multiplying & dividing fractions · multiplying fractions on a number line and dividing...

6
Multiplying & Dividing Fractions Storybook Essential Lessons Sharing Vanilla Wafers Painting a Wall- Area and Multiplication of Fractions Multiplying Fractions on a Number Line Dividing Fractions I Dividing Fractions II Dividing Fractions: Noticing Patterns Dividing Fractions on a Number Line Fraction Multiplication and Division Problem Solving How Accurate Are You? ZĞĨĞƌĞŶĐĞƐ ϭͿ WƌŽŐƌĞƐƐŝŽŶƐ ŽĐƵŵĞŶƚƐ ĨŽƌ ƚŚĞ ŽŵŵŽŶ ŽƌĞ DĂƚŚ ^ƚĂŶĚĂƌĚƐ dŚĞ hŶŝǀĞƌƐŝƚLJ ŽĨ ƌŝnjŽŶĂ ƌŽŽŬŚŝůů &ŽƵŶĚĂƟŽŶ ϮϬϬϳ ϮͿ DĂƚŚĞŵĂƟĐƐ &ƌĂŵĞǁŽƌŬ ŚĂƉƚĞƌƐ ƵƌƌŝĐƵůƵŵ &ƌĂŵĞǁŽƌŬƐ ; ĞƉƚ ŽĨ ĚƵĐĂƟŽŶͿ ϮϬϭϯ Formative Assessment #1- How are fractions and division related? Use lesson Sharing Vanilla Wafers, questions 11 and 12, to have students explain the meaning of the fractions in the context of sharing vanilla wafers. Look for students to connect the denominator of the fraction to the number of people in the group and the numerator to the number of vanilla wafers. Use the lesson Making a Zipline with attention to questions 9-12 and the summary question. Look for students to relate the division problem written as standard division and as a fraction (a mixed number is also acceptable, but the fraction form is essential). #2 - How can I model and explain fraction multiplication? Use lesson Painting a Wall: Area and Fractions to have students physically build a model for the multiplication of two fractions. Have students explain, orally or in writing, what they are doing when multiplying two fractions, looking for some version of an explanation that we are taking “a piece of a piece”. #3- What is the meaning (in context) for the division of fractions? /RRN IRU VWXGHQWV WR EH タH[LEOH LQ VZLWFKLQJ EHWZHHQ GLYLVLRQ GHソQLWLRQV GHSHQGLQJ XSRQ LI WKH ZKROH LV greater than or less than 1. Use lesson Dividing Fractions I to have students explain a measurement context to division of fractions, such as 2÷1/4=8 because there are 8 quarters (one-fourths) in 2 wholes or because I can jump one-fourth a meter 8 times in a total distance of 2 meters. Use lesson Dividing Fractions II WR KDYH VWXGHQWV H[SODLQ D IDLU VKDUH GHソQLWLRQ RI IDFWLRQV VXFK DV キ because if one-fourth of a pizza shared equally with two people, I cut the fourth in half and thus each person gets one-eighth of a pizza. You can choose to give contextual problems and have students provide an answer and explanation in context or allow them to make up both the problem and the context. #4- What is the size of the product or quotient in relation to the size of the factors or dividend/divisor? Use lessons Multiplying Fractions on a Number Line and Dividing Fractions on a Number Line to have students write conclusions about the “cases” presented; e.g. when is the product or quotient less than, equal to or greater than 1. Have students use the context of jumping fractions of meters and the number line to explain how they know the size of the product or quotient. Consider using a thinking map to have students compare fraction multiplication and division with whole number fraction and division in terms of both what is happening and the size of the product/quotient. Look for students to note similarities such as a number divided by itself is one. #5 - : How is the relationship between multiplication and division evident with fractions? 6WXGHQWV ソUVW XQGHUVWRRG GLYLVLRQ DV ソQGLQJ D PLVVLQJ IDFWRU LQ D PXOWLSOLFDWLRQ HTXDWLRQ +HUH ZH want to assess students’ understanding of how this relationship works with fractions. Look for students to make an initial connection between fraction division and multiplication in the lessons Dividing Fractions I and II. Use the lesson Dividing Fractions: Noticing Patters as a more formal formative assessment, having students use the conclusion section to explain the relationship that exists, namely that division of fractions is equivalent to multiplication by the multiplicative inverse.

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Page 1: Multiplying & Dividing Fractions · Multiplying Fractions on a Number Line and Dividing Fractions on a Number Line to have students write conclusions about the “cases” pr esented;

Mul

tipl

ying

&

Div

idin

g F

ract

ions

Storybook

Ess

ent

ial Less

ons

• Sh

arin

g V

anil

la W

afer

s•

Pai

nti

ng

a W

all-

Are

a an

d M

ult

ipli

cati

on

of

Fra

ctio

ns

• M

ult

iply

ing

Fra

ctio

ns

on

a N

um

ber

Lin

e•

Div

idin

g F

ract

ion

s I

• D

ivid

ing

Fra

ctio

ns

II•

Div

idin

g F

ract

ion

s: N

oti

cin

g P

atte

rns

• D

ivid

ing

Fra

ctio

ns

on

a N

um

ber

Lin

e•

Fra

ctio

n M

ult

ipli

cati

on

an

d D

ivis

ion

Pro

ble

m S

olv

ing

• H

ow

Acc

ura

te A

re Y

ou

?

For

mat

ive

Ass

essm

ent

#1

- H

ow

are

fra

cti

on

s a

nd

div

isio

n r

ela

ted

?U

se less

on S

ha

rin

g V

an

illa

Wa

fers

, quest

ions

11 a

nd 1

2, to

have s

tudents

expla

in t

he m

eanin

g o

f th

e f

ract

ions

in t

he c

onte

xt

of

sharing v

anill

a w

afe

rs. L

ook for

students

to c

onnect

the d

enom

inato

r of

the f

ract

ion t

o t

he n

um

ber

of

people

in t

he g

roup a

nd t

he n

um

era

tor

to t

he n

um

ber

of

vanill

a w

afe

rs.

Use

the less

on M

ak

ing

a Z

ipli

ne w

ith a

ttention t

o q

uest

ions

9-1

2 a

nd t

he s

um

mary

quest

ion. L

ook

for

students

to r

ela

te t

he d

ivis

ion p

roble

m w

ritt

en a

s st

andard

div

isio

n a

nd a

s a fra

ctio

n (

a m

ixed

num

ber

is a

lso a

ccepta

ble

, but

the fra

ctio

n form

is

ess

ential).

#2 -

Ho

w c

an

I m

od

el

an

d e

xp

lain

fra

cti

on

mu

ltip

lica

tio

n?

Use

less

on P

ain

tin

g a

Wa

ll:

Are

a a

nd

Fra

cti

on

s t

o h

ave s

tudents

physi

cally

build

a m

odel fo

r th

e

multip

lication o

f tw

o fra

ctio

ns.

H

ave s

tudents

expla

in, ora

lly o

r in

writing, w

hat

they a

re d

oin

g w

hen

multip

lyin

g t

wo fra

ctio

ns,

lookin

g for

som

e v

ers

ion o

f an e

xpla

nation t

hat

we a

re t

akin

g “

a p

iece

of

a

pie

ce”.

#3-

Wh

at

is t

he

me

an

ing

(in

co

nte

xt)

fo

r th

e d

ivis

ion

of

fra

cti

on

s?

gre

ate

r th

an o

r le

ss t

han 1

. U

se less

on D

ivid

ing

Fra

cti

on

s I

to h

ave s

tudents

expla

in a

measu

rem

ent

conte

xt

to d

ivis

ion o

f fr

act

ions,

such

as

1/4

=8 b

eca

use

there

are

8 q

uart

ers

(one-f

ourt

hs)

in 2

w

hole

s or

beca

use

I c

an jum

p o

ne-f

ourt

h a

mete

r 8 t

imes

in a

tota

l dis

tance

of

2 m

ete

rs. U

se less

on

Div

idin

g F

racti

on

s I

I beca

use

if

one-f

ourt

h o

f a p

izza

share

d e

qually

with t

wo p

eople

, I

cut

the fourt

h in h

alf a

nd t

hus

each

pers

on g

ets

one-e

ighth

of

a p

izza

. Y

ou c

an c

hoose

to g

ive c

onte

xtu

al pro

ble

ms

and h

ave s

tudents

pro

vid

e a

n a

nsw

er

and e

xpla

nation in c

onte

xt

or

allo

w t

hem

to m

ake u

p b

oth

the p

roble

m a

nd t

he

conte

xt.

#4-

Wh

at

is t

he

siz

e o

f th

e p

rod

uct

or

qu

oti

en

t in

re

lati

on

to

th

e s

ize

of

the

fa

cto

rs o

r d

ivid

en

d/d

ivis

or?

Use

less

ons

Mu

ltip

lyin

g F

racti

on

s o

n a

Nu

mb

er

Lin

e a

nd D

ivid

ing

Fra

cti

on

s o

n a

Nu

mb

er

Lin

e

to h

ave s

tudents

write

concl

usi

ons

about

the “

case

s” p

rese

nte

d;

e.g

. w

hen is

the p

roduct

or

quotient

less

than, equal to

or

gre

ate

r th

an 1

. H

ave s

tudents

use

the c

onte

xt

of

jum

pin

g fra

ctio

ns

of

mete

rs

and t

he n

um

ber

line t

o e

xpla

in h

ow

they k

now

the s

ize o

f th

e p

roduct

or

quotient.

Consi

der

usi

ng a

th

inkin

g m

ap t

o h

ave s

tudents

com

pare

fra

ctio

n m

ultip

lication a

nd d

ivis

ion w

ith w

hole

num

ber

fract

ion

and d

ivis

ion in t

erm

s of

both

what

is h

appenin

g a

nd t

he s

ize o

f th

e p

roduct

/quotient.

Look for

students

to

note

sim

ilarities

such

as

a n

um

ber

div

ided b

y its

elf is

one.

#5 -

:

Ho

w i

s t

he

re

lati

on

sh

ip b

etw

ee

n m

ult

ipli

ca

tio

n a

nd

div

isio

n e

vid

en

t w

ith

fra

cti

on

s?

want

to a

ssess

stu

dents

’ unders

tandin

g o

f how

this

rela

tionsh

ip w

ork

s w

ith f

ract

ions.

Look for

students

to

make a

n initia

l co

nnect

ion b

etw

een fra

ctio

n d

ivis

ion a

nd m

ultip

lication in t

he less

ons

Div

idin

g

Fra

cti

on

s I

an

d I

I.

Use

the less

on D

ivid

ing

Fra

cti

on

s:

No

ticin

g P

att

ers

as

a m

ore

form

al

form

ative a

ssess

ment,

havin

g s

tudents

use

the c

oncl

usi

on s

ect

ion t

o e

xpla

in t

he r

ela

tionsh

ip t

hat

exis

ts,

nam

ely

that

div

isio

n o

f fr

act

ions

is e

quiv

ale

nt

to m

ultip

lication b

y t

he m

ultip

licative invers

e.

Page 2: Multiplying & Dividing Fractions · Multiplying Fractions on a Number Line and Dividing Fractions on a Number Line to have students write conclusions about the “cases” pr esented;

Genera

l Str

ate

gie

s

For

Form

ative

Assessm

ents

str

ate

gie

s t

hro

ughout

the u

nit

sid

ew

ays

Ask s

tudents

to r

ate

their

means t

hey u

nders

tand t

he t

opic

,

thum

bs d

ow

n m

eans t

hey d

on’t

and in t

he m

iddle

means t

hey g

et

part

of

it b

ut

still

need a

dditio

nal

pro

ble

ms t

o s

olv

e o

n w

hite

board

s a

nd h

ave t

hem

rais

e t

heir

Sta

tem

ent

Ask s

tudents

to w

rite

a s

um

mary

stu

dents

rate

their u

nders

tandin

g

cla

ss,

giv

e s

tudents

a p

roble

m

or

two t

o c

om

ple

te o

n a

slip

of

need t

o s

ee t

hat

div

isio

n is n

ot

changin

g a

num

ber,

but

ch

angin

g h

ow

it

Div

isio

n o

nly

mean

s t

o m

ake e

qu

al

gro

up

s o

r sh

are

fair

ly

“Y

ou

rs i

s n

ot

to r

easo

n w

hy, ju

st

invert

an

d m

ult

iply

(or

oth

er

rule

s a

bo

ut

ho

w t

o d

ivid

e f

racti

on

s)

As t

he c

onceptu

al unders

tandin

g o

f th

e d

ivis

ion o

f fr

actions is n

ot

as

to s

implif

y t

he p

rocedure

to a

meanin

gle

ss s

hort

cut,

such a

s t

he o

ne

term

s o

f stu

dents

bein

g a

ble

to u

se it

quic

kly

and g

et

corr

ect

answ

ers

without

conceptu

al unders

tandin

g,

they w

ill n

ot

know

how

to a

pply

it

or

Ove

rvie

wSt

ud

ents

wil

l als

o u

se c

on

text

an

d c

on

cret

e m

od

els

to u

nd

erst

and

an

d

exp

lain

th

e m

ean

ing

of

frac

tio

n d

ivis

ion

. In

gra

de

5, d

ivis

ion

is

lim

ited

to

a

wh

ole

nu

mb

er a

nd

a u

nit

fra

ctio

n.

Stu

den

ts m

ust

be

"ex

ible

in

usi

ng

bo

th

a “f

air

shar

e” a

nd

a “

mea

sure

men

t” d

e#n

itio

n o

f d

ivis

ion

to

mo

del

th

e tw

o

maj

or

case

s: t

he

div

iso

r is

a p

osi

tive

nu

mb

er le

ss t

han

1, a

nd

th

e d

ivis

or

is a

wh

ole

nu

mb

er.

Stu

den

ts w

ill u

se a

rea

mo

del

s an

d n

um

ber

lin

es, a

nd

an

alyz

e th

e re

lati

on

ship

bet

wee

n t

he

size

of

the

div

iden

d, t

he

div

iso

r an

d

the

qu

oti

ent.

Wh

en m

od

elin

g d

ivis

ion

pro

ble

ms

wit

h a

rea

mo

del

s, s

tud

ents

w

ill n

oti

ce t

hat

th

ey s

eem

to

be

mu

ltip

lyin

g, a

nd

th

us

stu

den

ts w

ill s

tud

y th

e re

lati

on

ship

bet

wee

n f

ract

ion

div

isio

n a

nd

mu

ltip

lica

tio

n t

o c

on

clu

de

that

div

isio

n i

s eq

uiv

alen

t to

mu

ltip

lica

tio

n b

y th

e m

ult

ipli

cati

ve i

nve

rse.

St

ud

ents

wil

l use

fra

ctio

n m

ult

ipli

cati

on

an

d d

ivis

ion

to

pro

ble

m s

olv

e,

incl

ud

ing

anal

yzin

g m

easu

rem

ent

dat

a re

pre

sen

ted

on

a li

ne

plo

t.

Uni

t S

tory

TH

E R

EASO

NIN

G B

EH

IND

TH

E F

LO

W

The u

nit b

egin

s w

ith a

fam

iliar

pro

ble

m w

e f

ace in c

lassro

om

s:

som

eone h

as b

rought

a t

reat

to s

hare

for

a b

irth

day a

nd w

e

Sh

ari

ng

Van

illa

Wafe

rs,

stu

dents

build

vanill

a w

afe

rs f

rom

pla

y-d

oh a

nd

physic

ally

div

ide t

hem

to s

how

how

much e

ach s

tudent

would

sim

ple

, soon s

tudents

don’t h

ave a

n e

qual

num

ber

of

whole

cookie

s f

or

each s

tudent

or

they h

ave f

ew

er

cookie

s t

han s

tudents

and m

ust

dete

rmin

e h

ow

to c

ut

up a

nd s

hare

meth

ods o

thers

use,

stu

dents

com

e t

o s

ee f

ractions a

s a

means

Stu

dents

continue t

o

betw

een f

ractions a

nd

div

isio

n o

f w

hole

num

bers

in t

he lesson M

akin

g A

Zip

Lin

e

As in t

he p

rior

lesson,

stu

dents

connect

fractions t

o d

ivis

ion o

f

solu

tions t

o e

ach p

roble

m r

epre

sente

d o

n t

he n

um

ber

line s

o a

s

to c

onnect

their u

nders

tandin

g o

f fr

actions o

n t

he n

um

ber

line a

nd

Sta

ndard

s

Addre

ssed

Nu

mb

er

an

d O

pera

tio

ns–

Fra

cti

on

s

Ap

ply

an

d e

xte

nd

pre

vio

us

un

ders

tan

din

gs o

f m

ult

ipli

cati

on

an

d d

ivis

ion

to

mu

ltip

ly a

nd

div

ide

fracti

on

s.

div

isio

n o

f w

hole

num

bers

leadin

g

to a

nsw

ers

in t

he f

orm

of

fractions

vis

ual fr

action m

odels

or

equations t

o

of

rice e

qually

by w

eig

ht,

how

many

pounds o

f rice s

hould

each p

ers

on g

et?

Betw

een w

hat

two w

hole

num

bers

does

your

answ

er

lie?

unders

tandin

gs o

f m

ultip

lication t

o

multip

ly a

fra

ction o

r w

hole

num

ber

by

a p

art

s o

f a p

art

itio

n o

f q into

b e

qual

part

s;

equiv

ale

ntly,

as t

he r

esult o

f a

fractional sid

e length

s b

y t

iling it

with

unit s

quare

s o

f th

e a

ppro

priate

unit

fraction s

ide length

s,

and s

how

that

the a

rea is t

he s

am

e a

s w

ould

be

are

as o

f re

cta

ngle

s,

and r

epre

sent

Page 3: Multiplying & Dividing Fractions · Multiplying Fractions on a Number Line and Dividing Fractions on a Number Line to have students write conclusions about the “cases” pr esented;

& F

low

AN

D I

NTEN

TIO

N O

F E

ACH

LESSO

N

Pain

tin

g a

Wall

- A

rea a

nd

Mu

ltip

licati

on

of

Fra

cti

on

s, stu

dents

begin

usin

g p

lay-d

oh t

o r

epre

sent

a w

all

and

show

ing w

hat

it w

ould

look lik

e t

o p

ain

t a

port

ion o

f th

e w

all

would

be p

ain

ted if

they

follo

wed b

y r

epre

senting t

he s

cenario p

icto

rially

, stu

dents

see

solv

e m

ultip

le p

roble

ms involv

ing t

he m

ultip

lication o

f fr

actio

ns

for

patt

ern

s t

o c

onclu

de t

hat

they c

an a

rriv

e a

t th

e p

roduct

pro

cedura

lly b

y m

ultip

lyin

g t

he n

um

era

tors

and d

enom

inato

rs;

thus,

stu

dents

begin

the lesson c

onceptu

ally

with c

oncre

te

Once s

tudents

unders

tand f

raction m

ultip

lication c

onceptu

ally

and p

rocedura

lly,

they a

pply

their k

now

ledge t

o p

ractice a

nd

Mu

ltip

lyin

g F

racti

on

s o

n a

Nu

mb

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e, stu

dents

will

stu

dy

on m

odelin

g f

raction m

ultip

lication o

n t

he n

um

ber

line,

with f

ocus

giv

en t

o u

nders

tandin

g h

ow

the w

hole

is d

ivid

ed t

o b

e a

ble

to

able

to u

se t

he n

um

ber

line t

o m

ultip

ly f

ractions,

they a

gain

be s

malle

r th

an,

equal to

or

gre

ate

r th

an t

he f

acto

rs a

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ell

as t

o

Sta

ndard

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ssed

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of

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ithout

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an t

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um

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ultip

lyin

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en n

um

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by a

fra

ction

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um

ber;

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ela

ting t

he p

rincip

le

of

div

isio

n t

o d

ivid

e u

nit f

ractions b

y w

hole

num

bers

and w

hole

num

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nit

the r

ela

tionship

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the r

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ivis

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stu

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tandin

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ractions a

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ivis

ion o

f w

hole

to inte

rpre

t th

e d

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reatly h

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acto

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ltip

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d t

hu

s, r

elyi

ng

sole

ly o

n s

ho

rtcu

ts le

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st

ud

ents

no

t u

nd

erst

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mat

h a

nd

ass

um

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h i

s n

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ou

t fo

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ate

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po

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met

ho

d o

f te

ach

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, st

ud

ents

wil

l use

co

nte

xt a

nd

han

ds-

on

mat

eria

ls t

o u

nd

erst

and

wh

at

frac

tio

n m

ult

ipli

cati

on

is

and

mea

ns.

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den

ts w

ill u

se a

rea

mo

del

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d a

nu

mb

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ne

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pro

ble

ms

in c

on

text

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son

ing

abo

ut

the

size

of

the

pro

du

ct a

nd

fac

tors

. St

ud

ents

wil

l stu

dy

pat

tern

s w

ith

th

eir

wo

rk t

o d

eriv

e th

e p

roce

du

re (

sho

rtcu

t).

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ltip

lica

tio

n o

f fr

acti

on

s (i

ncl

ud

ing

mix

ed n

um

ber

s) s

ho

uld

be

mas

tere

d b

y th

e en

d o

f gr

ade

5.

Uni

t

Page 4: Multiplying & Dividing Fractions · Multiplying Fractions on a Number Line and Dividing Fractions on a Number Line to have students write conclusions about the “cases” pr esented;

The

Uni

t! (

Con

t.)

“Ho

w m

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-fo

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Stu

dent

Talk

Str

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s

This

Top

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it?

Gra

de 6

– H

igh

Sch

oo

l

num

bers

and u

nit f

ractions a

s t

hey n

ow

get

into

the m

ore

com

plic

ate

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ases o

f

have s

een w

hy d

ivis

ion o

f fr

actions c

an b

e r

epre

sente

d a

s m

ultip

lication b

y t

he

apply

their u

nders

tandin

g o

f fr

actions o

n t

he n

um

ber

line a

s t

hey learn

to locate

non-u

nit f

ractions,

and t

hus m

ultip

lication o

f fr

actions s

hould

be m

aste

red b

y

gra

de 7

on,

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hus s

tudent

maste

ry o

f fr

action o

pera

tions w

ill b

e r

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d u

pon

div

isio

n a

re invers

e o

pera

tions w

ill b

e u

sed n

ot

only

to s

olv

e e

quations,

but

late

r

to m

ultip

ly a

nd d

ivid

e f

ractions a

s t

hey learn

to m

ultip

ly a

nd

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ide r

ational

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tud

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Types O

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)

SBAC

Cla

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• • • •

Uni

t S

tory

Stu

dents

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pra

ctice a

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olv

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eal w

orld p

roble

ms involv

ing t

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pra

ctice f

raction m

ultip

lication c

om

es in t

he f

orm

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the g

am

e, T

he

Facto

r G

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racti

on

Mu

ltip

licati

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acto

rs f

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a lis

t, b

ut

only

be

ing a

ble

fraction m

ultip

lication,

stu

dents

reason t

o d

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rmin

e w

hat

facto

r to

not

use s

o t

hat

the o

pposin

g t

eam

cannot

make a

giv

en p

roduct

to

Div

idin

g

Fra

cti

on

s I

.

can e

asily

see t

here

are

tw

o h

alv

es in

one w

hole

, so t

hey c

onnect

this

concre

te

this

is a

gre

at

observ

ation,

as it

begin

s t

o p

lant

the s

eed t

o late

r

connect

to t

he f

raction d

ivis

ion a

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m,

nam

ely

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lyin

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y t

he

Div

idin

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racti

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s I

I,

the d

ivid

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ivis

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itched s

o t

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re n

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idin

g

div

isio

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or

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itiv

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ave a

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hen d

ivid

e t

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ount

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qual num

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gro

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dents

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ith t

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se o

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y-d

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a m

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ngle

s a

s t

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rt w

ith o

nly

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ractional am

ount

and

then

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g t

hese m

odels

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dents

notice t

hat

this

looks s

urp

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Page 5: Multiplying & Dividing Fractions · Multiplying Fractions on a Number Line and Dividing Fractions on a Number Line to have students write conclusions about the “cases” pr esented;

Cohere

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Connections t

o o

ther

Gra

de 5

Topic

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Th

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bu

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hole

num

bers

by u

nit f

ractions a

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nit f

ractions b

y w

hole

num

bers

, stu

dents

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s in t

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hat

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racti

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ultip

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the p

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ivid

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an

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as a

corr

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raction m

ultip

lication p

roble

m t

hat

begin

s

with t

he s

am

e n

um

ber

and h

as t

he s

am

e s

olu

tion;

stu

dents

must

dete

rmin

e t

he m

issin

g f

acto

r to

make t

hat

multip

lication s

ente

nce

Thus,

stu

dents

are

able

to d

ivid

e u

sin

g a

n a

rea m

odel as w

ell

as

usin

g t

he s

tandard

pro

cedure

, w

ith t

he f

orm

er

bein

g m

uch m

ore

import

ant!

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dents

will

furt

her

their u

nders

tandin

g o

f d

ivis

ion o

f

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idin

g F

racti

on

s o

n a

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mb

er

Lin

e,

stu

dents

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again

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easure

ment

div

isio

n t

o inte

rpre

t pro

ble

ms involv

ing a

pro

ble

ms involv

ing t

he s

am

e d

ivis

or

and t

hen s

tudy t

he r

ela

tionsh

ip

Stu

dents

develo

p f

raction n

um

ber

sense t

o s

ee w

hen a

nd w

hy t

he

verify

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isio

n is e

quiv

ale

nt

multip

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licative

Fra

cti

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Mu

ltip

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Pro

ble

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olv

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, stu

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w F

ar

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u J

um

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st

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Mat

h B

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arg

um

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Math

Pra

ctice

Sta

ndard

s

Page 6: Multiplying & Dividing Fractions · Multiplying Fractions on a Number Line and Dividing Fractions on a Number Line to have students write conclusions about the “cases” pr esented;

The

Uni

t!

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w m

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div

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re t

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re i

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ivis

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ent

with

fractions?