6th

Grad

e Co

mmon

Cor

e St

ate

Stan

dard

s

Math

emat

ics

Math

emat

ical P

ract

ices

1. M

ake

sens

e of

pro

blem

s an

d pe

rsev

ere

in s

olvi

ng t

hem

. 2.

Rea

son

abst

ract

ly a

nd q

uant

itat

ivel

y.

3. C

onst

ruct

via

ble

argu

men

ts a

nd c

riti

que

the

reas

onin

g of

oth

ers.

4.

Mod

el w

ith

mat

hem

atic

s.

5. U

se a

ppro

pria

te t

ools

str

ateg

ical

ly.

6. A

tten

d to

pre

cisi

on.

7. L

ook

for

and

mak

e us

e of

str

uctu

re.

8. L

ook

for

and

expr

ess

regu

lari

ty in

rep

eate

d re

ason

ing.

www.amazingclassroom

.blogspo

t.com

Man

y  of  th

e  grap

hics  by  www.th

istlegirld

esigns.com

6th

Grad

e Co

mmon

Cor

e St

ate

Stan

dard

s

Math

emat

ics

Ratio

s an

d Pr

opor

tiona

l Rela

tions

hips

6.RP

.1. U

nder

stan

d th

e co

ncep

t of

a r

atio

and

use

rat

io la

ngua

ge t

o de

-sc

ribe

a r

atio

rel

atio

nshi

p be

twee

n tw

o qu

anti

ties

. For

exa

mpl

e, “T

he

rati

o of

win

gs t

o be

aks

in t

he b

ird

hous

e at

the

zoo

was

2:1

, bec

ause

fo

r ev

ery

2 wi

ngs

ther

e wa

s 1

beak

.” “F

or e

very

vot

e ca

ndid

ate

A re

-ce

ived

, can

dida

te C

rec

eive

d ne

arly

thr

ee v

otes

.”

6.RP

.2. U

nder

stan

d th

e co

ncep

t of

a u

nit

rate

a/b

ass

ocia

ted

with

a r

a-ti

o a:

b wi

th b

≠ 0

, and

use

rat

e la

ngua

ge in

the

con

text

of

a ra

tio

rela

-ti

onsh

ip. F

or e

xam

ple,

“Thi

s re

cipe

has

a r

atio

of

3 cu

ps o

f fl

our

to 4

cu

ps o

f su

gar,

so

ther

e is

3/4

cup

of

flou

r fo

r ea

ch c

up o

f su

gar.”

“We

paid

$75

for

15

ham

burg

ers,

whi

ch is

a r

ate

of $

5 pe

r ha

mbu

rger

.”

Und

er

stan

d r

atio

con

cep

ts

and

use

rat

io r

eas

onin

g t

o so

lve

pr

oble

ms

- P

art

1

6th

Grad

e Co

mmon

Cor

e St

ate

Stan

dard

s

Math

emat

ics

Ratio

s an

d Pr

opor

tiona

l Rela

tions

hips

6.RP

.3. U

se r

atio

and

rat

e re

ason

ing

to s

olve

rea

l-wor

ld a

nd m

athe

mat

ical

pro

blem

s, e

.g.,

by r

easo

ning

ab

out

tabl

es o

f eq

uiva

lent

rat

ios,

tap

e di

agra

ms,

dou

ble

num

ber

line

diag

ram

s, o

r eq

uati

ons.

M

ake

tabl

es o

f eq

uiva

lent

rat

ios

rela

ting

qua

ntit

ies

with

who

le-n

umbe

r m

easu

rem

ents

, fin

d m

issi

ng

valu

es in

the

tab

les,

and

plo

t th

e pa

irs

of v

alue

s on

the

coo

rdin

ate

plan

e. U

se t

able

s to

com

pare

rat

i-os

.

Solv

e un

it r

ate

prob

lem

s in

clud

ing

thos

e in

volv

ing

unit

pri

cing

and

con

stan

t sp

eed.

For

exa

mpl

e, if

it

took

7 h

ours

to

mow

4 la

wns,

the

n at

tha

t ra

te, h

ow m

any

lawn

s co

uld

be m

owed

in 3

5 ho

urs?

At

what

rat

e we

re la

wns

bein

g m

owed

?

Find

a p

erce

nt o

f a

quan

tity

as

a ra

te p

er 1

00 (e

.g.,

30%

of

a qu

anti

ty m

eans

30/

100

tim

es t

he q

uan-

tity

); so

lve

prob

lem

s in

volv

ing

find

ing

the

whol

e, g

iven

a p

art

and

the

perc

ent.

Use

rat

io r

easo

ning

to

conv

ert

mea

sure

men

t un

its;

man

ipul

ate

and

tran

sfor

m u

nits

app

ropr

iate

ly

when

mul

tipl

ying

or

divi

ding

qua

ntit

ies.

Und

er

stan

d r

atio

con

cep

ts

and

use

rat

io r

eas

onin

g t

o so

lve

pr

oble

ms

- P

art

2

6th

Grad

e Co

mmon

Cor

e St

ate

Stan

dard

s

Math

emat

ics

The

Numbe

r Sy

stem

A

pp

ly a

nd e

xt

end

pr

ev

ious

und

er

stan

din

gs

of m

ult

iplic

atio

n an

d d

ivis

ion

to

div

ide

fr

act

ions

fr

act

ions

by

fr

act

ions

.

6.N

S.1.

Inte

rpre

t an

d co

mpu

te q

uoti

ents

of

frac

tion

s, a

nd s

olve

wor

d pr

oble

ms

invo

lvin

g di

visi

on o

f fr

acti

ons

by f

ract

ions

, e.g

., by

usi

ng v

isua

l fra

ctio

n m

odel

s an

d eq

uati

ons

to r

epre

sent

the

pro

blem

. For

exa

mpl

e, c

reat

e a

stor

y co

ntex

t fo

r (2

/3) ÷

(3/4

) and

use

a v

isua

l fra

ctio

n m

odel

to

show

the

quo

tien

t; u

se t

he

rela

tion

ship

bet

ween

mul

tipl

icat

ion

and

divi

sion

to

expl

ain

that

(2/3

) ÷ (3

/4) =

8/

9 be

caus

e 3/

4 of

8/9

is 2

/3. (

In g

ener

al, (

a/b)

÷ (c

/d) =

ad/

bc.)

How

muc

h ch

ocol

ate

will

each

per

son

get

if 3

peo

ple

shar

e 1/

2 lb

of

choc

olat

e eq

ually

? H

ow m

any

3/4-

cup

serv

ings

are

in 2

/3 o

f a

cup

of y

ogur

t? H

ow w

ide

is a

rec

tan-

gula

r st

rip

of la

nd w

ith

leng

th 3

/4 m

i and

are

a 1/

2 sq

uare

mi?

Com

pute

flu

entl

y wi

th m

ulti

-dig

it n

umbe

rs a

nd f

ind

com

mon

fac

tors

and

mul

tipl

es.

6th

Grad

e Co

mmon

Cor

e St

ate

Stan

dard

s

Math

emat

ics

The

Numbe

r Sy

stem

C

omp

ute

flu

ent

ly w

ith

mul

ti-

dig

it n

umb

er

s an

d f

ind

com

mon

fac

tor

s an

d m

ult

iple

s.

6.N

S.2.

Flu

entl

y di

vide

mul

ti-d

igit

num

bers

usi

ng t

he s

tand

ard

algo

rith

m.

6.N

S.3.

Flu

entl

y ad

d, s

ubtr

act,

mul

tipl

y, a

nd d

ivid

e m

ulti

-dig

it d

ecim

als

usin

g th

e st

anda

rd a

lgor

ithm

for

eac

h op

erat

ion.

6.N

S.4.

Fin

d th

e gr

eate

st c

omm

on f

acto

r of

two

who

le n

umbe

rs le

ss t

han

or

equa

l to

100

and

the

leas

t co

mm

on m

ulti

ple

of t

wo w

hole

num

bers

less

tha

n or

eq

ual t

o 12

. Use

the

dis

trib

utiv

e pr

oper

ty t

o ex

pres

s a

sum

of

two

whol

e nu

m-

bers

1–1

00 w

ith

a co

mm

on f

acto

r as

a m

ulti

ple

of a

sum

of

two

whol

e nu

mbe

rs

with

no

com

mon

fac

tor.

For

exa

mpl

e, e

xpre

ss 3

6 +

8 as

4 (9

+ 2

). Ap

ply

and

ex-

tend

pre

viou

s un

ders

tand

ings

of

num

bers

to

the

syst

em o

f ra

tiona

l num

bers

.

6th

Grad

e Co

mmon

Cor

e St

ate

Stan

dard

s

Math

emat

ics

The

Numbe

r Sy

stem

A

pp

ly a

nd e

xt

end

pr

ev

ious

und

er

stan

din

gs

of n

umb

er

s t

o t

he

sy

ste

m

of r

atio

nal n

umb

er

s -

Par

t 1

6.N

S.5.

Und

erst

and

that

pos

itiv

e an

d ne

gati

ve n

umbe

rs a

re u

sed

toge

ther

to

desc

ribe

qua

ntit

ies

havi

ng o

ppos

ite

dire

c-ti

ons

or v

alue

s (e

.g.,

tem

pera

ture

abo

ve/b

elow

zer

o, e

leva

tion

abo

ve/b

elow

sea

leve

l, cr

edit

s/de

bits

, pos

itiv

e/ne

gati

ve

elec

tric

cha

rge)

; use

pos

itiv

e an

d ne

gati

ve n

umbe

rs t

o re

pres

ent

quan

titi

es in

rea

l-wo

rld

cont

exts

, exp

lain

ing

the

mea

n-in

g of

0 in

eac

h si

tuat

ion.

6.N

S.6.

Und

erst

and

a ra

tion

al n

umbe

r as

a p

oint

on

the

num

ber

line.

Ext

end

num

ber

line

diag

ram

s an

d co

ordi

nate

axe

s fa

mili

ar f

rom

pre

viou

s gr

ades

to

repr

esen

t po

ints

on

the

line

and

in t

he p

lane

wit

h ne

gati

ve n

umbe

r co

ordi

nate

s.

Re

cogn

ize

oppo

site

sig

ns o

f nu

mbe

rs a

s in

dica

ting

loca

tion

s on

opp

osit

e si

des

of 0

on

the

num

ber

line;

rec

ogni

ze t

hat

the

oppo

site

of

the

oppo

site

of

a nu

mbe

r is

the

num

ber

itse

lf, e

.g., –(–3

) = 3

, and

tha

t 0

is it

s ow

n op

posi

te.

U

nder

stan

d si

gns

of n

umbe

rs in

ord

ered

pai

rs a

s in

dica

ting

loca

tion

s in

qua

dran

ts o

f th

e co

ordi

nate

pla

ne; r

ecog

nize

th

at w

hen

two

orde

red

pair

s di

ffer

onl

y by

sig

ns, t

he lo

cati

ons

of t

he p

oint

s ar

e re

late

d by

ref

lect

ions

acr

oss

one

or

both

axe

s.

Fi

nd a

nd p

osit

ion

inte

gers

and

oth

er r

atio

nal n

umbe

rs o

n a

hori

zont

al o

r ve

rtic

al n

umbe

r lin

e di

agra

m; f

ind

and

posi

-ti

on p

airs

of

inte

gers

and

oth

er r

atio

nal n

umbe

rs o

n a

coor

dina

te p

lane

.

6t

h Gr

ade

Common

Cor

e St

ate

Stan

dard

s

Math

emat

ics

The

Numbe

r Sy

stem

A

pp

ly a

nd e

xt

end

pr

ev

ious

und

er

stan

din

gs

of n

umb

er

s t

o t

he

sy

ste

m

of r

atio

nal n

umb

er

s -

Par

t 2

6.N

S.7.

Und

erst

and

orde

ring

and

abs

olut

e va

lue

of r

atio

nal n

umbe

rs.

In

terp

ret

stat

emen

ts o

f in

equa

lity

as s

tate

men

ts a

bout

the

rel

ativ

e po

siti

on o

f tw

o nu

mbe

rs o

n a

num

ber

line

diag

ram

. For

exa

mpl

e, in

terp

ret –3

> –7

as

a st

ate-

men

t th

at –

3 is

loca

ted

to t

he r

ight

of –7

on

a nu

mbe

r lin

e or

ient

ed f

rom

left

to

righ

t.

Wri

te, i

nter

pret

, and

exp

lain

sta

tem

ents

of

orde

r fo

r ra

tion

al n

umbe

rs in

rea

l-wo

rld

cont

exts

. For

exa

mpl

e, w

rite

–3 o C

> –7

o C t

o ex

pres

s th

e fa

ct t

hat –3

o C is

wa

rmer

tha

n –7

o C.

U

nder

stan

d th

e ab

solu

te v

alue

of

a ra

tion

al n

umbe

r as

its

dist

ance

fro

m 0

on

the

num

ber

line;

inte

rpre

t ab

solu

te v

alue

as

mag

nitu

de f

or a

pos

itiv

e or

neg

ativ

e qu

anti

ty in

a r

eal-w

orld

sit

uati

on. F

or e

xam

ple,

for

an

acco

unt

bala

nce

of –

30 d

ol-

lars

, wri

te |–

30| =

30

to d

escr

ibe

the

size

of

the

debt

in d

olla

rs.

6th

Grad

e Co

mmon

Cor

e St

ate

Stan

dard

s

Math

emat

ics

The

Numbe

r Sy

stem

A

pp

ly a

nd e

xt

end

pr

ev

ious

und

er

stan

din

gs

of n

umb

er

s t

o t

he

sy

ste

m

of r

atio

nal n

umb

er

s -

Par

t 3

6.N

S.8.

Sol

ve r

eal-w

orld

and

mat

hem

atic

al p

robl

ems

by g

raph

ing

poin

ts in

all

four

qua

dran

ts o

f th

e co

ordi

nate

pla

ne. I

nclu

de u

se o

f co

ordi

nate

s an

d ab

solu

te v

alue

to

find

dis

tanc

es b

etwe

en p

oint

s wi

th t

he s

ame

firs

t co

ordi

nate

or

the

sam

e se

cond

coo

rdin

ate.

6th

Grad

e Co

mmon

Cor

e St

ate

Stan

dard

s

Math

emat

ics

Expr

essio

ns a

nd E

quat

ions

Ap

ply

and

ex

te

nd p

re

vio

us u

nde

rst

and

ing

s of

ar

ith

me

tic

to

alge

br

aic

ex

pr

ess

ions

. - P

art

1

6.EE

.1. W

rite

and

eva

luat

e nu

mer

ical

exp

ress

ions

invo

lvin

g wh

ole-

num

ber

expo

nent

s.

6.EE

.2. W

rite

, rea

d, a

nd e

valu

ate

expr

essi

ons

in w

hich

lett

ers

stan

d fo

r nu

mbe

rs.

W

rite

exp

ress

ions

tha

t re

cord

ope

rati

ons

with

num

bers

and

wit

h le

tter

s st

andi

ng f

or n

umbe

rs. F

or

exam

ple,

exp

ress

the

cal

cula

tion

“Sub

trac

t y

from

5” a

s 5

– y.

Id

enti

fy p

arts

of

an e

xpre

ssio

n us

ing

mat

hem

atic

al t

erm

s (s

um, t

erm

, pro

duct

, fac

tor,

quo

tien

t, c

o-ef

fici

ent)

; vie

w on

e or

mor

e pa

rts

of a

n ex

pres

sion

as

a si

ngle

ent

ity.

For

exa

mpl

e, d

escr

ibe

the

ex-

pres

sion

2 (8

+ 7

) as

a pr

oduc

t of

two

fac

tors

; vie

w (8

+ 7

) as

both

a s

ingl

e en

tity

and

a s

um o

f tw

o te

rms.

Eval

uate

exp

ress

ions

at

spec

ific

val

ues

of t

heir

var

iabl

es. I

nclu

de e

xpre

ssio

ns t

hat

aris

e fr

om f

or-

mul

as u

sed

in r

eal-w

orld

pro

blem

s. P

erfo

rm a

rith

met

ic o

pera

tion

s, in

clud

ing

thos

e in

volv

ing

whol

e-nu

mbe

r ex

pone

nts,

in t

he c

onve

ntio

nal o

rder

whe

n th

ere

are

no p

aren

thes

es t

o sp

ecif

y a

part

icul

ar

orde

r (O

rder

of

Ope

rati

ons)

. For

exa

mpl

e, u

se t

he f

orm

ulas

V =

s3 a

nd A

= 6

s2 t

o fi

nd t

he v

olum

e an

d su

rfac

e ar

ea o

f a

cube

wit

h si

des

of le

ngth

s =

1/2

.

6th

Grad

e Co

mmon

Cor

e St

ate

Stan

dard

s

Math

emat

ics

Expr

essio

ns a

nd E

quat

ions

Ap

ply

and

ex

te

nd p

re

vio

us u

nde

rst

and

ing

s of

ar

ith

me

tic

to

alge

br

aic

ex

pr

ess

ions

. - P

art

2

6.EE

.3. A

pply

the

pro

pert

ies

of o

pera

tion

s to

gen

erat

e eq

uiva

lent

exp

res-

sion

s. F

or e

xam

ple,

app

ly t

he d

istr

ibut

ive

prop

erty

to

the

expr

essi

on 3

(2

+ x)

to

prod

uce

the

equi

vale

nt e

xpre

ssio

n 6

+ 3x

; app

ly t

he d

istr

ibut

ive

prop

erty

to

the

expr

essi

on 2

4x +

18y

to

prod

uce

the

equi

vale

nt e

xpre

s-si

on 6

(4x

+ 3y

); ap

ply

prop

erti

es o

f op

erat

ions

to

y +

y +

y to

pro

duce

the

eq

uiva

lent

exp

ress

ion

3y.

6.

EE.4

. Ide

ntif

y wh

en t

wo e

xpre

ssio

ns a

re e

quiv

alen

t (i.

e., w

hen

the

two

expr

essi

ons

nam

e th

e sa

me

num

ber

rega

rdle

ss o

f wh

ich

valu

e is

su

bsti

tute

d in

to t

hem

). Fo

r ex

ampl

e, t

he e

xpre

ssio

ns y

+ y

+ y

and

3y

are

equi

vale

nt b

ecau

se t

hey

nam

e th

e sa

me

num

ber

rega

rdle

ss o

f wh

ich

num

ber

y st

ands

for

. Rea

son

abou

t an

d so

lve

one-

vari

able

equ

a-ti

ons

and

ineq

ualit

ies.

6th

Grad

e Co

mmon

Cor

e St

ate

Stan

dard

s

Math

emat

ics

Expr

essio

ns a

nd E

quat

ions

Re

ason

ab

out

and

sol

ve

one

-v

aria

ble

equ

atio

ns a

nd in

equ

alit

ies.

6.EE

.5. U

nder

stan

d so

lvin

g an

equ

atio

n or

ineq

ualit

y as

a p

roce

ss o

f an

swer

ing

a qu

esti

on: w

hich

va

lues

fro

m a

spe

cifi

ed s

et, i

f an

y, m

ake

the

equa

tion

or

ineq

ualit

y tr

ue?

Use

sub

stit

utio

n to

de

term

ine

whet

her

a gi

ven

num

ber

in a

spe

cifi

ed s

et m

akes

an

equa

tion

or

ineq

ualit

y tr

ue.

6.EE

.6. U

se v

aria

bles

to

repr

esen

t nu

mbe

rs a

nd w

rite

exp

ress

ions

whe

n so

lvin

g a

real

-wor

ld o

r m

athe

mat

ical

pro

blem

; und

erst

and

that

a v

aria

ble

can

repr

esen

t an

unk

nown

num

ber,

or,

dep

end-

ing

on t

he p

urpo

se a

t ha

nd, a

ny n

umbe

r in

a s

peci

fied

set

.

6.EE

.7. S

olve

rea

l-wor

ld a

nd m

athe

mat

ical

pro

blem

s by

wri

ting

and

sol

ving

equ

atio

ns o

f th

e fo

rm x

+

p =

q an

d px

= q

for

cas

es in

whi

ch p

, q a

nd x

are

all

nonn

egat

ive

rati

onal

num

bers

.

6.EE

.8. W

rite

an

ineq

ualit

y of

the

for

m x

> c

or x

< c

to r

epre

sent

a c

onst

rain

t or

con

diti

on in

a r

e-al

-wor

ld o

r m

athe

mat

ical

pro

blem

. Rec

ogni

ze t

hat

ineq

ualit

ies

of t

he f

orm

x >

c or

x <

c ha

ve in

fi-

nite

ly m

any

solu

tion

s; r

epre

sent

sol

utio

ns o

f su

ch in

equa

litie

s on

num

ber

line

diag

ram

s.

6th

Grad

e Co

mmon

Cor

e St

ate

Stan

dard

s

Math

emat

ics

Expr

essio

ns a

nd E

quat

ions

Re

pr

ese

nt a

nd a

naly

ze

qua

ntit

ativ

e r

ela

tio

nsh

ips

be

tw

ee

n d

ep

end

ent

and

ind

ep

end

ent

var

iab

les.

.

6.EE

.9.U

se v

aria

bles

to

repr

esen

t tw

o qu

anti

ties

in a

rea

l-wor

ld

prob

lem

tha

t ch

ange

in r

elat

ions

hip

to o

ne a

noth

er; w

rite

an

equa

tion

to

expr

ess

one

quan

tity

, tho

ught

of

as t

he d

epen

dent

va

riab

le, i

n te

rms

of t

he o

ther

qua

ntit

y, t

houg

ht o

f as

the

inde

-pe

nden

t va

riab

le. A

naly

ze t

he r

elat

ions

hip

betw

een

the

depe

nd-

ent

and

inde

pend

ent

vari

able

s us

ing

grap

hs a

nd t

able

s, a

nd r

elat

e th

ese

to t

he e

quat

ion.

For

exa

mpl

e, in

a p

robl

em in

volv

ing

mot

ion

at c

onst

ant

spee

d, li

st a

nd g

raph

ord

ered

pai

rs o

f di

stan

ces

and

tim

es, a

nd w

rite

the

equ

atio

n d

= 65

t to

rep

rese

nt t

he r

elat

ion-

ship

bet

ween

dis

tanc

e an

d ti

me.

6th

Grad

e Co

mmon

Cor

e St

ate

Stan

dard

s

Math

emat

ics

Geom

etry

S

olv

e r

eal

-w

orld

and

mat

he

mat

ical

pr

oble

ms

inv

olv

ing

ar

ea,

sur

-

fac

e a

re

a, a

nd v

olum

e -

Par

t 1

6.G.

1. Fi

nd t

he a

rea

of r

ight

tri

angl

es, o

ther

tri

angl

es, s

peci

al q

uadr

ilate

rals

, and

po

lygo

ns b

y co

mpo

sing

into

rec

tang

les

or d

ecom

posi

ng in

to t

rian

gles

and

oth

er

shap

es; a

pply

the

se t

echn

ique

s in

the

con

text

of

solv

ing

real

-wor

ld a

nd m

athe

-m

atic

al p

robl

ems.

6.G.

2. F

ind

the

volu

me

of a

rig

ht r

ecta

ngul

ar p

rism

wit

h fr

acti

onal

edg

e le

ngth

s by

pac

king

it w

ith

unit

cub

es o

f th

e ap

prop

riat

e un

it f

ract

ion

edge

leng

ths,

and

sh

ow t

hat

the

volu

me

is t

he s

ame

as w

ould

be

foun

d by

mul

tipl

ying

the

edg

e le

ngth

s of

the

pri

sm. A

pply

the

for

mul

as V

= l

w h

and

V =

b h

to f

ind

volu

mes

of

righ

t re

ctan

gula

r pr

ism

s wi

th f

ract

iona

l edg

e le

ngth

s in

the

con

text

of

solv

ing

real

-wor

ld a

nd m

athe

mat

ical

pro

blem

s.

6th

Grad

e Co

mmon

Cor

e St

ate

Stan

dard

s

Math

emat

ics

Geom

etry

S

olv

e r

eal

-w

orld

and

mat

he

mat

ical

pr

oble

ms

inv

olv

ing

ar

ea,

sur

fac

e a

re

a, a

nd v

olum

e -

Par

t 2

6.G.

3. D

raw

poly

gons

in t

he c

oord

inat

e pl

ane

give

n co

ordi

nate

s fo

r th

e ve

rtic

es; u

se c

oord

inat

es t

o fi

nd t

he le

ngth

of

a si

de jo

inin

g po

ints

wit

h th

e sa

me

firs

t co

ordi

nate

or

the

sam

e se

cond

coo

rdin

ate.

App

ly t

hese

te

chni

ques

in t

he c

onte

xt o

f so

lvin

g re

al-w

orld

and

mat

hem

atic

al p

rob-

lem

s.

6.G.

4. R

epre

sent

thr

ee-d

imen

sion

al f

igur

es u

sing

net

s m

ade

up o

f re

ctan

-gl

es a

nd t

rian

gles

, and

use

the

net

s to

fin

d th

e su

rfac

e ar

ea o

f th

ese

figu

res.

App

ly t

hese

tec

hniq

ues

in t

he c

onte

xt o

f so

lvin

g re

al-w

orld

and

m

athe

mat

ical

pro

blem

s.

6th

Grad

e Co

mmon

Cor

e St

ate

Stan

dard

s

Math

emat

ics

Stat

istics

and

Pro

bability

De

ve

lop

und

er

stan

din

g o

f s

tat

ist

ical

var

iab

ility

.

6.SP

.1. R

ecog

nize

a s

tati

stic

al q

uest

ion

as o

ne t

hat

anti

cipa

tes

vari

abili

ty in

the

dat

a re

late

d to

the

que

stio

n an

d ac

coun

ts f

or it

in t

he a

nswe

rs. F

or e

xam

ple,

“How

old

am

I?”

is n

ot a

st

atis

tica

l que

stio

n, b

ut “H

ow o

ld a

re t

he s

tude

nts

in m

y sc

hool

?” is

a s

tati

stic

al q

uest

ion

beca

use

one

anti

cipa

tes

vari

abili

ty in

stu

dent

s’‛ ag

es.

6.SP

.2. U

nder

stan

d th

at a

set

of

data

col

lect

ed t

o an

swer

a s

tati

stic

al q

uest

ion

has

a di

stri

-bu

tion

whi

ch c

an b

e de

scri

bed

by it

s ce

nter

, spr

ead,

and

ove

rall

shap

e.

6.SP

.3. R

ecog

nize

tha

t a

mea

sure

of

cent

er f

or a

num

eric

al d

ata

set

sum

mar

izes

all

of it

s va

lues

wit

h a

sing

le n

umbe

r, w

hile

a m

easu

re o

f va

riat

ion

desc

ribe

s ho

w it

s va

lues

var

y wi

th a

si

ngle

num

ber.

6th

Grad

e Co

mmon

Cor

e St

ate

Stan

dard

s

Math

emat

ics

Stat

istics

and

Pro

bability

Sum

mar

ize

and

de

scr

ibe

dis

tr

ibut

ions

.

6.SP

.4. D

ispl

ay n

umer

ical

dat

a in

plo

ts o

n a

num

ber

line,

incl

udin

g do

t pl

ots,

his

togr

ams,

and

bo

x pl

ots.

6.

SP.5

. Sum

mar

ize

num

eric

al d

ata

sets

in r

elat

ion

to t

heir

con

text

, suc

h as

by:

Re

port

ing

the

num

ber

of o

bser

vati

ons.

Des

crib

ing

the

natu

re o

f th

e at

trib

ute

unde

r in

vest

igat

ion,

incl

udin

g ho

w it

was

mea

sure

d an

d it

s un

its

of m

easu

rem

ent.

·

Givi

ng q

uant

itat

ive

mea

sure

s of

cen

ter

(med

ian

and/

or m

ean)

and

var

iabi

lity

(inte

rqua

rtile

ra

nge

and/

or m

ean

abso

lute

dev

iati

on),

as w

ell a

s de

scri

bing

any

ove

rall

patt

ern

and

any

stri

king

dev

iati

ons

from

the

ove

rall

patt

ern

with

ref

eren

ce t

o th

e co

ntex

t in

whi

ch t

heda

ta

were

gat

here

d.

Re

lati

ng t

he c

hoic

e of

mea

sure

s of

cen

ter

and

vari

abili

ty t

o th

e sh

ape

of t

he d

ata

dist

ri-

buti

on a

nd t

he c

onte

xt in

whi

ch t

he d

ata

were

gat

here

d.