1.4

Des

igns

inst

ruct

iona

l act

iviti

es b

ased

on

stat

e co

nten

t sta

ndar

ds

Pre-

Serv

ice an

d Be

ginn

ing

Emer

ging

Ap

plyin

g In

tegr

atin

g In

nova

ting

□Pl

ans i

nstru

ction

alac

tivitie

s tha

t alig

n with

Alab

ama’s

Cou

rses o

fSt

udy.

…an

d

□De

signs

lear

ning a

ctivit

iestha

t integ

rate

multip

leco

ntent

stand

ards

.□

Comm

unica

tes cl

early

the

conn

ectio

ns be

twee

n the

stand

ards

and t

hekn

owled

ge an

d skil

ls be

ingtau

ght.

□De

signs

, dev

elops

, and

evalu

ates d

igital

-age

learn

ing ex

perie

nces

and

asse

ssme

nts.

…an

d

□Us

es m

ultipl

e res

ource

s,inc

luding

textb

ooks

, tode

velop

cohe

rent

shor

t-an

d lon

g- ra

nge p

lans t

hat

are a

ligne

d with

conte

ntsta

ndar

ds.

□Fo

rmula

tes es

senti

alqu

estio

ns to

orga

nize a

ndfoc

us co

ntent

for st

uden

ts.□

Diffe

renti

ates p

lans t

osu

ppor

t all l

earn

ers i

nac

cess

ing st

ate co

ntent

stand

ards

.

…an

d

□Co

llabo

rates

with

colle

ague

s in u

sing a

wide

rang

e of m

ateria

ls an

dme

thods

to pl

an an

dim

pleme

nt ins

tructi

onal

activ

ities t

hat p

romo

telea

rner

s’ de

epun

derst

andin

g of c

onten

tan

d ena

ble th

em to

demo

nstra

te the

know

ledge

and s

kills

embe

dded

in st

atesta

ndar

ds.

…an

d

□Fa

cilita

tes te

ams o

ftea

cher

s in t

he cr

eatio

n of

varie

d and

diffe

renti

ated

oppo

rtunit

ies fo

r lear

ners

to de

velop

, mon

itor,

and

exten

d lea

rning

relat

ed to

state

stand

ards

.□

Prov

ides l

eade

rship

that

enga

ges c

ollea

gues

inon

going

analy

sis an

dma

pping

of cu

rricu

lum to

ensu

re al

ignme

nt of

state

stand

ards

with

the

curri

culum

being

taug

ht.

15 Handout #1

2.7

Cre

ates

lear

ning

act

iviti

es th

at o

ptim

ize

each

indi

vidu

al’s

gro

wth

and

ach

ieve

men

t with

in a

sup

port

ive

envi

ronm

ent

Pre-

Serv

ice an

d Be

ginn

ing

Emer

ging

Ap

plyin

g In

tegr

atin

g In

nova

ting

□Cr

eates

lear

ning a

ctivit

iesus

ing av

ailab

le tea

ching

reso

urce

s and

scop

e and

sequ

ence

guide

s.□

Uses

effec

tive q

uesti

oning

strate

gies t

o eng

age

learn

ers i

n thin

king a

bout

and l

earn

ing th

e con

tent.

□Su

ppor

ts an

d enc

oura

ges

indivi

dual

learn

ers t

oac

hieve

. Bec

omes

infor

med a

bout

addit

ional

reso

urce

s, inc

luding

exist

ing an

d eme

rging

digita

l tools

and c

onten

t, to

supp

ort le

arne

rs.

…an

d

□Se

lects

spec

ificins

tructi

onal

strate

gies t

hat

refle

ct hig

h exp

ectat

ions

and a

re re

spon

sive t

o the

char

acter

istics

of va

rious

grou

ps of

lear

ners.

□Fo

rmula

tes an

d use

squ

estio

ns to

enga

gestu

dents

in th

inking

at al

lco

gnitiv

e lev

els an

d in

maste

ring t

he co

ntent.

□Mo

dels

a beli

ef tha

t all

learn

ers c

an ac

hieve

and

persi

sts in

supp

ortin

g eac

hlea

rner

’s su

cces

s.□

Plan

s and

imple

ments

equit

able

and e

ffecti

vestu

dent

acce

ss to

avail

able

techn

ologie

s and

othe

rre

sour

ces t

o enh

ance

stude

nt lea

rning

.

…an

d

□Ho

lds hi

gh ex

pecta

tions

for

each

lear

ner a

nddif

feren

tiates

and s

caffo

ldsins

tructi

onal

prac

tices

tomo

ve al

l lear

ners

forwa

rdin

their g

rowt

h and

deve

lopme

nt.□

Enco

urag

es an

d tea

ches

learn

ers t

o for

mulat

equ

estio

ns to

guide

their

learn

ing. U

ses e

ffecti

vequ

estio

ning s

trateg

ies to

facilit

ate le

arne

rint

erac

tions

and

discu

ssion

s.□

Pres

ents

conc

epts

and

princ

iples

at va

rious

leve

lsof

comp

lexity

to op

timize

the gr

owth

of lea

rner

s at a

lllev

els of

deve

lopme

nt.□

Uses

a wi

de ra

nge o

fstu

dent

resp

onse

strate

gies t

o ens

ure t

hat a

llstu

dents

are e

ngag

ed in

think

ing ab

out a

ndre

spon

ding t

o ins

tructi

onal

ques

tions

.

…an

d

□En

gage

s coll

eagu

es in

the

desig

n of d

iffere

ntiate

dlea

rning

activ

ities t

oop

timize

each

lear

ner’s

grow

th an

d ach

ievem

ent.

□Le

ads c

ollea

gues

in th

efor

mulat

ion of

esse

ntial

ques

tions

that

cross

the

discip

lines

and t

hat e

nable

learn

ers t

o inte

grate

know

ledge

from

diffe

rent

sour

ces a

nd m

ake

mean

ingful

conn

ectio

nsac

ross

conte

nt ar

eas.

□W

orks

with

colle

ague

s to

susta

in the

ir com

mitm

ent

to se

eking

appr

oach

es th

atsu

ppor

t the o

ptima

lac

hieve

ment

of ea

chlea

rner

.

…an

d

□Le

ads c

ollea

gues

in th

ean

alysis

of st

uden

t wor

kan

d/or p

erfor

manc

es to

desig

n res

pons

ive an

ddif

feren

tiated

instr

uctio

nal

activ

ities t

hat m

eet

indivi

dual

learn

er ne

eds

and e

nsur

e suc

cess

.□

Advo

cates

for c

urric

ular

and i

nstru

ction

alad

aptat

ions a

ndre

sour

ces t

hat s

uppo

rtthe

need

s of in

dividu

alan

d dive

rse le

arne

rssc

hoolw

ide.

□Mo

dels

effec

tive

ques

tionin

g skil

ls wh

enlea

ding c

ollea

gues

inpr

ofess

ional

learn

ingac

tivitie

s rela

ted to

impr

oved

instr

uctio

n.

23 Handout #1a

5.3

Par

ticip

ates

as

a te

ache

r lea

der a

nd p

rofe

ssio

nal l

earn

ing

com

mun

ity m

embe

r to

adva

nce

scho

ol im

prov

emen

t in

itiat

ives

Pre-

Serv

ice an

d Be

ginn

ing

Emer

ging

Ap

plyin

g In

tegr

atin

g In

nova

ting

□Sh

ares

reso

urce

s with

colle

ague

s, fam

ilies,

and

comm

unity

mem

bers

toim

prov

e lea

rning

for a

llstu

dents

.

…an

d

□An

alyze

s ben

chma

rkas

sess

ment

data

with

colle

ague

s to i

denti

fyins

tructi

onal

gaps

and

chall

enge

s. Ge

nera

tespo

ssibl

e solu

tions

, and

plans

and i

mplem

ents

next

steps

.□

Enga

ges s

tuden

ts an

dfam

ilies i

n the

imple

menta

tion a

ndmo

nitor

ing of

next

steps

toad

vanc

e stud

ent

achie

veme

nt

.

…an

d

□En

gage

s with

colle

ague

san

d othe

r stak

ehold

ers t

ode

velop

and i

mplem

ent

scho

olwide

initia

tives

that

addr

ess a

chiev

emen

t gap

san

d enh

ance

lear

ning f

orind

ividu

al stu

dents

and

acro

ss cl

assro

oms a

ndgr

ade l

evels

.

…an

d

□Fa

cilita

tes sc

hoolw

ide,

inquir

y-bas

ed pr

ofess

ional

learn

ing co

mmun

ities t

hat

explo

re pa

ttern

s and

gaps

in ac

adem

ic ac

hieve

ment.

Base

d on f

inding

s, gu

ides

profe

ssion

al lea

rning

comm

unity

in id

entify

ingco

ntent-

spec

ific an

dins

tructi

onal

strate

gies t

oen

sure

succ

ess f

or al

lstu

dents

and t

o nar

row

achie

veme

nt ga

ps.

…an

d

□Le

ads s

tanda

rds-b

ased

profe

ssion

al lea

rning

activ

ities f

or co

lleag

ues,

familie

s, an

d the

comm

unity

that

supp

ort

quali

ty im

pleme

ntatio

n of

educ

ation

al im

prov

emen

tini

tiativ

es. A

ssum

esinc

reas

ed le

ader

ship

toad

vanc

e refo

rm in

itiativ

esat

the sc

hool,

distr

ict,

state,

and n

ation

al lev

els.

48 Handout #1b

Ala

bam

a E

Qu

IP R

ub

ric

fo

r L

es

so

ns

& U

nit

s:

Ma

the

ma

tic

s G

rad

e:

Ma

the

ma

tic

s L

es

so

n/U

nit

Tit

le:

Ove

rall R

ati

ng

:

Th

e EQ

uIP

ru

bri

c is

der

ived

fro

m t

he

Tri-

Sta

te R

ub

ric

an

d t

he

colla

bo

rati

ve d

evel

op

men

t p

roce

ss le

d b

y M

ass

ach

use

tts,

New

Yo

rk, a

nd

Rh

od

e Is

lan

d a

nd

fa

cilit

ate

d b

y A

chie

ve.

This

ver

sio

n o

f th

e EQ

uIP

ru

bri

c is

cu

rren

t a

s o

f 0

6-1

5-1

3.

V

iew

Cre

ati

ve C

om

mo

ns

Att

rib

uti

on

3.0

Un

po

rted

Lic

ense

at

htt

p:/

/cre

ati

veco

mm

on

s.o

rg/l

icen

ses/

by/

3.0

/. E

du

cato

rs m

ay

use

or

ad

ap

t. If

mo

dif

ied

, ple

ase

att

rib

ute

EQ

uIP

an

d r

e-ti

tle.

I. A

lign

me

nt

to t

he

D

ep

th o

f th

e C

CRS

II.K

ey

Shif

ts in

th

e C

CRS

III.

Inst

ruct

ion

al S

up

po

rts

IV.A

sses

sme

nt

The

less

on

/un

it a

lign

s w

ith

th

e le

tter

an

d s

pir

it o

f th

e C

CRS

:

oTa

rget

s a

set

of

grad

e-

leve

l CC

RS m

ath

emat

ics

stan

dar

d(s

) to

th

e fu

lld

epth

of

the

stan

dar

ds

for

teac

hin

g an

d le

arn

ing.

oSt

and

ard

s fo

rM

ath

emat

ical

Pra

ctic

eth

at a

re c

entr

al t

o t

he

less

on

are

iden

tifi

ed,

han

dle

d in

a g

rad

e-ap

pro

pri

ate

way

, an

d w

ell

con

nec

ted

to

th

e co

nte

nt

bei

ng

add

ress

ed

.

oP

rese

nts

a b

alan

ce o

fm

ath

emat

ical

pro

ced

ure

san

d d

eep

er c

on

cep

tual

un

der

stan

din

g in

her

ent

inth

e C

CRS

.

The

less

on

/un

it r

efle

cts

evid

ence

of

key

shif

ts t

ha

t a

re r

efle

cted

in t

he

CCRS

:

oFo

cus:

Les

son

s an

d u

nit

s ta

rget

ing

the

maj

or

wo

rk o

f th

e gr

ade

pro

vid

e an

esp

ecia

lly in

-dep

th t

reat

men

t, w

ith

esp

ecia

lly h

igh

exp

ecta

tio

ns.

Les

son

s an

d u

nit

s ta

rget

ing

sup

po

rtin

g w

ork

of

the

grad

e h

ave

visi

ble

co

nn

ecti

on

to

th

e m

ajo

r w

ork

of

the

grad

ean

d a

re s

uff

icie

ntl

y b

rief

. Le

sso

ns

and

un

its

do

no

t h

old

stu

den

tsre

spo

nsi

ble

fo

r m

ater

ial f

rom

late

r gr

ades

.o

Co

he

ren

ce:

The

con

ten

t d

evel

op

s th

rou

gh r

easo

nin

g ab

ou

t th

en

ew c

on

cep

ts o

n t

he

bas

is o

f p

revi

ou

s u

nd

erst

and

ings

. Wh

ere

app

rop

riat

e, p

rovi

des

op

po

rtu

nit

ies

for

stu

den

ts t

o c

on

nec

tkn

ow

led

ge a

nd

ski

lls w

ith

in o

r ac

ross

clu

ster

s, d

om

ain

s an

dle

arn

ing

pro

gres

sio

ns.

oR

igo

r: R

equ

ire

s st

ud

ents

to

en

gage

wit

h a

nd

dem

on

stra

tech

alle

ngi

ng

mat

he

mat

ics

wit

h a

pp

rop

riat

e b

alan

ce a

mo

ng

the

follo

win

g:−

Ap

plic

atio

n:

Pro

vid

es o

pp

ort

un

itie

s fo

r st

ud

ents

to

ind

epen

den

tly

app

ly m

ath

emat

ical

co

nce

pts

in r

eal-

wo

rld

si

tuat

ion

s an

d s

olv

e ch

alle

ngi

ng

pro

ble

ms

wit

h p

ersi

sten

ce,

cho

osi

ng

and

ap

ply

ing

an a

pp

rop

riat

e m

od

el o

r st

rate

gy t

o

new

sit

uat

ion

s.

−

Co

nce

ptu

al U

nd

ers

tan

din

g: D

evel

op

s st

ud

ents

’ co

nce

ptu

al

un

der

stan

din

g th

rou

gh t

asks

, bri

ef p

rob

lem

s, q

ues

tio

ns,

m

ult

iple

rep

rese

nta

tio

ns

and

op

po

rtu

nit

ies

for

stu

den

ts t

o

wri

te a

nd

sp

eak

abo

ut

thei

r u

nd

erst

and

ing.

−

Pro

ced

ura

l Ski

ll an

d F

lue

ncy

: E

xpec

ts, s

up

po

rts

and

pro

vid

es

guid

elin

es f

or

pro

ced

ura

l ski

ll an

d f

luen

cy w

ith

co

re

calc

ula

tio

ns

and

mat

hem

atic

al p

roce

du

res

(wh

en c

alle

d f

or

in

the

stan

dar

ds

for

the

grad

e)

to b

e p

erfo

rmed

qu

ickl

y an

d

accu

rate

ly.

The

less

on

/un

it is

res

po

nsi

ve t

o v

ari

ed s

tud

ent

lea

rnin

g n

eed

s:

oIn

clu

des

cle

ar a

nd

su

ffic

ien

t gu

idan

ce t

o s

up

po

rt t

each

ing

and

lear

nin

g o

f th

eta

rget

ed s

tan

dar

ds,

incl

ud

ing,

wh

en a

pp

rop

riat

e, t

he

use

of

tech

no

logy

an

dm

edia

.

oU

ses

and

en

cou

rage

s p

reci

se a

nd

acc

ura

te m

ath

emat

ics,

aca

dem

ic la

ngu

age,

term

ino

logy

an

d c

on

cret

e o

r ab

stra

ct r

epre

sen

tati

on

s (e

.g.,

pic

ture

s, s

ymb

ols

,ex

pre

ssio

ns,

eq

uat

ion

s, g

rap

hic

s, m

od

els)

in t

he

dis

cip

line.

oEn

gage

s st

ud

ents

in p

rod

uct

ive

stru

ggle

th

rou

gh r

ele

van

t, t

ho

ugh

t-p

rovo

kin

gq

ues

tio

ns,

pro

ble

ms

and

tas

ks t

hat

sti

mu

late

inte

rest

an

d e

licit

mat

he

mat

ical

thin

kin

g.

oA

dd

ress

es

inst

ruct

ion

al e

xpe

ctat

ion

s an

d is

eas

y to

un

der

stan

d a

nd

use

.

oP

rovi

de

s ap

pro

pri

ate

leve

l an

d t

ype

of

scaf

fold

ing,

dif

fere

nti

atio

n, i

nte

rven

tio

nan

d s

up

po

rt f

or

a b

road

ran

ge o

f le

arn

ers.

−

Sup

po

rts

div

erse

cu

ltu

ral a

nd

lin

guis

tic

bac

kgro

un

ds,

inte

rest

s an

d s

tyle

s.

−

Pro

vid

es

extr

a su

pp

ort

s fo

r st

ud

ents

wo

rkin

g b

elo

w g

rad

e le

vel.

−

Pro

vid

es

exte

nsi

on

s fo

r st

ud

en

ts w

ith

hig

h in

tere

st o

r w

ork

ing

abo

vegr

ade

leve

l.

A u

nit

or

lon

ger

less

on

sh

ou

ld:

oR

eco

mm

end

an

d f

acili

tate

a m

ix o

f in

stru

ctio

nal

ap

pro

ach

es f

or

a va

riet

y o

fle

arn

ers

such

as

usi

ng

mu

ltip

le r

epre

sen

tati

on

s (e

.g.,

incl

ud

ing

mo

del

s, u

sin

g a

ran

ge o

f q

ues

tio

ns,

ch

ecki

ng

for

un

der

stan

din

g, f

lexi

ble

gro

up

ing,

pai

r-sh

are)

.

oG

rad

ual

ly r

emo

ve s

up

po

rts,

req

uir

ing

stu

den

ts t

o d

emo

nst

rate

th

eir

mat

hem

atic

al u

nd

erst

and

ing

ind

epen

den

tly.

oD

emo

nst

rate

an

eff

ecti

ve s

equ

ence

an

d a

pro

gres

sio

n o

f le

arn

ing

wh

ere

the

con

cep

ts o

r sk

ills

adva

nce

an

d d

eep

en o

ver

tim

e.

oEx

pec

t, s

up

po

rt a

nd

pro

vid

e gu

idel

ines

fo

r p

roce

du

ral s

kill

and

flu

ency

wit

hco

re c

alcu

lati

on

s an

d m

ath

em

atic

al p

roce

du

res

(wh

en c

alle

d f

or

in t

he

stan

dar

ds

for

the

grad

e) t

o b

e p

erfo

rmed

qu

ickl

y an

d a

ccu

rate

ly.

The

less

on

/un

it r

egu

larl

y a

sses

ses

wh

eth

er s

tud

ents

are

ma

ster

ing

st

an

da

rds-

ba

sed

co

nte

nt

an

d

skill

s:

oIs

des

ign

ed t

o e

licit

dir

ect

,o

bse

rvab

le e

vid

ence

of

the

deg

ree

to w

hic

h a

stu

den

t ca

nin

dep

end

entl

y d

emo

nst

rate

the

targ

eted

CC

RS.

oA

sses

ses

stu

den

t p

rofi

cien

cyu

sin

g m

eth

od

s th

at a

reac

cess

ible

an

d u

nb

iase

d,

incl

ud

ing

the

use

of

grad

e-

leve

l lan

guag

e in

stu

den

tp

rom

pts

.

oIn

clu

des

alig

ned

ru

bri

cs,

answ

er k

eys

and

sco

rin

ggu

idel

ines

th

at p

rovi

de

suff

icie

nt

guid

ance

fo

rin

terp

reti

ng

stu

den

tp

erfo

rman

ce.

A u

nit

or

lon

ger

less

on

sh

ou

ld:

oU

se v

arie

d m

od

es

of

curr

icu

lum

-em

bed

ded

asse

ssm

ents

th

at m

ay in

clu

de

pre

-, f

orm

ativ

e, s

um

mat

ive

and

sel

f-as

sess

men

tm

easu

res.

Rat

ing:

3

2

1

0

R

atin

g:

3

2

1

0

Rat

ing:

3

2

1

0

R

atin

g:

3

2

1

0

Ada

pted

by

Ala

bam

a, Ju

ne 2

013

Handout #2

EQ

uIP

Ru

bri

c f

or

Les

so

ns

& U

nit

s:

Math

em

ati

cs

Dir

ect

ion

s: T

he

Qu

alit

y R

evie

w R

ub

ric

pro

vid

es c

rite

ria

to d

eter

min

e th

e q

ual

ity

and

alig

nm

ent

of

less

on

s an

d u

nit

s to

th

e C

olle

ge a

nd C

aree

r Rea

dy S

tan

dar

ds

(CC

RS)

in o

rder

to

: (1

) Id

enti

fy e

xem

pla

rs/

mo

del

s fo

r te

ach

ers’

use

wit

hin

an

dac

ross

sta

tes;

(2

) p

rovi

de

con

stru

ctiv

e cr

iter

ia-b

ased

fee

db

ack

to d

evel

op

ers;

an

d (

3)

revi

ew e

xist

ing

inst

ruct

ion

al m

ater

ials

to

det

erm

ine

wh

at r

evis

ion

s ar

e n

eed

ed.

Ste

p 1

– R

evi

ew

Mat

eri

als

Rec

ord

th

e gr

ade

and

tit

le o

f th

e le

sso

n/u

nit

on

th

e re

cord

ing

form

.

Scan

to

see

wh

at t

he

less

on

/un

it c

on

tain

s an

d h

ow

it is

org

aniz

ed.

R

ead

key

mat

eria

ls r

elat

ed t

o in

stru

ctio

n, a

sses

smen

t an

d t

each

er g

uid

ance

.

Stu

dy

and

wo

rk t

he

task

th

at s

erve

s as

th

e ce

nte

rpie

ce f

or

the

less

on

/un

it, a

nal

yzin

g th

e co

nte

nt

and

mat

hem

atic

al p

ract

ices

th

e ta

sks

req

uir

e.St

ep

2 –

Ap

ply

Cri

teri

a in

Dim

en

sio

n I:

Alig

nm

en

t

Iden

tify

th

e gr

ade-

leve

l CC

SS t

hat

th

e le

sso

n/u

nit

tar

gets

.

Clo

sely

exa

min

e th

e m

ater

ials

th

rou

gh t

he

“len

s” o

f ea

ch c

rite

rio

n.

In

div

idu

ally

ch

eck

each

cri

teri

on

fo

r w

hic

h c

lear

an

d s

ub

stan

tial

evi

den

ce is

fo

un

d.

Id

enti

fy a

nd

rec

ord

inp

ut

on

sp

ecif

ic im

pro

vem

ents

th

at m

igh

t b

e m

ade

to m

eet

crit

eria

or

stre

ngt

hen

alig

nm

ent.

En

ter

you

r ra

tin

g 0

– 3

fo

r D

imen

sio

n I:

Alig

nm

ent.

No

te: D

imen

sio

n I

is n

on

-neg

oti

ab

le.

In o

rder

fo

r th

e re

view

to

co

nti

nu

e, a

ra

tin

g o

f 2

or

3 is

req

uir

ed. I

f th

e re

view

is d

isco

nti

nu

ed, c

on

sid

er g

ener

al f

eed

ba

ck t

ha

t m

igh

t b

e g

iven

to

dev

elo

per

s/te

ach

ers

reg

ard

ing

nex

t st

eps.

St

ep

3 –

Ap

ply

Cri

teri

a in

Dim

en

sio

ns

II –

IV

C

lose

ly e

xam

ine

the

less

on

/un

it t

hro

ugh

th

e “

len

s” o

f ea

ch c

rite

rio

n.

R

eco

rd c

om

men

ts o

n c

rite

ria

met

, im

pro

vem

ents

nee

ded

an

d t

hen

rat

e 0

– 3

.W

hen

wo

rkin

g in

a g

rou

p, i

nd

ivid

ua

ls m

ay

cho

ose

to

co

mp

are

ra

tin

gs

aft

er e

ach

dim

ensi

on

or

del

ay

con

vers

ati

on

un

til e

ach

per

son

ha

s ra

ted

an

d r

eco

rded

th

eir

inp

ut

for

the

rem

ain

ing

Dim

ensi

on

s II

– IV

. St

ep

4 –

Ap

ply

an

Ove

rall

Ra

tin

g an

d P

rovi

de

Su

mm

ary

Co

mm

en

ts

R

evie

w r

atin

gs f

or

Dim

ensi

on

s I –

IV a

dd

ing/

clar

ifyi

ng

com

men

ts a

s n

eed

ed.

W

rite

su

mm

ary

com

men

ts f

or

you

r o

vera

ll ra

tin

g o

n y

ou

r re

cord

ing

shee

t.

Tota

l dim

ensi

on

rat

ings

an

d r

eco

rd o

vera

ll ra

tin

g E,

E/I

, R, N

– a

dju

st a

s n

eces

sary

.If

wo

rkin

g in

a g

rou

p, i

nd

ivid

ua

ls s

ho

uld

rec

ord

th

eir

ove

rall

rati

ng

pri

or

to c

on

vers

ati

on

. St

ep

5 –

Co

mp

are

Ove

rall

Ra

tin

gs a

nd

De

term

ine

Ne

xt S

tep

s

N

ote

th

e ev

iden

ce c

ited

to

arr

ive

at f

inal

rat

ings

, su

mm

ary

com

men

ts a

nd

sim

ilari

ties

an

d d

iffe

ren

ces

amo

ng

rate

rs.

Rec

om

me

nd

nex

t st

eps

for

the

less

on

/un

it a

nd

pro

vid

e re

com

men

dat

ion

s fo

r im

pro

vem

ent

and

/or

rati

ngs

to

dev

elo

per

s/te

ach

ers.

Ad

dit

ion

al G

uid

ance

on

Dim

en

sio

n II

: Sh

ifts

- W

hen

co

nsi

der

ing

Focu

s it

is im

po

rtan

t th

at le

sso

ns

or

un

its

targ

etin

g ad

dit

ion

al a

nd

su

pp

ort

ing

clu

ster

s ar

e su

ffic

ien

tly

bri

ef –

th

is e

nsu

res

that

stu

den

ts w

ill s

pen

d t

he

stro

ng

maj

ori

ty o

f th

e ye

ar o

n m

ajo

r w

ork

of

the

grad

e. S

ee t

he

K-8

Pu

blis

her

s C

rite

ria

fo

r th

e C

om

mo

n C

ore

Sta

te S

tan

da

rds

in M

ath

ema

tics

, par

ticu

larl

y p

ages

8-9

fo

r fu

rth

er in

form

atio

n o

n t

he

focu

s cr

iter

ion

wit

h r

esp

ect

to m

ajo

r w

ork

of

the

grad

e at

w

ww

.co

rest

and

ard

s.o

rg/a

sset

s/M

ath

_Pu

blis

her

s_C

rite

ria_

K-8

_Su

mm

er%

20

20

12

_FIN

AL.

pd

f. W

ith

res

pec

t to

Co

her

ence

it is

imp

ort

ant

that

th

e le

arn

ing

ob

ject

ives

are

lin

ked

to

CC

SS c

lust

er h

ead

ings

(se

e w

ww

.co

rest

and

ard

s.o

rg/M

ath

).

Rat

ing

Sca

les

R

ati

ng

fo

r D

imen

sio

n I:

Alig

nm

ent

is n

on

-neg

oti

ab

le a

nd

req

uir

es a

ra

tin

g o

f 2

or

3.

If r

ati

ng

is 0

or

1 t

hen

th

e re

view

do

es n

ot

con

tin

ue.

Rat

ing

Sca

le f

or

Dim

en

sio

ns

I, II

, III

, IV

:

3: M

eets

mo

st t

o a

ll o

f th

e cr

iter

ia in

th

e d

ime

nsi

on

2

: Mee

ts m

any

of

the

crit

eria

in t

he

dim

ensi

on

1: M

eets

so

me

of

the

crit

eria

in t

he

dim

ensi

on

0

: Do

es n

ot

mee

t th

e cr

ite

ria

in t

he

dim

ensi

on

Ove

rall

Rat

ing

for

the

Le

sso

n/U

nit

:

E: E

xem

pla

r –

Alig

ne

d a

nd

mee

ts m

ost

to

all

of

the

crit

eria

in d

ime

nsi

on

s II

, III

, IV

(to

tal 1

1 –

12

) E/

I: E

xem

pla

r if

Imp

rove

d –

Alig

ned

an

d n

eed

s so

me

imp

rove

men

t in

on

e o

r m

ore

dim

en

sio

ns

(to

tal 8

– 1

0)

R:

Rev

isio

n N

eed

ed

– A

lign

ed p

arti

ally

an

d n

eed

s si

gnif

ican

t re

visi

on

in o

ne

or

mo

re d

imen

sio

ns

(to

tal 3

– 7

) N

: N

ot

Rea

dy

to R

evie

w –

No

t al

ign

ed a

nd

do

es n

ot

mee

t cr

iter

ia (

tota

l 0 –

2)

De

scri

pto

rs f

or

Dim

en

sio

ns

I, II

, III

, IV

:

3: E

xem

plif

ies

CC

SS Q

ual

ity

- m

eets

th

e st

and

ard

des

crib

ed b

y cr

iter

ia in

th

e d

imen

sio

n, a

s ex

pla

ine

d in

cr

iter

ion

-bas

ed o

bse

rvat

ion

s.

2: A

pp

roac

hin

g C

CSS

Qu

alit

y -

mee

ts m

any

crit

eria

bu

t w

ill b

enef

it f

rom

re

visi

on

in o

ther

s, a

s su

gges

ted

in

crit

erio

n-b

ased

ob

serv

atio

ns.

1: D

eve

lop

ing

tow

ard

CC

SS Q

ual

ity

- n

eed

s si

gnif

ican

t re

visi

on

, as

sugg

este

d in

cri

teri

on

-bas

ed

ob

serv

atio

ns.

0

: No

t re

pre

sen

tin

g C

CSS

Qu

alit

y -

do

es n

ot

add

ress

th

e cr

iter

ia in

th

e d

imen

sio

n.

De

scri

pto

r fo

r O

vera

ll R

atin

gs:

E: E

xem

plif

ies

CC

SS Q

ual

ity –

Alig

ned

an

d e

xem

plif

ies

the

qu

alit

y st

and

ard

an

d e

xem

plif

ies

mo

st o

f th

e cr

iter

ia a

cro

ss D

imen

sio

ns

II, I

II, I

V o

f th

e ru

bri

c.

E/I:

Ap

pro

ach

ing

CC

SS Q

ua

lity –

Alig

ned

an

d e

xem

plif

ies

the

qu

alit

y st

and

ard

in s

om

e d

ime

nsi

on

s b

ut

will

ben

efit

fro

m s

om

e re

visi

on

in

oth

ers

.

R:

De

velo

pin

g to

war

d C

CSS

Qu

alit

y –

Alig

ned

par

tial

ly a

nd

ap

pro

ach

es t

he

qu

alit

y st

and

ard

in s

om

e d

ime

nsi

on

s an

d n

eed

s si

gnif

ica

nt

revi

sio

n

in o

ther

s.

N:

No

t re

pre

sen

tin

g C

CSS

Qu

alit

y –

No

t al

ign

ed a

nd

do

es n

ot

add

ress

cri

teri

a.

Handout #2a

Journal Reflection When you planned your lesson, what do you think you gained by developing questions prior to the “Explore” phase that helped assess and advance students’ learning?

Handout #3

Handout #4

Examine and Plan Questions Examining one’s own questions and questioning patterns is an important start when looking more closely at the classroom discourse (see, e.g., Herbel-Eisenmann & Cirillo, 2009). This examination alone, however, has not been shown to do enough to support teachers in facilitating productive discussions that “focus on mathematical meaning and relationships and make links between mathematical ideas and relationships” (M. Smith & Stein, 2011, p. 50). A single, well formulated question can be sufficient for an hour’s discussion (Dillon, 1983). However, many studies have shown that while teachers ask a lot of questions, these questions frequently call for specific factual answers, resulting in lower cognitive thought (Gall, 1984; Perrot, 2002). Some question-types open up discussion, while others are more “closed” (Ainley, 1987). For example, one type of question takes the form of part-sentences “left hovering in mid-air for the student to supply the missing word or phrase” (Ainley, 1987, p. 24). An example of this ‘fill-in-the-blank’ type of question is: “This polygon has three sides so we call it a …?” This kind of question is closed, both because it relates to matters of established fact and because the teacher has one “right” answer in mind. On the other hand, it creates the illusion of participation and cooperative activity (Ainley, 1987).

Examples of well-formulated questions are: “What is the relationship between the solutions to a quadratic equation and its graph?” or “Why did you solve the quadratic equation to help you graph the parabola?” To answer these types of questions, students need to provide more than just one word answers because the answers are complex and require a deeper level of thinking to give complete answers. More open questions are often better for opening discussion and maximizing the chances of individuals to contribute to the discussion, yet such questions tend to be underused (J. Smith, 1986). It can be useful to plan not only tasks but also good questions in advance of the lesson (M. Smith & Stein, 2011), and to consider what questions we can ask to avoid too much “telling.”

Excerpt from NCTM Research Brief 20 (January 23, 2013) What Are Some Strategies For Facilitating Productive Classroom Discussions? (3)

Th

ink

ing

Thro

ugh t

he

Les

son

Pro

toco

l

Th

ink

ing T

hro

ugh

a L

esso

n P

roto

col

The

mai

n p

urp

ose

of

the

Thin

king T

hro

ugh a

Les

son P

roto

col

is t

o p

rom

pt

yo

u i

n t

hin

kin

g d

eeply

ab

out

a sp

ecif

ic l

esso

n

yo

u w

ill

be

teac

hin

g t

hat

is

bas

ed o

n a

co

gnit

ivel

y c

hal

len

gin

g m

athem

atic

al t

ask.

SE

T-U

P

Sel

ecti

ng

and

set

tin

g u

p a

ma

them

ati

cal

task

E

XP

LO

RE

S

up

po

rtin

g s

tud

ents

’ ex

plo

rati

on

of

the

task

S

HA

RE

, D

ISC

US

S,

AN

D A

NA

LY

ZE

S

ha

rin

g a

nd

dis

cuss

ing

th

e ta

sk

W

hat

are

yo

ur

mat

hem

atic

al g

oal

s fo

r th

e le

sso

n

(i.e

., w

hat

is

it t

hat

yo

u w

ant

stud

ents

to

kno

w a

nd

und

erst

and

ab

out

mat

hem

atic

s as

a r

esult

of

this

less

on)?

In

what

ways

do

es t

he

task

buil

d o

n s

tud

ents

’

pre

vio

us

kno

wle

dge?

W

hat

def

init

ion

s, c

once

pts

,

or

idea

s d

o s

tud

ents

nee

d t

o k

no

w i

n o

rder

to

beg

in t

o w

ork

on t

he

task

?

W

hat

are

all

the

ways

the

task

can

be

solv

ed?

- W

hic

h o

f th

ese

met

ho

ds

do

yo

u t

hin

k y

our

stud

ents

wil

l u

se?

- W

hat

mis

conce

pti

on

s m

ight

stud

ents

have?

- W

hat

err

ors

mig

ht

stud

ents

mak

e?

W

hat

are

yo

ur

exp

ecta

tio

ns

for

stud

ents

as

they

wo

rk o

n a

nd

co

mp

lete

this

task

?

- W

hat

res

ourc

es o

r to

ols

wil

l st

ud

ents

have

to

use

in t

heir

wo

rk?

- H

ow

wil

l th

e st

ud

ents

wo

rk –

ind

epen

den

tly,

in s

mal

l gro

up

s, o

r in

pai

rs –

to

exp

lore

this

task

?

- H

ow

lo

ng w

ill

they w

ork

ind

ivid

ual

ly o

r in

smal

l gro

up

s/p

airs

?

Wil

l st

ud

ents

be

par

tner

ed i

n a

sp

ecif

ic w

ay?

If s

o,

in w

hat

way?

- H

ow

wil

l st

ud

ents

rec

ord

and

rep

ort

thei

r

wo

rk?

H

ow

wil

l yo

u i

ntr

od

uce

stu

dents

to

the

acti

vit

y s

o

as n

ot

to r

educe

the

dem

and

s o

f th

e ta

sk?

W

hat

wil

l yo

u h

ear

that

let

s y

ou k

no

w s

tud

ents

und

erst

and

the

task

?

A

s st

ud

ents

are

wo

rkin

g i

nd

epen

den

tly o

r in

sm

all

gro

up

s:

- W

hat

ques

tio

ns

wil

l yo

u a

sk t

o f

ocu

s th

eir

thin

kin

g?

- W

hat

wil

l yo

u s

ee o

r hea

r th

at l

ets

yo

u k

no

w

ho

w s

tud

ents

are

thin

kin

g a

bo

ut

the

mat

hem

ati

cal

idea

s?

- W

hat

ques

tio

ns

wil

l yo

u a

sk t

o a

sses

s

stud

ents

’ u

nd

erst

and

ing o

f key m

athem

atic

al

idea

s, p

rob

lem

so

lvin

g s

trat

egie

s, o

r th

e

rep

rese

nta

tio

ns?

- W

hat

ques

tio

ns

wil

l yo

u a

sk t

o a

dvan

ce

stud

ents

’ u

nd

erst

and

ing o

f th

e m

athem

atic

al

idea

s?

- W

hat

ques

tio

ns

wil

l yo

u a

sk t

o e

nco

ura

ge

stud

ents

to

shar

e th

eir

thin

kin

g w

ith o

ther

s o

r

to a

sses

s th

eir

und

erst

and

ing o

f th

eir

pee

r’s

idea

s?

H

ow

wil

l yo

u e

nsu

re t

hat

stud

ents

rem

ain e

ngag

ed

in t

he

task

?

- W

hat

wil

l yo

u d

o i

f a

stud

ent

do

es n

ot

kno

w

ho

w t

o b

egin

to

so

lve

the

task

?

- W

hat

wil

l yo

u d

o i

f a

stud

ent

finis

hes

the

task

alm

ost

im

med

iate

ly a

nd

bec

om

es b

ore

d o

r

dis

rup

tive?

- W

hat

wil

l yo

u d

o i

f st

ud

ents

fo

cus

on n

on

-

mat

hem

ati

cal

asp

ects

of

the

acti

vit

y (

e.g.,

spen

d m

ost

of

thei

r ti

me

mak

ing b

eau

tifu

l

po

ster

of

thei

r w

ork

)?

H

ow

wil

l yo

u o

rchest

rate

the

clas

s d

iscuss

ion s

o

that

yo

u a

cco

mp

lish

yo

ur

math

em

ati

cal

go

als?

Sp

ecif

ical

ly:

- W

hic

h s

olu

tio

n p

aths

do

yo

u w

ant

to h

ave

shar

ed d

uri

ng t

he

clas

s d

iscu

ssio

n? I

n w

hat

ord

er w

ill

the

solu

tio

ns

be

pre

sente

d? W

hy?

- In

what

ways

wil

l th

e o

rder

in w

hic

h

solu

tio

ns

are

pre

sente

d h

elp

dev

elo

p

stud

ents

’ u

nd

erst

and

ing o

f th

e m

athem

atic

al

idea

s th

at a

re t

he

focu

s o

f yo

ur

less

on?

- W

hat

sp

ecif

ic q

ues

tio

ns

wil

l yo

u a

sk s

o t

hat

stud

ents

wil

l:

mak

e se

nse

of

the

math

em

atic

al i

dea

s

that

yo

u w

ant

them

to

lea

rn?

exp

and

on,

deb

ate,

and

ques

tio

n t

he

solu

tio

ns

bei

ng s

har

ed?

mak

e co

nnec

tio

ns

bet

wee

n t

he

dif

fere

nt

stra

tegie

s th

at a

re p

rese

nte

d?

loo

k f

or

pat

tern

s?

beg

in t

o f

orm

gener

aliz

atio

ns?

W

hat

wil

l yo

u s

ee o

r hea

r th

at l

ets

yo

u k

no

w t

hat

stud

ents

in t

he

class

und

erst

an

d t

he

mat

hem

atic

al

idea

s th

at y

ou i

nte

nd

ed f

or

them

to

lea

rn?

W

hat

wil

l yo

u d

o t

om

orr

ow

th

at w

ill

buil

d o

n t

his

less

on?

Handout #5

Assessing Questions “Why did you choose to add? How did you decide Sam has enough money?”

“Why did you decide to group the $2.25s the way you did? What can you tell me about this group – how many $2.25s are in this group?”

“Why did you split the money into dollars and a quarter? How did that help you?”

“When you split the money into dollars and quarters, how many dollars do you have for the week? Can you write an equation for that?”

“How much money does Sam have? How many days will Sam buy lunch at school this week? How much does lunch cost for one day?”

Handout #6

Advancing Questions

“Can you write your equation another way using multiplication?”

“How can you represent this group of $2.25s with an equation? Are there other ways to group the $2.25s?”

“When you split the money into dollars and quarters, how many dollars do you have for the week? Can you write an equation for that? How many quarters do you have for the week? Can you write an equation for that? Can you write an equation that shows how to combine the dollars and quarters?”

“If lunch costs $2.25 for one day, how could you decide how much lunch will cost for two days? What operation will you use? Why?”

Handout #6a

Journal Reflection • Explain how a question can be used to assess one student’s thinking while

the same question can be used to advance the thinking of another student.What message do you send to students if you ask ONLY assessingquestions?

• Do we ask more content-focused questions or questions related to themathematical practices?

• What have you learned about assessing and advancing questions that youcan use in your classroom tomorrow?

Handout #7

© 2

013

UN

IVER

SITY

OF

PITT

SBU

RG

H

Pizz

a Ta

sk

Jolla

has

1 4 o

f a p

izza

.

Sara

h ha

s 30 100 o

f a p

izza

.

Mar

ia h

as 3 100 o

f a p

izza

.

Tim

’s p

izza

is s

hade

d on

the

pizz

a. H

ow m

uch

pizz

a is

Tim

’s s

hare

?

Jake

has

3 10 o

f a p

izza

.

Juan

has

1 5 of a

piz

za.

1.Sh

ow e

ach

of th

e st

uden

t’s a

mou

nt o

f piz

za.

2.C

ompa

re th

e st

uden

ts’ a

mou

nts

of p

izza

. Exp

lain

with

wor

ds a

nd u

se th

e >,

<, o

r =

sym

bols

to s

how

who

has

the

mos

tpi

zza.

3.Ex

plai

n w

ith w

ords

and

use

the

>, <

, or =

sym

bols

to s

how

who

has

the

leas

t am

ount

of p

izza

.

-7-

Handout #8

© 2

013

UN

IVER

SITY

OF

PITT

SBU

RG

H

J

olla

’s P

izza

Ti

m’s

Piz

za

Juan

’s P

izza

S

arah

’s P

izza

Mar

ia’s

Piz

za

Ja

ke’s

Piz

za

-8-

Handout #8

Que

stion

Type

s Obs

erve

d in V

ideo

Hav

e yo

ur p

aren

ts e

ver

orde

red

pizz

a

befo

re?

To a

dvan

ce t

hink

ing

Whe

n it

was

del

iver

ed, w

hat

did

you

no

tice

?

Hav

e yo

u ev

er h

ad a

rec

tang

ular

sh

aped

piz

za?

How

was

it d

ivid

ed?

Let’s

say

you

hav

e tw

o re

ctan

gula

r

pi

zzas

, one

div

ided

into

10

piec

es a

nd

one

divi

ded

into

100

pie

ces.

Wou

ld

yo

u ra

ther

eat

2 p

iece

s of

the

fir

st

pizz

a, o

r 20

pie

ces

of t

he s

econ

d

pizz

a?

Que

stio

ning

and

St

uden

t En

gage

men

t

To f

ocus

thi

nkin

g

To a

sses

s th

inki

ng

Journal Reflection • What is monitoring?• Why is it important to teaching and

learning?

Handout #10

Anticipate Strategies That Students Might Use to Solve the Tasks and Monitor Their Work

Monitoring, as described by M. Smith and Stein (2011), is attending to the thinking of students during the actual lesson as they work either individually or collectively on the task. This involves not only listening to students’ discussions with their peers, but also observing what they are doing and keeping track of the approaches students are using. Monitoring can support teachers by allowing them to help students get ready for the classroom discussion (e.g., asking students to have an explanation prepared that uses mathematically precise language). It can also help teachers identify strategies that will advance the “collective reflection” (Cobb, Boufi, McClain, & Whitenack, 1997) of the classroom community and prepare for the end-of-class discussion (M. Smith &Stein,2011).

Excerpt from NCTM Research Brief 20 (January 23, 2013) What Are Some Strategies For Facilitating Productive Classroom Discussions? (4)

Handout #11

Leaves and Caterpillar Task

A fourth-grade class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would they need each day for 12 caterpillars? Use drawings, words, or numbers to show how you got your answer.

• Solve the task in as many ways as youcan, and consider other approachesthat you think students might use tosolve it.

• Identify errors or misconceptions thatyou would expect to emerge asstudents work on this task.

Handout #12

Anticipating Students’ Responses and Monitoring Their Work

Strategy Who and What Order

Handout #13

Leaves and Caterpillars: The Case of David Crane (Part 2 – Monitoring)

After introducing the task to students and making sure that they understood what they needed to do, David Crane sent students to work on the task with their partner.

Armed with his monitoring tool – the chart – Mr. Crane listened in on the partner conversations. He asked questions as needed to get students on the right track or to press them to make sense of what they were doing while he kept track of who was doing what. For example, when Mr. Crane approached Jamal and his partner, he noticed that they had made a table with leaves and caterpillars increasing in increments of 2 and 5. When he asked the students what they learned from the table, they responded that every time the number of caterpillars increased by 2, the number of leaves increased by 5. Since his goal was for them to see the problem as multiplicative, he asked them a few questions to get them thinking: “How many times did the caterpillars increase by 2 to get to 12? In comparison, how many times did the leaves increase by 5? How can knowing this help you solve the problem more efficiently?” He left the students to think about the last question.

Mr. Crane then approached Jason and his partner. The pair had chosen to write about their solution instead of using a diagram or table. When asked about their strategy, Jason stated that using the fact that it took 5 leaves for two caterpillars all you had to do was count by twos until you get to half of 12. That number would be six, and so you would multiply 5 x 6 and it would equal 30. Although the solution was correct, Mr. Crane asked some questions to determine their level of mathematical understanding. He asked: “Why did you stop counting by 2’s when you got to half of 12? Jason explained that he did not mean half of 12, he meant to count by 2’s until you get to 12. Mr. Crane then asked, “Why did you multiply 5 x 6?” Jason stated, “Since you multiply by 6 to get the number of caterpillars, you have to multiply by 6 to get the number of leaves. What you do to one you have to do to the other.” Mr. Crane walked away knowing that they understood that the task was multiplicative and that the two quantities need to grow at a constant rate.

On the other hand, when he approached Missy and Kate he noticed that they were trying to solve the problem using an additive strategy, but it was incorrect. They thought that to get to 12 caterpillars all you did was add 10 to the 2. In turn, if you add 10 to the caterpillars you have to add 10 to the leaves. Mr. Crane engaged the pair in a conversation that he hoped would help them see and correct the problem.

Mr. Crane: What is the task asking you to find?

Missy: How many leaves the students would need each day for 12 caterpillars?

Mr. Crane: What information is given to help you find the solution?

Kate: They need 5 leaves each day to feed 2 caterpillars.

Mr. Crane: If 5 leaves would feed 2 caterpillars, how many leaves would you need for 4

Handout #14

caterpillars? For 6? For 8?

Although Mr. Crane’s goal was for the class to see the task as multiplicative, he saw that Missy and Kate did not even see it as additive. Before they could move to the mathematical understanding of multiplicative, he needed to question them so that they saw it as additive before moving any further. He asked them to continue the pattern for 10 caterpillars and 12 caterpillars. He then asked them to think about what they did and see if there was a more efficient way to show their solution.

As Mr. Crane moved around the room, he saw that Janine’s group and Kyra’s group used a similar strategy. Janine’s group realized that if 2 caterpillars shared 5 leaves, that would be 2 ½ leaves per caterpillar. They then multiplied 12 x 2.5 to get 30. It showed that they understood that the problem was multiplicative. Kyra and her partner also saw that 1 caterpillar would eat 2 ½ leaves. But, instead of multiplying, they added 2 ½ leaves 12 times to get 30. To get them to see it as multiplicative Mr. Crane asked, “I see that you added 2 ½ leaves 12 times to get 30. When looking at your representation, is there a more efficient way that you could have gotten 30 without adding 12 times?” He left them to think about what he was asking.

The next two groups that Mr. Crane approached also used a similar strategy. Martin’s group and Melissa’s group both showed sets of 2 leaves and 5 caterpillars. The only difference was that they represented them differently. Melissa’s group drew a table, while Martin’s group drew a picture. Both groups solved the problem correctly, but did so by counting up (scaling up). They were on the right track, but he still wanted them to see the more efficient way of multiplying to solve. He asked them the same question he asked Janine’s and Kyra’s group: “Is there a more efficient way that you could have gotten 30 without adding 12 times? As he left the groups, he heard them discussing the question asked of them.

The last group that he approached, Darnell and Marcus, had solved the problem simply by multiplying 5 leaves times 12 caterpillars to get 60. They were trying to solve it multiplicatively, but had no idea what numbers to use. They did not see the 2 to 5 ratio in the problem. Mr. Crane sat down with them to see if he could get them started in the right direction with a few simple questions:

Mr. Crane: Why did you decide to multiply 5 leaves times 12 caterpillars?

Marcus: The problem gives us the 5 leaves that the caterpillar ate each day. So if it is for 12 days, we just multiply 5 times 12.

Mr. Crane: Where do you see the 5 leaves per caterpillar in the problem? Read the problem aloud to me.

Darnell: “A fourth-grade class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would the students need each day for 12 caterpillars?”

Mr. Crane: Okay, 5 leaves for how many caterpillars?

Marcus: 2

Mr. Crane: What does your problem represent?

Darnell: 5 leaves for every caterpillar?

Mr. Crane: So, is your representation correct?

Darnell and Marcus thought about this for a minute.

Marcus: No. We showed 5 leaves for every caterpillar and it should be 5 leaves for every two caterpillars.

Mr. Crane: Think about what you can do to correct your solution.

Mr. Crane felt good about the direction that Marcus and Darnell were headed in. They saw the problem as multiplicative, but did not see the ratio between the two numbers. After getting them to examine the problem more closely, he felt that they would be successful.

At the end of 30 minutes, Mr. Crane had completed the monitoring chart. He was pleased to see that groups used a variety of strategies to solve the problem. He had done a good job in anticipating what would occur, and was ready with some advancing questions. Armed with the data that he had collected, Mr. Crane felt that he was now able to determine which solutions he wanted to focus on during the discussion.

Journal Reflection “If I watch and listen during small group independent work, I am then able to use my observations to decide what and who to make focal” during whole-class discussion.

Lampert (2001, page 140)

Explain how you plan on implementing one idea explored today.

Handout #15

•Ide

ntify

stan

dard

s and

selec

t a hi

gh le

vel t

ask a

nd pl

an a

lesso

n to i

mplem

ent

that t

ask.

•Anti

cipate

stud

ent r

espo

nses

, erro

rs, an

d misc

once

ption

s. W

rite a

ssessi

ng an

dad

vanc

ing qu

estio

ns re

lated

to st

uden

t res

pons

es. K

eep c

opies

of pl

annin

gno

tes.

•Tea

ch th

e les

son.

Whe

n you

are i

n the

Exp

lore p

hase

of th

e les

son,

m onit

orwh

at stu

dents

are d

oing.

•Ide

ntify

/reco

rd th

e app

roac

hes t

hat c

an he

lp ad

vanc

e the

math

emati

cal

discu

ssion

later

in th

e les

son

•Coll

ect s

tude

nt w

ork

sam

ples

and

brin

g to t

he n

ext

Quar

terly

Mee

ting.

Next

Step

s (to

prep

are fo

r QM

#4)

The Q

M #4

goal

is to

be a

ble t

o sele

ct, se

quen

ce an

d co

nnec

t stu

dent

wor

k in

orde

r to o

rche

strat

e a w

hole-

class

disc

ussio

n th

at ta

rgets

the m

athe

mat

ical p

urpo

se(s)

of th

e les

son.

Handout #16