y C
rens
haw
Har
riman
, Dar
uby
Ear
lyLe
arni
ng C
ente
r
Jean
nie
Edw
ards
, St.
Loui
s C
omm
unity
Col
lege
at F
loris
sant
Val
ley
Rut
h F
lynn
, DE
SE
Ter
rie F
oltz
, Pro
ject
Con
stru
ct N
atio
nal C
ente
r
She
ri G
riffin
, Cen
tral
Met
hodi
st C
olle
ge
Ang
ie K
oetti
ng, D
ES
E
Jane
Kos
telc
, Par
ents
as
Tea
cher
s N
atio
nal
Cen
ter
Val
Lan
e, C
hild
ren'
s T
hera
py C
ente
r
Peg
Lee
, Fra
ncis
How
ell S
choo
l Dis
tric
t
Am
y Li
ghtie
, New
Blo
omfie
ld S
choo
l Dis
tric
t
Bia
nca
Love
, Kan
sas
City
Sch
ool D
istr
ict
Fre
da M
arkl
ey, C
onsu
ltant
Mau
rita
McC
arth
y, P
roje
ct C
onst
ruct
Nat
iona
l
Cen
ter
Tw
anna
McD
anie
l Asi
a's
Lear
n an
d P
lay
Hou
se
Bec
ky M
yers
, Pro
ject
Rea
ch
Dar
in P
reis
, Hea
d S
tart
Col
labo
ratio
n O
ffice
Kel
lie Q
uinn
, LIF
T
JoA
nne
Ral
ston
, Dep
artm
ent o
f Hea
lth a
nd
Sen
ior
Ser
vice
s
Tam
my
Ran
dolp
h, S
outh
east
Mis
sour
i Sta
te
Uni
vers
ity
Cin
dy R
eese
, Div
isio
n of
Fam
ily S
ervi
ces
Sha
ron
Sch
neeb
erge
r, P
roje
ct C
onst
ruct
Nat
iona
l Cen
ter
Cin
dy S
egal
hors
t, F
ranc
is H
owel
l Sch
ool
Dis
tric
t
Jodi
Tra
utw
ein,
Sou
thea
st M
isso
uri S
tate
Uni
vers
ity
The
resa
Vill
mer
, DE
SE
Sus
an W
hitin
g, D
ES
E
Lisa
Will
ough
by, C
ole
Cam
p S
choo
l Dis
tric
t
Kat
hi W
inkl
er, H
ickm
an M
ills
Sch
ool D
istr
ict
Mau
reen
Zup
anec
, Lee
's S
umm
it S
choo
l
Dis
tric
t
Tea
cher
's G
uide
: Ear
ly M
athe
mat
ics
9
Num
ber
and
oper
atio
nsU
ses
num
ber
to s
how
qua
ntity
.
Thi
s st
anda
rd r
efer
s to
the
child
's in
crea
sing
und
erst
andi
ng th
at n
umbe
rsre
pres
ent q
uant
ities
. It i
s an
impo
rtan
t com
pone
nt o
f nu
mbe
r se
nse
the
abili
ty to
und
erst
and
how
num
bers
are
use
d an
d ho
w th
ey a
re r
epre
sent
edas
wel
l as
rela
tions
hips
am
ong
num
bers
.
The
re a
re th
ree
indi
cato
rs fo
r th
is s
tand
ard:
Indi
cato
rsT
he c
hild
...
Exa
mpl
esT
he c
hild
...
Sho
ws
inte
rest
uses
fing
ers
to in
dica
te th
e nu
mbe
r (e
.g.,
hold
s up
five
fing
ers
toIn
cou
ntin
g an
dsh
ow a
ge).
quan
tity.
repe
ats
coun
ting
rhym
es a
nd s
ingi
ng g
ames
with
num
bers
.
coun
ts fa
mili
ar o
bjec
ts (
e.g,
fam
ily m
embe
rs, f
riend
s, to
ys)
alth
ough
not
alw
ays
accu
rate
ly.
asks
how
man
y.
Dev
elop
s an
incr
easi
ngab
ility
to r
ote
coun
t In
sequ
ence
.
coun
ts o
ne to
lo o
r be
yond
.
Cou
nts
obje
cts
with
coun
ts fi
ve it
ems
(e.g
., bl
ocks
, cra
yons
, car
s) a
ccur
atel
y.un
ders
tand
ing.
hand
s on
e to
five
obj
ects
upo
n re
ques
t (e.
g, h
ands
you
thre
e
pota
toes
whe
n yo
u sa
y, 'J
oe, h
and
me
thre
e po
tato
es."
)
Tea
cher
str
ateg
ies
to p
rom
ote
use
of n
umbe
r to
sho
w q
uant
ity In
clud
e:
enco
urag
ing
child
ren
to e
xper
imen
t with
cou
ntin
g in
way
s th
at a
rem
eani
ngfu
l to
them
.en
gagi
ng c
hild
ren
in s
ingi
ng c
ount
ing
song
s.re
adin
g bi
g bo
oks
that
fea
ture
cou
ntin
g or
num
bers
(e.
g, T
en B
lack
Dot
s).
mod
elin
g co
untin
g of
obj
ects
or
peop
le in
mea
ning
ful c
onte
xts
(e.g
., to
dete
rmin
e ho
w m
any
child
ren
are
at a
tabl
e).
prov
idin
g op
port
uniti
es f
or c
ount
ing
obje
cts.
mod
elin
g th
at w
e us
e on
e co
untin
g w
ord/
num
ber
for
each
obj
ect.
aski
ng "
how
man
y" q
uest
ions
.po
stin
g a
num
ber
char
t at c
hild
ren'
s ey
e le
vel a
nd m
odel
ing
how
to u
se it
.pl
ayin
g co
untin
g ga
mes
.
10T
each
er's
Guk
ie: E
arly
Mat
hem
atic
s
Num
ber
and
oper
atio
nsU
ses
lang
uage
to r
epre
sent
num
ber
of o
bjec
ts.
Thi
s st
anda
rd r
efle
cts
the
child
's g
row
ing
know
ledg
e an
d us
e of
voca
bula
ry a
ssoc
iate
d w
ith n
umbe
r an
d qu
antit
y. I
t pro
vide
s a
build
ing
bloc
kfo
r m
athe
mat
ical
und
erst
andi
ng a
nd c
omm
unic
atin
g m
athe
mat
ical
idea
s. I
tis
impo
rtan
t to
rem
embe
r th
at c
hild
ren
can
mak
e m
athe
mat
ical
obs
erva
tions
and
conn
ectio
ns th
roug
hout
the
day
and
in a
ll ar
eas
of th
e cu
rric
ulum
.
The
re a
re fo
ur In
dica
tors
for
this
sta
ndar
d:
indi
cato
rsT
be c
hild
...
Exa
mpl
esT
he c
hild
...
Use
s ta
mpi
ng to
look
s at
his
ow
n an
d an
othe
r ch
ild's
blo
cks
and
dete
rmin
es w
ho
com
pare
mem
ber
has
mor
e bl
ocks
.(e
.g.,
mor
e/le
ss,
grea
ter/
few
er,
equa
l to)
.
com
pare
s ra
isin
s w
ith a
frie
nd's
and
dec
ides
they
hav
e th
e sa
me
amou
nt
asks
, "H
ow m
any
mor
e do
you
hav
er'
Com
bine
s an
dpu
ts th
e re
d, y
ello
w a
nd b
lue
cray
ons
toge
ther
and
cou
nts
how
nam
es h
ow m
any.
man
y cr
ayon
s th
ere
are.
reco
gniz
es th
at th
ree
cars
and
two
truc
ks is
a to
tal o
f fiv
e ve
hicl
es.
Sep
ante
s m
idpa
rtic
ipat
es in
fing
er p
lays
, son
gs o
r st
orie
s su
ch a
s R
ye li
tffe
nam
es h
ow m
any.
Mon
keys
or
Fiv
e Li
nk D
ucks
that
use
bac
hvar
d co
untin
g.
play
s w
ith a
pla
stic
bal
l and
bow
ling
pins
and
can
tell
how
man
y
fen
dow
n an
d ho
w m
any
are
left
stan
ding
.
Exp
lore
s ev
eryd
aysa
ys (
alth
ough
not
alw
ays
accu
rate
ly),
1 h
ave
a w
hole
ora
nge,
"
frac
tions
.or
1 h
ave
half
an a
pple
."
Tea
cher
str
ateg
ies
that
pro
mot
e th
e us
e of
mat
hem
atic
al la
ngua
ge in
clud
e: ""
choo
sing
boo
ks in
volv
ing
coun
ting
and
mat
h co
ncep
ts d
urin
g sh
ared
read
ing
(see
the
list i
n th
e R
esou
rces
sec
tion
for
sugg
este
d tit
les)
.en
gagi
ng c
hild
ren
in id
entif
ying
env
iron
men
tal p
rint
with
num
bers
and
mak
ing
envi
ronm
enta
l pri
nt "
mat
h" b
ooks
.gi
ving
chi
ldre
n m
ater
ials
to m
ake
colle
ctio
ns w
ith a
nd c
onve
rsin
g w
ithth
em a
bout
how
they
sor
t or
clas
sify
obj
ects
and
how
man
y th
ere
are.
enga
ging
chi
ldre
n in
fin
ger
play
s, s
ongs
and
sto
ries
that
invo
lve
coun
ting
(for
war
d an
d ba
ckw
ard)
.pr
ovid
ing
oppo
rtun
ities
for
cou
ntin
g ob
ject
s an
d as
king
abo
ut q
uant
ities
.m
odel
ing
voca
bula
ry f
or m
akin
g co
mpa
riso
ns a
nd in
dica
ting
quan
tity.
help
ing
child
ren
mak
e m
athe
mat
ical
con
nect
ions
at s
nack
tim
e (e
.g, a
skin
g,".
Are
ther
e en
ough
cra
cker
s fo
r ev
eryo
ne?
How
man
y do
we
need
?").
Tea
cher
's G
uide
: Ear
ly M
athe
mat
ics
II
Num
ber
and
oper
atio
n5S
olve
s pr
oble
ms
usin
g nu
mbe
r.
Thi
s st
anda
rd r
efer
s to
a c
hild
's a
bilit
y to
iden
tify
and
solv
e pe
rson
ally
mea
ning
ful p
robl
ems
invo
lvin
g nu
mbe
r. A
s ch
ildre
n be
gin
to w
ork
with
num
bers
to s
olve
pro
blem
s th
at a
re o
f in
tere
st to
them
, the
y de
epen
thei
run
ders
tand
ing
of w
hat n
umbe
rs r
epre
sent
as
wel
l as
of th
e re
latio
nshi
psam
ong
num
bers
. The
re a
re fo
ur in
dkat
ors
for
this
sta
ndar
d:
Indi
cato
rsT
he c
hild
...
Exa
mpl
esT
he c
hild
...
Nam
es h
ow m
any
reco
gniz
es th
at th
ere
are
two
or th
ree
cray
ons
in a
box
.
ther
e ar
e in
a g
roup
rolls
a n
umbe
r cu
be a
nd te
lh h
ow m
any
dots
are
on
it w
ithou
t(u
p to
five
obj
ects
)w
ithou
t cou
ntin
g.co
untin
g .
Use
s oe
e-to
-ose
can
coun
t fiv
e bl
ocks
in a
row
and
say
the
num
ber
as e
ach
bloc
k
corr
espo
nden
ceis
touc
hed.
whe
n co
untin
gge
ts a
car
ton
of m
ilk fo
r ea
ch c
hild
at t
he ta
ble.
obje
cts.
puts
a c
up w
ith e
ach
napk
in w
hen
setti
ng th
e ta
ble.
hold
s an
add
ition
al fi
nger
up
for
each
num
ber
whe
n co
untin
g
oral
ly.
Use
s oo
e-to
-one
cone
spoo
denc
e to
com
pare
s tw
o ro
ws
of b
lock
s, tw
o in
one
line
and
four
in a
noth
er,
and
can
tell
whi
ch o
ne h
as m
ore
or le
ss.
Com
Par
t Mt s
ilt O
fa
grou
p of
obj
ects
.m
atch
es n
umbe
r of
car
s to
a fr
iend
's a
nd s
ays,
1 h
ave
mor
e.'
Est
imat
es, t
hen
whi
le p
layi
ng in
the
sand
gue
sses
how
man
y cu
ps it
wou
ld ta
ke to
coun
ts to
ver
ify th
efil
l a b
ucke
t and
cou
nts
the
cups
of s
and
put i
n th
e bu
cket
num
ber
of o
bjec
ts.
gues
ses
how
man
y pe
nnie
s ar
e on
the
tabl
e, th
en c
ount
s th
e
penn
ies.
Tea
cher
str
ateg
ies
that
pro
mot
e pr
oble
m s
olvi
ng w
ith n
umbe
rs In
clud
e:
taki
ng a
dvan
tage
of
natu
ral c
onte
xts
duri
ng th
e da
y (e
.g.,
at s
nack
tim
e or
whe
n ta
king
atte
ndan
ce)
to e
ncou
rage
pro
blem
sol
ving
with
num
bers
.sh
owin
g ch
ildre
n a
glim
pse
of a
sm
all g
roup
of
item
s (i
.e.,
1 to
3)
and
aski
ng th
em h
ow m
any
ther
e ar
e.su
pply
ing
the
mat
h ce
nter
with
a v
arie
ty o
f m
ath
gam
es, i
nclu
ding
teac
her-
mad
e ga
mes
, for
chi
ldre
n to
exp
lore
.en
gagi
ng c
hild
ren
in a
ll ki
nds
of g
roup
gam
es (
e.g.
, aim
ing
gam
es, h
idin
gga
mes
, gue
ssin
g ga
mes
, boa
rd g
ames
).
Tea
cher
's G
uide
: Ear
ly M
athe
mat
ics
enco
urag
ing
child
ren
to m
ake
up b
oard
gam
es o
r m
ake
thei
r. o
wn
rule
sfo
r ga
mes
.pr
ovid
ing
oppo
rtun
ities
for
chi
ldre
n to
est
imat
e am
ount
s an
d te
st th
eir
pred
ictio
ns.
supp
ortin
g ch
ildre
n in
mak
ing
mat
hem
atic
al o
bser
vatio
ns a
ndco
nnec
tions
in th
e bl
ock
area
and
oth
er c
ente
rs.
havi
ng c
hild
ren
vote
in. a
ppro
pria
te c
onte
xts
(e.g
., in
det
erm
m. M
g th
ena
me
of th
e cl
ass
pet)
.de
scri
bing
rea
l-lif
e si
tuat
ions
invo
lvin
g nu
mbe
rs a
nd a
pro
blem
for
child
ren
to s
olve
(e.
g., s
ayin
g, 'W
e ha
ve 1
0 ca
rton
s of
milk
for
sna
ck b
uton
ly s
ix s
traw
s. H
ow m
any
mor
e st
raw
s do
we
need
?).
ot:
5 up
pty
the
mat
h ce
nter
with
a v
arie
ty o
f mat
h ga
mes
for
child
ren
to e
xpta
re
Tea
cher
's G
ukie
: Ear
ly tl
athe
rnal
ic.s
13
Num
ber
and
oper
atio
nsU
ses
num
eric
al r
epre
sent
atio
n.
Thi
s st
anda
rd r
efer
s to
the
child
's a
bilit
y to
iden
tify
and
dist
ingu
ish
num
eral
s as
wel
l as
deve
lop
an u
nder
stan
ding
of
ordi
nal n
umbe
rs (
i.e.,
num
bers
that
indi
cate
whe
re a
n ob
ject
is p
ositi
oned
in a
seq
uenc
e). T
his
skill
is a
noth
er b
uild
ing
bloc
k of
num
ber
sens
e an
d pr
ovid
es a
mea
ns f
orch
ildre
n to
com
mun
icat
e m
athe
mat
ical
idea
s.
The
re a
re fl
ve In
dica
tor
Recommended