reproductions supplied by edrs are the best that can be ...families, and a 62-item resource list of...

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

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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.")


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."


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.


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.


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.


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."


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.


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.


15

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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."


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.


17

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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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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

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