Stud

ent

Vita

l Act

ions

Prin

cipl

es

All

stud

ents

par

tici

pate

(e.g

., bo

ys a

nd g

irls

, ELL

and

sp

ecia

l nee

ds s

tude

nts)

, not

just

the

hand

-rai

sers

. Eq

uity

requ

ires

part

icip

atio

n.A

➤

Stud

ents

say

a s

econ

d se

nten

ce (s

pont

aneo

usly

or

prom

pted

by

the

teac

her

or a

noth

er s

tude

nt) t

o ex

tend

and

exp

lain

thei

r th

inki

ng.

CCSS

-M p

ract

ices

1 |

2 |

3 |

6

Logi

c co

nnec

ts

sent

ence

s.B ➤

Stud

ents

tal

k ab

out

each

oth

er’s

thi

nkin

g (n

ot ju

st th

eir

own)

.

CCSS

-M p

ract

ices

1 |

2 |

3 |

6 |

7 |

8

Und

erst

andi

ng e

ach

othe

r’s re

ason

ing

deve

lops

reas

onin

g pr

ofici

ency

. C ➤

Stud

ents

rev

ise

thei

r th

inki

ng, a

nd th

eir

wri

tten

wor

k

incl

udes

revi

sed

expl

anat

ions

and

just

ifica

tions

. CC

SS-M

pra

ctic

es 1

| 2

| 3

| 4

Revi

sing

exp

lana

tions

sol

idifi

es

unde

rsta

ndin

g.D

➤

Stud

ents

look

for

mor

e pr

ecis

e w

ays

of e

xpre

ssin

g th

eir

thin

king

, en

cour

agin

g ea

ch o

ther

to lo

ok fo

r an

d us

e ac

adem

ic la

ngua

ge. 

CCS

S-M

pra

ctic

es 3

| 6

Acad

emic

lang

uage

pro

mot

es

prec

ise

thin

king

.E ➤

Engl

ish

lear

ners

pro

duce

lang

uage

that

com

mun

icat

es

idea

s an

d re

ason

ing,

eve

n w

hen

that

lang

uage

is im

perf

ect.

CCSS

-M p

ract

ices

1 |

2 |

3 |

6

ELLs

dev

elop

lang

uage

thro

ugh

expl

anat

ion.

F ➤

Stud

ents

eng

age

and

pers

ever

e

at p

oint

s of

diffi

culty

, cha

lleng

e, o

r er

ror.

C

CSS-

M p

ract

ice

1

Prod

uctiv

e st

rugg

le

prod

uces

gro

wth

.G

➤

Abo

ut L

ooki

ng fo

r St

anda

rds

in t

he M

athe

mat

ics

Clas

sroo

mTh

e Co

mm

on C

ore

Stat

e St

anda

rds

(CCS

S) d

e!ne

eig

ht s

tand

ards

for

stud

ents

‘ Mat

hem

atic

al P

ract

ice.

You

will

!nd

evi

denc

e of

the

stud

ents

’ pra

ctic

es b

y ob

serv

ing

thei

r ac

tions

and

by

revi

ewin

g th

eir

wor

k. T

his

card

is in

tend

ed to

focu

s at

tent

ion

on s

ome

of th

e vi

tal s

tude

nt a

ctio

ns th

at w

ill b

e ob

serv

able

in

CCSS

-M c

lass

room

s (s

ee re

vers

e). H

owev

er, n

ot a

ll st

anda

rds

will

be

evid

ent a

t all

times

or

appl

icab

le fo

r ev

ery

activ

ity.

The

prac

tices

are

ava

ilabl

e at

cor

esta

ndar

ds.o

rg

A !

Equi

ty r

equi

res

part

icip

atio

n: E

xpla

inin

g on

e's

idea

s an

d he

arin

g th

e re

actio

ns o

f oth

ers

prom

otes

lear

ning

. Thu

s in

cla

ssro

oms

in w

hich

a fe

w

stud

ents

do

all t

he ta

lkin

g, le

arni

ng o

ppor

tuni

ties

are

dist

ribu

ted

ineq

uita

bly.

Ove

r tim

e si

lent

stu

dent

s m

ay c

ome

to b

elie

ve th

ey a

re n

ot e

xpec

ted

to ta

lk, a

nd m

ay d

isen

gage

ent

irely

. Whe

n al

l stu

dent

s ar

e gi

ven

the

time

to e

xpla

in th

eir

thin

king

, a g

reat

er in

vest

men

t of e

very

stu

dent

in th

e in

stru

ctio

nal a

ctiv

ity is

dem

ande

d an

d re

war

ded,

and

the

oppo

rtun

ity fo

r st

uden

ts to

ser

ve a

s le

arni

ng re

sour

ces

for

each

oth

er is

max

imiz

ed. "

B !

Logi

c co

nnec

ts s

ente

nces

: A h

allm

ark

of th

e un

ders

tand

ing

prio

ritiz

ed b

y th

e CC

SS-M

is th

e ab

ility

to u

se m

athe

mat

ical

reas

onin

g to

con

stru

ct a

nd

defe

nd a

n ar

gum

ent (

this

is w

hat I

did

and

why

it m

akes

sen

se).

Brie

f, si

ngle

-sen

tenc

e st

uden

t utt

eran

ces

are

gene

rally

insu#

cien

t for

a v

iabl

e ar

gum

ent.

C !

Und

erst

andi

ng e

ach

othe

r’s r

easo

ning

dev

elop

s re

ason

ing

pro!

cien

cy: S

tude

nts

lear

n ab

out m

athe

mat

ics

by e

xplo

ring

thei

r ow

n an

d ot

hers

' re

ason

ing

in p

robl

em-s

olvi

ng s

ituat

ions

. Act

ivel

y lis

teni

ng to

pee

rs in

crea

ses

the

time

focu

sed

on m

athe

mat

ical

thin

king

and

pro

mot

es th

e co

gniti

ve $

exib

ility

that

is h

ighl

y va

lued

in c

olle

ge a

nd c

aree

r."

D !

Revi

sing

exp

lana

tion

s so

lidi!

es u

nder

stan

ding

: As

stud

ents

bec

ome

mor

e m

athe

mat

ical

ly p

ro!c

ient

and

thei

r re

ason

ing

impr

oves

, the

y sh

ould

be

abl

e to

iden

tify $a

ws

in th

eir

own

and

othe

rs' t

hink

ing.

Rev

isin

g w

ork

as a

rout

ine

mat

ter

lead

s to

bet

ter

prob

lem

sol

ving

.

E !

Acad

emic

lang

uage

pro

mot

es p

reci

se th

inki

ng: M

athe

mat

ical

ly p

ro!c

ient

stu

dent

s co

mpr

ehen

d an

d pr

oduc

e m

athe

mat

ical

repr

esen

tatio

ns

(sym

bolic

exp

ress

ions

, gra

phs,

tabl

es, n

umbe

r lin

es, e

tc.)

that

are

em

bedd

ed in

ord

inar

y an

d ac

adem

ic e

xpla

natio

ns a

nd ju

sti!

catio

ns. S

tude

nts

com

preh

end

and

prod

uce

the

para

grap

hs, s

ente

nces

, phr

ases

and

wor

ds c

hara

cter

istic

of j

usti!

catio

ns, e

xpla

natio

ns a

nd w

ord

prob

lem

s ty

pica

l fo

r th

eir

grad

e le

vel.

F !

ELLs

dev

elop

lang

uage

thro

ugh

expl

anat

ion:

Eng

lish

lear

ners

may

hes

itate

to s

peak

in c

lass

pre

cise

ly b

ecau

se th

eir

cont

rol o

f Eng

lish

is li

mite

d.

But p

ract

ice

spea

king

allo

ws

them

to b

ecom

e m

ore

pro!

cien

t. Br

idgi

ng th

e la

ngua

ge b

arri

er is

impo

rtan

t for

ELL

s to

thri

ve in

the

type

s of

cl

assr

oom

s th

e CC

SS-M

pro

mot

es.

G !

Prod

ucti

ve s

trug

gle

prod

uces

gro

wth

: Whe

n st

uden

ts"p

ersi

st in

mak

ing

sens

e of

a c

halle

ngin

g pr

oble

m a

nd tr

ying

di%

eren

t str

ateg

ies

for

solu

tion,

th

ey a

re m

ore

likel

y to

lear

n th

e m

athe

mat

ics

than

stu

dent

s w

ho g

ive

up q

uick

ly o

r av

oid

chal

leng

e to

the

grea

test

ext

ent p

ossi

ble.

mat

h.se

rpm

edia

.org

/5x8

card

re

vise

d 9/

26/1

4