Grade 7

Grade 7: Suggested Sequence for CMP31 Suggested Instructional Time

Unit 1 Accentuate the Negative: Integers and Rational Numbers

22 days

Unit 2 Stretching and Shrinking: Understanding Similarity

18 days

NYCDOE Fall Benchmark Assessment

Unit 3 Comparing and Scaling: Ratios, Rates, Percents, and Proportions

16 days

Unit 4 Moving Straight Ahead: Linear Relationships 26 days

Unit 5 What Do You Expect? Probability and Expected Value

28 days

NYCDOE Spring Benchmark Assessment

Unit 6 Filling and Wrapping: Three-Dimensional Measurement

24 days

Unit 7 Samples and Populations: Making Comparisons and Predictions

23 days

State Examination

Unit 8 Shapes and Designs: Two-Dimensional Geometry

21 days

1This Scope and Sequence represents one way a school may teach the full year’s content and incorporates the state’s pre-post test standards. As the transition to the PARCC assessments progresses, schools may choose to make decisions around the sequence and pacing of Units that address post-test concepts prior to the state examination in consideration of the state’s testing program guidance (see http://www.p12.nysed.gov/assessment/math/math-ei.html).

Scope and Sequence for Grade 7 75

Ac

ce

ntu

Ate

th

e n

eg

Ati

ve

Inte

ger

s an

d R

atio

nal N

umb

ers

Inst

ruct

iona

l Ti

me

22 d

ays

Ess

enti

al Id

eas

•R

atio

nal n

umb

ers

can

be

com

par

ed, o

rder

ed, a

nd lo

cate

d o

n a

num

ber

lin

e. T

hey

can

also

be

used

to

ind

icat

e a

dis

tanc

e o

r d

iffer

ence

bet

wee

n p

oin

ts o

n a

num

ber

line

. Num

ber

line

s ar

e us

eful

mo

del

s fo

r so

lvin

g

pro

ble

ms

with

rat

iona

l num

ber

s.

•M

od

els

faci

litat

e un

der

stan

din

g t

he m

eani

ng o

f ad

diti

on,

sub

trac

tion,

m

ultip

licat

ion,

and

div

isio

n o

f po

sitiv

e an

d n

egat

ive

num

ber

s an

d im

pro

ve

und

erst

and

ing

of t

he s

tand

ard

alg

orit

hms

for

thes

e o

per

atio

ns.

•M

athe

mat

ical

sen

tenc

es, w

ith o

r w

itho

ut v

aria

ble

s, c

an m

od

el re

al-w

orld

p

rob

lem

s. S

om

etim

es re

writ

ing

a p

rob

lem

usi

ng a

diff

eren

t o

per

atio

n ca

n b

e he

lpfu

l in

find

ing

the

so

lutio

n.

•Pr

op

ertie

s o

f op

erat

ions

ext

end

to

all

ratio

nal n

umb

ers

and

und

erst

and

ing

th

ese

pro

per

ties

is h

elp

ful i

n so

lvin

g p

rob

lem

s.

Go

als

•D

evel

op

und

erst

and

ing

of r

atio

nal n

umb

ers

by

incl

udin

g n

egat

ive

ratio

nal

num

ber

s.•

Dev

elo

p u

nder

stan

din

g o

f op

erat

ions

with

rat

iona

l num

ber

s an

d t

heir

pro

per

ties.

Mai

n C

om

mo

n C

ore

Sta

ndar

ds

Com

mon

Cor

e C

onte

nt S

tand

ard

s 7.

NS.

A.1

: Ap

ply

and

ext

end

pre

vio

us u

nder

stan

din

gs

of a

dd

itio

n an

d

sub

trac

tion

to a

dd

and

sub

trac

t ra

tiona

l num

ber

s; re

pre

sent

ad

diti

on

and

su

btr

actio

n o

n a

horiz

ont

al o

r ve

rtic

al n

umb

er li

ne d

iag

ram

.

7.N

S.A

.2: A

pp

ly a

nd e

xten

d p

revi

ous

und

erst

and

ing

s o

f mul

tiplic

atio

n an

d

div

isio

n an

d o

f fra

ctio

ns t

o m

ultip

ly a

nd d

ivid

e ra

tiona

l num

ber

s.

7.N

S.A

.3: S

olv

e re

al-w

orld

and

mat

hem

atic

al p

rob

lem

s in

volv

ing

the

four

o

per

atio

ns w

ith r

atio

nal n

umb

ers.

7.E

E.B

.3: S

olv

e m

ulti-

step

real

-life

and

mat

hem

atic

al p

rob

lem

s p

ose

d

with

po

sitiv

e an

d n

egat

ive

ratio

nal n

umb

ers

in a

ny fo

rm (w

hole

num

ber

s,

frac

tions

, and

dec

imal

s), u

sing

to

ols

str

ateg

ical

ly. A

pp

ly p

rop

ertie

s o

f o

per

atio

ns t

o c

alcu

late

with

num

ber

s in

any

form

; co

nver

t b

etw

een

form

s as

ap

pro

pria

te; a

nd a

sses

s th

e re

aso

nab

lene

ss o

f ans

wer

s us

ing

men

tal

com

put

atio

n an

d e

stim

atio

n st

rate

gie

s.

7.E

E.B

.4: U

se v

aria

ble

s to

rep

rese

nt q

uant

ities

in a

real

-wo

rld o

r m

athe

mat

ical

pro

ble

m, a

nd c

ons

truc

t si

mp

le e

qua

tions

and

ineq

ualit

ies

to

solv

e p

rob

lem

s b

y re

aso

ning

ab

out

the

qua

ntiti

es.

Com

mon

Cor

e St

and

ard

s fo

r M

athe

mat

ical

Pra

ctic

eM

P.1:

Mak

e se

nse

of p

rob

lem

s an

d p

erse

vere

in s

olv

ing

the

m.

MP.

2: R

easo

n ab

stra

ctly

and

qua

ntita

tivel

y.M

P.3:

Co

nstr

uct

viab

le a

rgum

ents

and

crit

ique

the

reas

oni

ng o

f oth

ers.

MP.

4: M

od

el w

ith m

athe

mat

ics.

MP.

5: U

se a

pp

rop

riate

to

ols

str

ateg

ical

ly.

MP.

6: A

tten

d t

o p

reci

sio

n.M

P.7:

Lo

ok

for

and

mak

e us

e o

f str

uctu

re.

MP.

8: L

oo

k fo

r an

d e

xpre

ss re

gul

arity

in re

pea

ted

reas

oni

ng.

Flue

ncy

Go

als*

•So

lve

mul

tiste

p p

rob

lem

s p

ose

d w

ith p

osi

tive

and

neg

ativ

e

ratio

nal n

umb

ers.

•Flue

ntlyadd,sub

tract,m

ultip

ly,a

nddivideratio

naln

umbers.

Ass

essm

ents

Uni

t R

ead

ines

s Pa

rtne

r Q

uiz

Che

ck-u

pU

nit

Pro

ject

Self-

Ass

essm

ent

Uni

t Te

st

*CM

P3 d

evel

op

s flu

ency

in p

roce

dur

al s

kills

fro

m a

foun

dat

ion

of c

onc

eptu

al u

nder

stan

din

g, a

n ap

pro

ach

that

lead

s to

long

-ter

m re

tent

ion

of s

kills

and

ab

ility

to

ap

ply

tho

se s

kills

in p

rob

lem

so

lvin

g.

New

Yor

k Ci

ty S

cope

and

Seq

uenc

e fo

r CM

P3

Gra

de 7

Teacher Implementation Toolkit76

New

Yor

k Ci

ty S

cope

and

Seq

uenc

e fo

r CM

P3

cont

inued

G

rade

7

Str

etc

hin

g A

nd

Sh

rin

kin

g U

nder

stan

din

g S

imila

rity

Inst

ruct

iona

l Ti

me

18 d

ays

Ess

enti

al Id

eas

•Si

mila

r fig

ures

hav

e co

ngru

ent

corr

esp

ond

ing

ang

les

and

co

rres

po

ndin

g

sid

es le

ngth

s ar

e in

a p

rop

ort

iona

l rel

atio

nshi

p.

•Th

e sc

ale

fact

or

for

two

sim

ilar

figur

es is

est

ablis

hed

by

find

ing

the

rat

io

of a

pai

r o

f co

rres

po

ndin

g s

ides

. Sca

le fa

cto

r, us

ed w

ith o

ther

to

ols

, allo

ws

you

to m

ake

dra

win

gs

of s

imila

r fig

ures

and

to

co

mp

are

the

per

imet

ers

and

are

as o

f sim

ilar

figur

es.

•If

two

fig

ures

are

sim

ilar,

then

yo

u ca

n us

e a

pro

po

rtio

nal r

elat

ions

hip

b

etw

een

corr

esp

ond

ing

sid

es t

o fi

nd u

nkno

wn

sid

e le

ngth

s.

Go

als

•Und

erstan

dwha

titmea

nsfo

rfig

urestobesimilar.

•Dev

elopstrateg

iesforusingsim

ilarfig

urestosolveproblems.

Mai

n C

om

mo

n C

ore

Sta

ndar

ds

Com

mon

Cor

e C

onte

nt S

tand

ard

s7.

RP.

A.2

: Rec

og

nize

and

rep

rese

nt p

rop

ort

iona

l rel

atio

nshi

ps

bet

wee

n q

uant

ities

.

7.R

P.A

.3: U

se p

rop

ort

iona

l rel

atio

nshi

ps

to s

olv

e m

ultis

tep

rat

io a

nd

per

cent

pro

ble

ms.

7.E

E.B

.3: S

olv

e m

ulti-

step

real

-life

and

mat

hem

atic

al p

rob

lem

s p

ose

d

with

po

sitiv

e an

d n

egat

ive

ratio

nal n

umb

ers

in a

ny fo

rm (w

hole

num

ber

s,

frac

tions

, and

dec

imal

s), u

sing

to

ols

str

ateg

ical

ly. A

pp

ly p

rop

ertie

s o

f o

per

atio

ns t

o c

alcu

late

with

num

ber

s in

any

form

; co

nver

t b

etw

een

form

s as

ap

pro

pria

te; a

nd a

sses

s th

e re

aso

nab

lene

ss o

f ans

wer

s us

ing

men

tal

com

put

atio

n an

d e

stim

atio

n st

rate

gie

s.

7.G

.A.1

: So

lve

pro

ble

ms

invo

lvin

g s

cale

dra

win

gs

of g

eom

etric

fig

ures

, in

clud

ing

co

mp

utin

g a

ctua

l len

gth

s an

d a

reas

fro

m a

sca

le d

raw

ing

and

re

pro

duc

ing

a s

cale

dra

win

g a

t a

diff

eren

t sc

ale.

7.G

.A.2

: Dra

w (f

reeh

and

, with

rul

er a

nd p

rotr

acto

r, an

d w

ith t

echn

olo

gy)

geo

metric

sha

peswith

given

cond

itions.F

ocu

sonco

nstruc

tingtria

ngles

fro

m t

hree

mea

sure

s o

f ang

les

or

sid

es, n

otic

ing

whe

n th

e co

nditi

ons

d

eter

min

e a

uniq

ue t

riang

le, m

ore

tha

n o

ne t

riang

le, o

r no

tria

ngle

.

Com

mon

Cor

e St

and

ard

s fo

r M

athe

mat

ical

Pra

ctic

eM

P.1:

Mak

e se

nse

of p

rob

lem

s an

d p

erse

vere

in s

olv

ing

the

m.

MP.

2: R

easo

n ab

stra

ctly

and

qua

ntita

tivel

y.M

P.3:

Co

nstr

uct

viab

le a

rgum

ents

and

crit

ique

the

reas

oni

ng o

f oth

ers.

MP.

4: M

od

el w

ith m

athe

mat

ics.

MP.

5: U

se a

pp

rop

riate

to

ols

str

ateg

ical

ly.

MP.

6: A

tten

d t

o p

reci

sio

n.M

P.7:

Lo

ok

for

and

mak

e us

e o

f str

uctu

re.

MP.

8: L

oo

k fo

r an

d e

xpre

ss re

gul

arity

in re

pea

ted

reas

oni

ng.

Flue

ncy

Go

als*

•So

lve

mul

tiste

p p

rob

lem

s p

ose

d w

ith p

osi

tive

and

neg

ativ

e

ratio

nal n

umb

ers.

•Flue

ntlyadd,sub

tract,m

ultip

ly,a

nddivideratio

naln

umbers.

•Dividefractio

ns.**

Ass

essm

ents

Uni

t R

ead

ines

sC

heck

-up

1Pa

rtne

r Q

uiz

Che

ck-u

p 2

Uni

t Pr

oje

ctSe

lf-A

sses

smen

tU

nit

Test

NY

CD

OE

Fal

l Ben

chm

ark

Ass

essm

ent

*CM

P3 d

evel

op

s flu

ency

in p

roce

dur

al s

kills

fro

m a

foun

dat

ion

of c

onc

eptu

al u

nder

stan

din

g, a

n ap

pro

ach

that

lead

s to

long

-ter

m re

tent

ion

of s

kills

and

ab

ility

to

ap

ply

tho

se s

kills

in p

rob

lem

so

lvin

g.

**re

info

rcin

g fl

uenc

y ex

pec

tatio

ns fr

om

pre

vio

us g

rad

es

Scope and Sequence for Grade 7 77

New

Yor

k Ci

ty S

cope

and

Seq

uenc

e fo

r CM

P3

cont

inued

Gra

de 7

co

mpA

rin

g A

nd

Sc

Ali

ng

Rat

ios,

Rat

es, P

erce

nts,

and

Pro

por

tion

s

Inst

ruct

iona

l Ti

me

16 d

ays

Ess

enti

al Id

eas

•R

atio

s m

ake

com

par

iso

ns b

etw

een

two

par

ts o

f the

who

le o

r o

ne p

art

to

the

who

le. R

ates

, uni

t ra

tes,

and

per

cent

s ar

e al

l typ

es o

f rat

ios.

•B

eing

ab

le t

o c

hang

e th

e fo

rm o

f a r

atio

is a

use

ful p

rob

lem

- so

lvin

g s

trat

egy.

•A

pro

po

rtio

nal r

elat

ions

hip

has

par

ticul

ar c

hara

cter

istic

s w

hen

rep

rese

nted

in

a t

able

, gra

ph

or

equa

tion.

•K

now

ing

the

des

ired

rat

io b

etw

een

two

var

iab

les

allo

ws

you

to s

cale

the

ra

tio o

r fin

d a

mis

sing

par

t o

f a r

atio

.

Go

als

•Find

and

useratios,rates,a

ndperce

nts.

• Rep

resentand

reco

gnizeproportiona

lityintab

les,graphsand

equa

tions.

•D

evel

op

and

use

str

ateg

ies

for

solv

ing

pro

ble

ms

that

req

uire

p

rop

ort

iona

l rea

soni

ng.

Mai

n C

om

mo

n C

ore

Sta

ndar

ds

Com

mon

Cor

e C

onte

nt S

tand

ard

s7.

RP.

A.1

: Co

mp

ute

unit

rate

s as

soci

ated

with

rat

ios

of f

ract

ions

, inc

lud

ing

ra

tios

of l

eng

ths,

are

as a

nd o

ther

qua

ntiti

es m

easu

red

in li

ke o

r d

iffer

ent

units

.

7.R

P.A

.2: R

eco

gni

ze a

nd re

pre

sent

pro

po

rtio

nal r

elat

ions

hip

s b

etw

een

qua

ntiti

es.

7.R

P.A

.3: U

se p

rop

ort

iona

l rel

atio

nshi

ps

to s

olv

e m

ultis

tep

rat

io a

nd

per

cent

pro

ble

ms.

7.E

E.A

.2: U

nder

stan

d t

hat

rew

ritin

g a

n ex

pre

ssio

n in

diff

eren

t fo

rms

in a

p

rob

lem

co

ntex

t ca

n sh

ed li

ght

on

the

pro

ble

m a

nd h

ow

the

qua

ntiti

es in

it

are

rela

ted

.

Com

mon

Cor

e St

and

ard

s fo

r M

athe

mat

ical

Pra

ctic

eM

P.1:

Mak

e se

nse

of p

rob

lem

s an

d p

erse

vere

in s

olv

ing

the

m.

MP.

2: R

easo

n ab

stra

ctly

and

qua

ntita

tivel

y.M

P.3:

Co

nstr

uct

viab

le a

rgum

ents

and

crit

ique

the

reas

oni

ng o

f oth

ers.

MP.

4: M

od

el w

ith m

athe

mat

ics.

MP.

5: U

se a

pp

rop

riate

to

ols

str

ateg

ical

ly.

MP.

6: A

tten

d t

o p

reci

sio

n.M

P.7:

Lo

ok

for

and

mak

e us

e o

f str

uctu

re.

MP.

8: L

oo

k fo

r an

d e

xpre

ss re

gul

arity

in re

pea

ted

reas

oni

ng.

Flue

ncy

Go

als*

•So

lve

mul

tiste

p p

rob

lem

s p

ose

d w

ith p

osi

tive

and

neg

ativ

e ra

tiona

l nu

mb

ers.

•Flue

ntlyadd,sub

tract,m

ultip

ly,a

nddivideratio

naln

umbers.

•Dividefractio

ns.**

Ass

essm

ents

Uni

t R

ead

ines

sC

heck

-up

1Pa

rtne

r Q

uiz

Che

ck-u

p 2

Uni

t Pr

oje

ctSe

lf-A

sses

smen

tU

nit

Test

*CM

P3 d

evel

op

s flu

ency

in p

roce

dur

al s

kills

fro

m a

foun

dat

ion

of c

onc

eptu

al u

nder

stan

din

g, a

n ap

pro

ach

that

lead

s to

long

-ter

m re

tent

ion

of s

kills

and

ab

ility

to

ap

ply

tho

se s

kills

in p

rob

lem

so

lvin

g.

**re

info

rcin

g fl

uenc

y ex

pec

tatio

ns fr

om

pre

vio

us g

rad

es

Teacher Implementation Toolkit78

New

Yor

k Ci

ty S

cope

and

Seq

uenc

e fo

r CM

P3

cont

inued

Gra

de 7

mo

vin

g S

trA

igh

t A

he

Ad

Lin

ear

Rel

atio

nshi

ps

Inst

ruct

iona

l Ti

me

26 d

ays

Ess

enti

al Id

eas

•Tw

o v

aria

ble

s ar

e in

a li

near

rela

tions

hip

if o

ne v

aria

ble

is c

hang

ing

by

a co

nsta

nt a

mo

unt

whe

n th

e o

ther

var

iab

le c

hang

es b

y in

crem

ents

of 1

uni

t.

•Th

e ra

te o

f cha

nge

in a

line

ar re

latio

nshi

p is

rep

rese

nted

by

the

slo

pe

of

the

line

rep

rese

ntin

g t

he re

latio

nshi

p.

•Th

e eq

uatio

n y

= mx

is a

par

ticul

ar k

ind

of l

inea

r re

latio

nshi

p w

here

x a

nd

y ar

e p

rop

ort

iona

l to

eac

h o

ther

.

•So

lutio

ns fo

r lin

ear

equa

tions

of t

he fo

rm y

= mx

+ b

are

pai

rs o

f val

ues

(x

, y) w

hich

mak

e th

is e

qua

tion

true

. Gra

phi

cally

, so

lutio

n p

airs

are

po

ints

o

n th

e g

rap

h o

f the

line

.

•Pr

op

ertie

s o

f eq

ualit

y ca

n b

e us

ed t

o m

aint

ain

equi

vale

nt e

xpre

ssio

ns o

n ea

ch s

ide

of t

he e

qua

tion

whe

n fin

din

g a

so

lutio

n.

Go

als

•R

eco

gni

ze p

rob

lem

situ

atio

ns in

whi

ch t

wo

or

mo

re v

aria

ble

s ha

ve a

line

ar

rela

tions

hip

to

eac

h o

ther

.•

Und

erst

and

tha

t th

e eq

ualit

y si

gn

ind

icat

es t

hat

two

exp

ress

ions

ar

e eq

uiva

lent

.

Mai

n C

om

mo

n C

ore

Sta

ndar

ds

Com

mon

Cor

e C

onte

nt S

tand

ard

s7.

RP.

A.2

: Rec

og

nize

and

rep

rese

nt p

rop

ort

iona

l rel

atio

nshi

ps

b

etw

een

qua

ntiti

es.

7.E

E.A

.1: A

pp

ly p

rop

ertie

s o

f op

erat

ions

as

stra

teg

ies

to a

dd

, sub

trac

t,

fact

or,

and

exp

and

line

ar e

xpre

ssio

ns w

ith r

atio

nal c

oef

ficie

nts.

7.E

E.A

.2: U

nder

stan

d t

hat

rew

ritin

g a

n ex

pre

ssio

n in

diff

eren

t fo

rms

in a

p

rob

lem

co

ntex

t ca

n sh

ed li

ght

on

the

pro

ble

m a

nd h

ow

the

qua

ntiti

es in

it

are

rela

ted

.

7.E

E.B

.4: U

se v

aria

ble

s to

rep

rese

nt q

uant

ities

in a

real

-wo

rld o

r m

athe

mat

ical

pro

ble

m, a

nd c

ons

truc

t si

mp

le e

qua

tions

and

ineq

ualit

ies

to

solv

e p

rob

lem

s b

y re

aso

ning

ab

out

the

qua

ntiti

es.

Com

mon

Cor

e St

and

ard

s fo

r M

athe

mat

ical

Pra

ctic

eM

P.1:

Mak

e se

nse

of p

rob

lem

s an

d p

erse

vere

in s

olv

ing

the

m.

MP.

2: R

easo

n ab

stra

ctly

and

qua

ntita

tivel

y.M

P.3:

Co

nstr

uct

viab

le a

rgum

ents

and

crit

ique

the

reas

oni

ng o

f oth

ers.

MP.

4: M

od

el w

ith m

athe

mat

ics.

MP.

5: U

se a

pp

rop

riate

to

ols

str

ateg

ical

ly.

MP.

6: A

tten

d t

o p

reci

sio

n.M

P.7:

Lo

ok

for

and

mak

e us

e o

f str

uctu

re.

MP.

8: L

oo

k fo

r an

d e

xpre

ss re

gul

arity

in re

pea

ted

reas

oni

ng.

Flue

ncy

Go

als*

•So

lve

mul

tiste

p p

rob

lem

s p

ose

d w

ith p

osi

tive

and

neg

ativ

e ra

tiona

l nu

mb

ers

in a

ny fo

rm.

•So

lve

one

-var

iab

le e

qua

tions

of t

he fo

rm px

+ q

= r

and

p

(x +

q) =

r flu

ently

.

Ass

essm

ents

Uni

t R

ead

ines

sC

heck

-up

1Pa

rtne

r Q

uiz

Che

ck-u

p 2

Uni

t Pr

oje

ctSe

lf-A

sses

smen

tU

nit

Test

*CM

P3 d

evel

op

s flu

ency

in p

roce

dur

al s

kills

fro

m a

foun

dat

ion

of c

onc

eptu

al u

nder

stan

din

g, a

n ap

pro

ach

that

lead

s to

long

-ter

m re

tent

ion

of s

kills

and

ab

ility

to

ap

ply

tho

se s

kills

in p

rob

lem

so

lvin

g.

Scope and Sequence for Grade 7 79

New

Yor

k Ci

ty S

cope

and

Seq

uenc

e fo

r CM

P3

cont

inued

Gra

de 7

Wh

At

do

Yo

u e

xp

ec

t? P

rob

abili

ty a

nd E

xpec

ted

Val

ue

Inst

ruct

iona

l Ti

me

28 d

ays

Ess

enti

al Id

eas

•Pr

ob

abili

ties

are

ratio

s. P

rob

abili

ty c

an b

e us

ed t

o p

red

ict

out

com

es in

re

al-w

orld

eve

nts

or

to a

naly

ze g

ames

for

fairn

ess.

•Th

eore

tical

pro

bab

ility

is d

eter

min

ed b

y re

aso

ning

ab

out

the

like

liho

od

of

a sp

ecifi

c o

utco

me

bas

ed o

n al

l po

ssib

le o

utco

mes

of a

n ev

ent.

Lis

ts, t

ree

dia

gra

ms,

or

area

mo

del

s ca

n sh

ow

all

of t

he p

oss

ible

out

com

es a

nd c

an

be

used

to

det

erm

ine

the

theo

retic

al p

rob

abili

ty o

f a c

om

po

und

eve

nt.

•Th

e ex

per

imen

tal p

rob

abili

ty o

f an

even

t ca

n b

e fo

und

by

gat

herin

g d

ata

fro

m e

xper

imen

ts o

r o

bse

rvat

ions

, co

untin

g t

he n

umb

er o

f tim

es t

he

spec

ified

out

com

e o

ccur

red

, and

co

mp

arin

g t

hat

to t

he n

umb

er o

f tria

ls.

Long

run

rela

tive

freq

uenc

ies

colle

cted

fro

m e

xper

imen

ts m

ake

go

od

ap

pro

xim

atio

ns o

f the

ore

tical

pro

bab

ilitie

s.

Go

als

•E

xplo

re a

nd le

arn

bas

ic p

rob

abili

ty c

onc

epts

and

und

erst

and

tha

t th

ere

are

two

way

s to

bui

ld p

rob

abili

ty m

od

els:

by

gat

herin

g d

ata

fro

m

exp

erim

ents

(exp

erim

enta

l pro

bab

ility

) and

by

anal

yzin

g t

he p

oss

ible

eq

ually

like

ly o

utco

mes

(the

ore

tical

pro

bab

ility

).

•E

xplo

re a

nd d

evel

op

pro

bab

ility

mo

del

s b

y id

entif

ying

po

ssib

le o

utco

mes

an

d a

naly

ze p

rob

abili

ties

to s

olv

e p

rob

lem

s.

Mai

n C

om

mo

n C

ore

Sta

ndar

ds

Com

mon

Cor

e C

onte

nt S

tand

ard

s7.

SP.C

.5: U

nder

stan

d t

hat

the

pro

bab

ility

of a

cha

nce

even

t is

a n

umb

er

bet

wee

n 0

and

1 t

hat

exp

ress

es t

he li

kelih

oo

d o

f the

eve

nt o

ccur

ring

. Lar

ger

nu

mb

ers

ind

icat

e g

reat

er li

kelih

oo

d. A

pro

bab

ility

nea

r 0 in

dic

ates

an

unlik

ely

even

t, a

pro

bab

ility

aro

und

1/2

ind

icat

es a

n ev

ent

that

is n

eith

er u

nlik

ely

nor

likel

y, a

nd a

pro

bab

ility

nea

r 1

ind

icat

es a

like

ly e

vent

.

7.SP

.C.6

: Ap

pro

xim

ate

the

pro

bab

ility

of a

cha

nce

even

t b

y co

llect

ing

d

ata

on

the

chan

ce p

roce

ss t

hat

pro

duc

es it

and

ob

serv

ing

its

long

-run

re

lativ

e fr

eque

ncy,

and

pre

dic

t th

e ap

pro

xim

ate

rela

tive

freq

uenc

y g

iven

th

e p

rob

abili

ty.

7.SP

.C.7

: Dev

elo

p a

pro

bab

ility

mo

del

and

use

it t

o fi

nd p

rob

abili

ties

of

even

ts. C

om

par

e p

rob

abili

ties

fro

m a

mo

del

to

ob

serv

ed fr

eque

ncie

s; if

the

ag

reem

ent

is n

ot

go

od

, exp

lain

po

ssib

le s

our

ces

of t

he d

iscr

epan

cy.

7.SP

.C.8

:Findprobab

ilitie

sofc

ompoun

deve

ntsusingorgan

ized

lists,tab

les,

tr

ee d

iag

ram

s, a

nd s

imul

atio

n.

Com

mon

Cor

e St

and

ard

s fo

r M

athe

mat

ical

Pra

ctic

eM

P.1:

Mak

e se

nse

of p

rob

lem

s an

d p

erse

vere

in s

olv

ing

the

m.

MP.

2: R

easo

n ab

stra

ctly

and

qua

ntita

tivel

y.M

P.3:

Co

nstr

uct

viab

le a

rgum

ents

and

crit

ique

the

reas

oni

ng o

f oth

ers.

MP.

4: M

od

el w

ith m

athe

mat

ics.

MP.

5: U

se a

pp

rop

riate

to

ols

str

ateg

ical

ly.

MP.

6: A

tten

d t

o p

reci

sio

n.M

P.7:

Lo

ok

for

and

mak

e us

e o

f str

uctu

re.

MP.

8: L

oo

k fo

r an

d e

xpre

ss re

gul

arity

in re

pea

ted

reas

oni

ng.

Flue

ncy

Go

als*

•So

lve

mul

tiste

p p

rob

lem

s p

osed

with

pos

itive

and

neg

ativ

e ra

tiona

l num

ber

s.•

Flue

ntlyadd,sub

tract,m

ultip

ly,a

nddivideratio

naln

umbers.

Ass

essm

ents

Uni

t R

ead

ines

sC

heck

-up

1Pa

rtne

r Q

uiz

Che

ck-u

p 2

Uni

t Pr

oje

ctSe

lf-A

sses

smen

tU

nit

Test

NY

CD

OE

Sp

ring

Ben

chm

ark

Ass

essm

ent

*CM

P3 d

evel

op

s flu

ency

in p

roce

dur

al s

kills

fro

m a

foun

dat

ion

of c

onc

eptu

al u

nder

stan

din

g, a

n ap

pro

ach

that

lead

s to

long

-ter

m re

tent

ion

of s

kills

and

ab

ility

to

ap

ply

tho

se s

kills

in p

rob

lem

so

lvin

g.

Teacher Implementation Toolkit80

New

Yor

k Ci

ty S

cope

and

Seq

uenc

e fo

r CM

P3

cont

inued

Gra

de 7

Fill

ing

An

d W

rA

pp

ing

Thr

ee-D

imen

sion

al M

easu

rem

ent

Inst

ruct

iona

l Ti

me

24 d

ays

Ess

enti

al Id

eas

•Pr

ism

s ar

e na

med

for

thei

r b

ases

. The

nam

e o

f a p

rism

ind

icat

es t

he

num

ber

of v

ertic

es, e

dg

es, a

nd fa

ces

the

pris

m h

as.

•Sl

icin

g p

rism

s ve

rtic

ally

, ho

rizo

ntal

ly, o

r o

n a

slan

t, c

an e

xpo

se d

iffer

ent

shap

es o

f cro

ss-s

ectio

ns, d

epen

din

g o

n w

hich

of t

he o

rigin

al e

dg

es

are

inte

rsec

ted

.

•C

om

par

ing

, rea

soni

ng a

bo

ut, a

nd e

xten

din

g w

hat

you

kno

w a

bo

ut a

rea

and

vo

lum

e le

ads

to a

n un

der

stan

din

g o

f the

form

ulas

for

find

ing

the

su

rfac

e ar

ea a

nd v

olu

me

of p

rism

s, c

one

s, a

nd p

yram

ids.

•Pr

op

ort

iona

l cha

nges

to

dim

ensi

ons

of t

he s

ides

of a

pris

m le

ads

to

pre

dic

tab

le c

hang

es in

the

sur

face

are

a an

d t

he v

olu

me.

•A

pp

roxi

mat

ions

of t

he r

atio

of t

he c

ircum

fere

nce

of a

circ

le t

o t

he

circ

le’s

dia

met

er le

ads

to e

xact

form

ulas

for

the

area

and

circ

umfe

renc

e

of a

circ

le.

Go

als

•U

nder

stan

d s

urfa

ce a

rea

and

vo

lum

e o

f pris

ms

and

cyl

ind

ers

and

ho

w t

hey

are

rela

ted

.•

Und

erst

and

the

are

a an

d c

ircum

fere

nce

of c

ircle

s an

d h

ow

the

y ar

e re

late

d.

•U

nder

stan

d t

he re

latio

nshi

p b

etw

een

the

volu

me

of c

ylin

der

s an

d c

one

s,

sphe

res,

and

pyr

amid

s.

Mai

n C

om

mo

n C

ore

Sta

ndar

ds

Com

mon

Cor

e C

onte

nt S

tand

ard

s7.

RP.

A.2

: Rec

og

nize

and

rep

rese

nt p

rop

ort

iona

l rel

atio

nshi

ps

bet

wee

n q

uant

ities

.

7.N

S.A

.3: S

olv

e re

al-w

orld

and

mat

hem

atic

al p

rob

lem

s in

volv

ing

the

four

o

per

atio

ns w

ith r

atio

nal n

umb

ers.

7.G

.A.3

: Des

crib

e th

e tw

o-d

imen

sio

nal fi

gur

es t

hat

resu

lt fr

om

slic

ing

thr

ee-

dim

ensi

ona

l fig

ures

, as

in p

lane

sec

tions

of r

ight

rect

ang

ular

pris

ms

and

rig

ht

rect

ang

ular

pyr

amid

s.

7.G

.B.4

: Kno

w t

he fo

rmul

as fo

r th

e ar

ea a

nd c

ircum

fere

nce

of a

circ

le a

nd

use

them

to

so

lve

pro

ble

ms;

giv

e an

info

rmal

der

ivat

ion

of t

he re

latio

nshi

p

bet

wee

n th

e ci

rcum

fere

nce

and

are

a o

f a c

ircle

.

7.G

.B.6

: So

lve

real

-wo

rld a

nd m

athe

mat

ical

pro

ble

ms

invo

lvin

g a

rea,

vo

lum

e an

d s

urfa

ce a

rea

of t

wo

- an

d t

hree

-dim

ensi

ona

l ob

ject

s co

mp

ose

d o

f tr

iang

les,

qua

dril

ater

als,

po

lyg

ons

, cub

es, a

nd r

ight

pris

ms.

Com

mon

Cor

e St

and

ard

s fo

r M

athe

mat

ical

Pra

ctic

eM

P.1:

Mak

e se

nse

of p

rob

lem

s an

d p

erse

vere

in s

olv

ing

the

m.

MP.

2: R

easo

n ab

stra

ctly

and

qua

ntita

tivel

y.M

P.3:

Co

nstr

uct

viab

le a

rgum

ents

and

crit

ique

the

reas

oni

ng o

f oth

ers.

MP.

4: M

od

el w

ith m

athe

mat

ics.

MP.

5: U

se a

pp

rop

riate

to

ols

str

ateg

ical

ly.

MP.

6: A

tten

d t

o p

reci

sio

n.M

P.7:

Lo

ok

for

and

mak

e us

e o

f str

uctu

re.

MP.

8: L

oo

k fo

r an

d e

xpre

ss re

gul

arity

in re

pea

ted

reas

oni

ng.

Flue

ncy

Go

als*

•So

lve

mul

tiste

p p

rob

lem

s p

ose

d w

ith p

osi

tive

and

neg

ativ

e ra

tiona

l nu

mb

ers.

•Flue

ntlyadd,sub

tract,m

ultip

ly,a

nddivideratio

naln

umbers.

•So

lve

one

-var

iab

le e

qua

tions

of t

he fo

rm px

+ q

= r

and

p

(x +

q) =

r flu

ently

.

Ass

essm

ents

Uni

t R

ead

ines

sC

heck

-up

1Pa

rtne

r Q

uiz

Che

ck-u

p 2

Uni

t Pr

oje

ctSe

lf-A

sses

smen

tU

nit

Test

*CM

P3 d

evel

op

s flu

ency

in p

roce

dur

al s

kills

fro

m a

foun

dat

ion

of c

onc

eptu

al u

nder

stan

din

g, a

n ap

pro

ach

that

lead

s to

long

-ter

m re

tent

ion

of s

kills

and

ab

ility

to

ap

ply

tho

se s

kills

in p

rob

lem

so

lvin

g.

Scope and Sequence for Grade 7 81

New

Yor

k Ci

ty S

cope

and

Seq

uenc

e fo

r CM

P3

cont

inued

Gra

de 7

SAm

ple

S A

nd

po

pu

lAti

on

S D

ata

and

Sta

tist

ics

Inst

ruct

iona

l Ti

me

23 d

ays

Ess

enti

al Id

eas

•A

sur

vey

allo

ws

you

to g

athe

r d

ata

usin

g a

sam

ple

of a

po

pul

atio

n an

d

use

that

dat

a to

rep

rese

nt t

he p

op

ulat

ion.

Tab

les

and

gra

phs

, as

wel

l as

mea

sure

s o

f cen

ter

and

var

iab

ility

ena

ble

yo

u to

co

mp

are

dat

a fr

om

d

iffer

ent

sam

ple

s an

d d

raw

co

nclu

sio

ns a

bo

ut t

he s

amp

les

and

the

p

op

ulat

ions

.

•R

and

om

sam

ple

s ar

e w

itho

ut b

ias,

and

the

refo

re a

re u

sefu

l fo

r p

red

ictin

g

po

pul

atio

n ch

arac

teris

tics.

Pro

bab

ility

mo

del

s al

low

yo

u to

sel

ect

a ra

ndo

m s

amp

le fr

om

a p

op

ulat

ion.

Ran

do

m s

amp

les,

eve

n o

f the

sam

e si

ze, v

ary

fro

m e

ach

oth

er a

nd fr

om

the

und

erly

ing

po

pul

atio

n.

•Yo

u ca

n co

mp

are

two

sam

ple

s w

ith a

pp

roxi

mat

ely

the

sam

e m

easu

re o

f va

riab

ility

by

usin

g t

hat

mea

sure

to

det

erm

ine

the

dis

tanc

e b

etw

een

the

cent

ers

of t

he s

amp

les.

Go

als

•U

nder

stan

d a

nd u

se t

he p

roce

ss o

f sta

tistic

al in

vest

igat

ion.

•

Und

erst

and

dat

a d

istr

ibut

ions

and

wha

t it

mea

ns t

o a

naly

ze t

hem

.•

Und

erst

and

tha

t st

atis

tics

can

be

used

to

gai

n in

form

atio

n ab

out

a

po

pul

atio

n b

y ex

amin

ing

a re

pre

sent

ativ

e sa

mp

le o

f the

po

pul

atio

n.

Mai

n C

om

mo

n C

ore

Sta

ndar

ds

Com

mon

Cor

e C

onte

nt S

tand

ard

s7.

SP.A

.1: U

nder

stan

d t

hat

stat

istic

s ca

n b

e us

ed t

o g

ain

info

rmat

ion

abo

ut a

p

op

ulat

ion

by

exam

inin

g a

sam

ple

of t

he p

op

ulat

ion;

gen

eral

izat

ions

ab

out

a

po

pul

atio

n fr

om

a s

amp

le a

re v

alid

onl

y if

the

sam

ple

is re

pre

sent

ativ

e o

f tha

t p

op

ulat

ion.

Und

erst

and

tha

t ra

ndo

m s

amp

ling

ten

ds

to p

rod

uce

rep

rese

ntat

ive

sam

ple

s an

d s

upp

ort

val

id in

fere

nces

.

7.SP

.A.2

: Use

dat

a fr

om

a r

and

om

sam

ple

to

dra

w in

fere

nces

ab

out

a

po

pul

atio

n w

ith a

n un

kno

wn

char

acte

ristic

of i

nter

est.

Gen

erat

e m

ultip

le

sam

ple

s (o

r si

mul

ated

sam

ple

s) o

f the

sam

e si

ze t

o g

aug

e th

e va

riatio

n in

es

timat

es o

r p

red

ictio

ns.

7.SP

.B.3

: Inf

orm

ally

ass

ess

the

deg

ree

of v

isua

l ove

rlap

of t

wo

num

eric

al d

ata

dis

trib

utio

ns w

ith s

imila

r va

riab

ilitie

s, m

easu

ring

the

diff

eren

ce b

etw

een

the

cent

ers

by

exp

ress

ing

it a

s a

mul

tiple

of a

mea

sure

of v

aria

bili

ty.

7.SP

.B.4

: Use

mea

sure

s o

f cen

ter

and

mea

sure

s o

f var

iab

ility

for

num

eric

al

dat

a fr

om

ran

do

m s

amp

les

to d

raw

info

rmal

co

mp

arat

ive

infe

renc

es a

bo

ut

two

po

pul

atio

ns.

Com

mon

Cor

e St

and

ard

s fo

r M

athe

mat

ical

Pra

ctic

eM

P.1:

Mak

e se

nse

of p

rob

lem

s an

d p

erse

vere

in s

olv

ing

the

m.

MP.

2: R

easo

n ab

stra

ctly

and

qua

ntita

tivel

y.M

P.3:

Co

nstr

uct

viab

le a

rgum

ents

and

crit

ique

the

reas

oni

ng o

f oth

ers.

MP.

4: M

od

el w

ith m

athe

mat

ics.

MP.

5: U

se a

pp

rop

riate

to

ols

str

ateg

ical

ly.

MP.

6: A

tten

d t

o p

reci

sio

n.M

P.7:

Lo

ok

for

and

mak

e us

e o

f str

uctu

re.

MP.

8: L

oo

k fo

r an

d e

xpre

ss re

gul

arity

in re

pea

ted

reas

oni

ng.

Flue

ncy

Goa

ls*

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tiste

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osi

tive

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ativ

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umbers.

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nder

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g, a

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pro

ach

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-ter

m re

tent

ion

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kills

and

ab

ility

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ap

ply

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se s

kills

in p

rob

lem

so

lvin

g.

Teacher Implementation Toolkit82

ShA

pe

S A

nd

de

Sig

nS

Two-

Dim

ensi

onal

Geo

met

ry

Inst

ruct

iona

l Ti

me

21 d

ays

Ess

enti

al Id

eas

•Th

e su

m o

f the

inte

rior

ang

les

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po

lyg

on

rela

tes

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he n

umb

er o

f tr

iang

les

that

are

form

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y d

raw

ing

dia

go

nals

fro

m o

ne v

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x.

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iang

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3 s

ides

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t ev

ery

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bin

atio

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ide

leng

ths

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ake

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iang

le.

•A

s w

ith t

riang

les,

sp

ecifi

c co

mb

inat

ions

of s

ide

leng

ths

of a

po

lyg

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pro

duc

e co

ngru

ent

cop

ies

of t

he p

oly

go

n.

•A

ngle

s ca

n b

e cl

assi

fied

by

thei

r si

ze, t

heir

loca

tion

in re

latio

n to

eac

h o

ther

in a

fig

ure

or

des

ign,

and

the

ir co

mb

ined

ang

le m

easu

re. A

ngle

cl

assi

ficat

ion

by

loca

tion

or

com

bin

ed a

ngle

mea

sure

can

hel

p y

ou

writ

e eq

uatio

ns t

o fi

nd u

nkno

wn

ang

le m

easu

res.

Go

als

•U

nder

stan

d t

he p

rop

ertie

s o

f po

lyg

ons

tha

t af

fect

the

ir sh

ape.

•U

nder

stan

d s

pec

ial r

elat

ions

hip

s am

ong

ang

les.

•U

nder

stan

d t

he p

rop

ertie

s ne

eded

to

co

nstr

uct

po

lyg

ons

.

Mai

n C

om

mo

n C

ore

Sta

ndar

ds

Com

mon

Cor

e C

onte

nt S

tand

ard

s7.

EE

.B.4

: Use

var

iab

les

to re

pre

sent

qua

ntiti

es in

a re

al-w

orld

or

mat

hem

atic

al p

rob

lem

, and

co

nstr

uct

sim

ple

eq

uatio

ns a

nd in

equa

litie

s to

so

lve

pro

ble

ms

by

reas

oni

ng a

bo

ut t

he q

uant

ities

.

7.G

.A.2

: Dra

w (f

reeh

and

, with

rul

er a

nd p

rotr

acto

r, an

d w

ith t

echn

olo

gy)

geo

metric

sha

peswith

given

cond

itions.F

ocu

sonco

nstruc

tingtria

ngles

fro

m t

hree

mea

sure

s o

f ang

les

or

sid

es, n

otic

ing

whe

n th

e co

nditi

ons

d

eter

min

e a

uniq

ue t

riang

le, m

ore

tha

n o

ne t

riang

le, o

r no

tria

ngle

.

7.G

.B.5

: Use

fact

s ab

out

sup

ple

men

tary

, co

mp

lem

enta

ry, v

ertic

al, a

nd

adja

cent

ang

les

in a

mul

ti-st

ep p

rob

lem

to

writ

e an

d s

olv

e si

mp

le e

qua

tions

fo

r an

unk

now

n an

gle

in a

fig

ure.

Com

mon

Cor

e St

and

ard

s fo

r M

athe

mat

ical

Pra

ctic

eM

P.1:

Mak

e se

nse

of p

rob

lem

s an

d p

erse

vere

in s

olv

ing

the

m.

MP.

2: R

easo

n ab

stra

ctly

and

qua

ntita

tivel

y.M

P.3:

Co

nstr

uct

viab

le a

rgum

ents

and

crit

ique

the

reas

oni

ng o

f oth

ers.

MP.

4: M

od

el w

ith m

athe

mat

ics.

MP.

5: U

se a

pp

rop

riate

to

ols

str

ateg

ical

ly.

MP.

6: A

tten

d t

o p

reci

sio

n.M

P.7:

Lo

ok

for

and

mak

e us

e o

f str

uctu

re.

MP.

8: L

oo

k fo

r an

d e

xpre

ss re

gul

arity

in re

pea

ted

reas

oni

ng.

Flue

ncy

Go

als*

•O

per

ate

with

mul

tidig

it d

ecim

als

fluen

tly.*

*

Ass

essm

ents

Uni

t R

ead

ines

sC

heck

-up

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rtne

r Q

uiz

Uni

t Pr

oje

ctSe

lf-A

sses

smen

tU

nit

Test

*CM

P3 d

evel

op

s flu

ency

in p

roce

dur

al s

kills

fro

m a

foun

dat

ion

of c

onc

eptu

al u

nder

stan

din

g, a

n ap

pro

ach

that

lead

s to

long

-ter

m re

tent

ion

of s

kills

and

ab

ility

to

ap

ply

tho

se s

kills

in p

rob

lem

so

lvin

g.

**re

info

rcin

g fl

uenc

y ex

pec

tatio

ns fr

om

pre

vio

us g

rad

es

New

Yor

k Ci

ty S

cope

and

Seq

uenc

e fo

r CM

P3

cont

inued

Gra

de 7

Scope and Sequence for Grade 7 83