Plan 3: Fair Trials with Two Dice - Scoilnet · 2019. 6. 25. · Fair Trials with Two Dice Aims •...
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Teaching & Learning Plans Plan 3: Fair Trials with Two Dice Leaving Certificate Syllabus
Transcript of Plan 3: Fair Trials with Two Dice - Scoilnet · 2019. 6. 25. · Fair Trials with Two Dice Aims •...
Teaching & Learning PlansPlan 3: Fair Trials with Two Dice
Leaving Certificate Syllabus
The Teaching & Learning Plans are structured as follows:
Aims outline what the lesson, or series of lessons, hopes to achieve.
Prior Knowledge points to relevant knowledge students may already have and also to knowledge which may be necessary in order to support them in accessing this new topic.
Learning Outcomes outline what a student will be able to do, know and understand having completed the topic.
Relationship to Syllabus refers to the relevant section of either the Junior and/or Leaving Certificate Syllabus.
Resources Required lists the resources which will be needed in the teaching and learning of a particular topic.
Introducing the topic (in some plans only) outlines an approach to introducing the topic.
Lesson Interaction is set out under four sub-headings:
i. Student Learning Tasks – Teacher Input: This section focuses on teacher input and gives details of the key student tasks and teacher questions which move the lesson forward.
ii. Student Activities – Possible and Expected Responses: Gives details of possible student reactions and responses and possible misconceptions students may have.
iii. Teacher’s Support and Actions: Gives details of teacher actions designed to support and scaffold student learning.
iv. Checking Understanding: Suggests questions a teacher might ask to evaluate whether the goals/learning outcomes are being/have been achieved. This evaluation will inform and direct the teaching and learning activities of the next class(es).
Student Activities linked to the lesson(s) are provided at the end of each plan.
© Project Maths Development Team 2009 www.projectmaths.ie 1
Teaching & Learning Plan 3: Fair Trials with Two Dice
AimsTo learn that not all results are equally probable•
To consider a given set of rules and the outcomes that produce a ‘win’ for •one of two players and to be able to determine whether the game is ‘fair’, i.e. whether each of the two players has the same chance of winning
To consider the theoretical probability of each result and devise a set of •rules to make the game ‘fair’
Prior Knowledge Students should have prior knowledge (from T and L Plan 1 and/or from primary school) of some terms associated with chance and uncertainty. They should be familiar with probability expressed as fraction or decimal in the range 0 to 1, or as a percentage in the range 0% to 100%.
Learning OutcomesAs a result of studying this topic, students will be able to
investigate further what the concept of fairness means in a game with 2 •dice
list all the possible outcomes for throwing 2 dice using a two way table•
relate the number of outcomes to the fundamental principle of counting•
come up with rules for a game which make it fair/unfair•
construct a probability table•
understand the relationship between an event and its complement•
determine the probability of an event using the results of an experiment •and use this to predict the result of a repetition of the experiment, for equally likely outcomes
Teaching & Learning Plan 3: Fair Trials with Two Dice
© Project Maths Development Team 2009 www.projectmaths.ie 2
Relationship to Leaving Certificate Syllabus
Sub-topics Foundation Level
Ordinary Level Higher Level
1.1 Counting List outcomes of an experiment.
Apply the fundamental principle of counting.
Count the arrangements of distinct objects.
1.2 Concepts of probability
Recognise that probability is a measure on a scale of 01- of how likely an event is to occur.
Recognise the role of expected value in decision making with a focus on fair games.
Extend the students’ understanding of the basic rules of probability.
Discrete probability
(as relative frequency)
Probability of desired outcomes in problems involving experiments, such as, dice throwing.
1.3 Outcomes of random processes
Apply the principle that, in the case of equally likely outcomes, the probability is given by the number of outcomes of interest divided by the total number of outcomes.
Resources RequiredCounters, 2 dice and a Game Sheet for each pair of students
Teac
hing
& L
earn
ing
Plan
3: F
air T
rial
s w
ith
Two
Dic
e
© P
roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
w
ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
3
Less
on
In
tera
ctio
nSt
uden
t Le
arni
ng T
asks
: Te
ache
r In
put
Stud
ent A
ctiv
itie
s: P
ossi
ble
and
Expe
cted
Res
pons
esTe
ache
r’s S
uppo
rt a
nd
Act
ions
Chec
king
Und
erst
andi
ng
In e
ach
gro
up
of
two
, on
e »
per
son
is n
om
inat
ed a
s A
an
d o
ne
as B
. Pla
yers
A
and
B t
ake
turn
s to
ro
ll th
e d
ie, a
nd
th
e w
inn
er is
d
eter
min
ed b
y th
e su
m o
f th
e n
um
ber
s o
n t
he
face
s as
fo
llow
s:
Stu
den
ts A
an
d B
»
alte
rnat
ely
roll
the
die
, ea
ch t
ime
add
ing
th
e sc
ore
s o
n e
ach
die
to
get
th
e o
utc
om
e. T
hey
pla
ce a
co
un
ter
on
eac
h o
utc
om
e.
A w
ins
if s
um
(i.e
. ou
tco
me)
»
is 2
, 3, 4
, 10,
11
or
12.
B w
ins
if s
um
i.e.
is 5
, 6,
»7,
8, 9
. Pla
y th
e g
ame
on
G
ame
Shee
t 1.
Dis
trib
ute
»
Stu
den
t A
ctiv
ity
1 so
th
at s
tud
ents
can
wri
te
thei
r p
red
icti
on
(St
ud
ent
Act
ivit
y 1A
) an
d k
eep
a
cou
nt
of
the
nu
mb
er o
f ti
mes
eac
h p
laye
r w
ins
(Stu
den
t A
ctiv
ity
1B).
Dis
trib
ute
co
un
ters
an
d
»G
ame
Shee
t 1
and
dic
e to
ea
ch p
air,
chec
kin
g t
hat
st
ud
ents
hav
e a
wri
tten
p
red
icti
on
an
d a
rea
son
fo
r it
.
Can
stu
den
ts r
eco
rd t
hei
r »
init
ial r
esu
lts
in t
hei
r co
pie
s?
Thin
k ab
ou
t th
is f
or
a fe
w
»m
inu
tes
and
wri
te d
ow
n
wh
ich
pla
yer
you
th
ink
will
w
in t
he
gam
e m
ost
oft
en if
it
is p
laye
d m
any
tim
es, a
nd
w
hy
you
th
ink
this
.
Stu
den
ts m
ay t
hin
k th
at
»si
nce
11
nu
mb
ers
hav
e b
een
list
ed, a
nd
sin
ce A
ca
n w
in o
n 6
of
thes
e an
d
B o
nly
on
5, t
hat
A is
mo
re
likel
y to
win
th
an B
.
Ask
fo
r a
sho
w o
f h
and
s o
n
»w
ho
th
inks
A w
ill w
in a
nd
w
ho
th
inks
B w
ill w
in.
Teac
hing
& L
earn
ing
Plan
3: F
air T
rial
s w
ith
Two
Dic
e
© P
roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
w
ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
4
Stud
ent
Lear
ning
Tas
ks:
Teac
her
Inpu
tSt
uden
t Act
ivit
ies:
Pos
sibl
e an
d Ex
pect
ed R
espo
nses
Teac
her’s
Sup
port
and
A
ctio
nsCh
ecki
ng U
nder
stan
ding
The
gam
e is
pla
yed
un
til
»o
ne
per
son
has
rea
ched
th
e b
ott
om
of
the
gri
d o
n
Gam
e Sh
eet
1 an
d s
tud
ents
co
un
t th
e n
um
ber
of
tim
es
A w
on
an
d t
he
nu
mb
er o
f ti
mes
B w
on
an
d fi
ll o
ut
the
Mas
ter
Shee
t o
n t
he
bo
ard
als
o.
The
stu
den
ts s
ho
uld
fin
d
»th
at A
win
s o
nly
ab
ou
t 1/
3 o
f th
e ti
me.
Ch
eck
that
eac
h p
air
»u
nd
erst
and
s w
hat
th
ey a
re
do
ing
an
d o
ccas
ion
ally
, as
yo
u c
ircu
late
, ask
“h
and
s u
p h
ow
man
y A
’s
are
win
nin
g?”
an
d t
hen
“h
and
s u
p h
ow
man
y B
’s
are
win
nin
g?”
so
stu
den
ts
are
awar
e o
f an
ove
rall
tren
d.
Plac
e »
Mas
ter
Shee
t 1
(res
ult
s fr
om
th
e w
ho
le
clas
s) o
n t
he
bo
ard
.
Wer
e st
ud
ents
ab
le
»to
co
nd
uct
th
e g
ame
succ
essf
ully
an
d d
id t
hey
n
oti
ce B
win
nin
g m
uch
m
ore
oft
en?
Ho
w m
any
stu
den
ts in
th
e »
clas
s w
ere
able
to
mak
e ac
cura
te p
red
icti
on
s w
ith
va
lid r
easo
ns?
Did
th
ey r
eact
to
th
is a
s »
bei
ng
un
fair
?
Wh
en y
ou
are
fin
ish
ed fi
ll »
ou
t St
ud
ent
Act
ivit
y 1B
an
d fi
ll in
yo
ur
resu
lts
on
M
aste
r Sh
eet
1 (r
esu
lts
fro
m t
he
wh
ole
cla
ss)
on
th
e b
oar
d.
Stu
den
ts c
hec
k th
is a
gai
nst
»
thei
r p
red
icti
on
, an
alys
ing
an
y d
iffe
ren
ce a
nd
fill
in
Stu
den
t A
ctiv
ity
1C.
The
rela
tive
fre
qu
ency
is
»n
ow
clo
ser
to 1
/3.
As
you
cir
cula
te c
hec
k »
pre
dic
tio
ns
agai
nst
o
utc
om
es o
f th
e ex
per
imen
t, a
nd
ask
st
ud
ents
ab
ou
t th
eir
just
ifica
tio
ns.
Wh
ich
nu
mb
er o
n e
ach
»
die
can
no
t b
e a
po
ssib
le
ou
tco
me?
“1 “
can
nev
er b
e an
•
ou
tco
me
as t
he
smal
lest
su
m p
oss
ible
is 2
.
Do
es t
his
gam
e ap
pea
r to
»
be
fair
?N
o. F
air
– if
A a
nd
B h
ave
•an
eq
ual
ch
ance
of
win
nin
g
oth
erw
ise
un
fair.
Giv
e st
ud
ents
a m
inu
te t
o
»th
ink
and
th
en a
sk o
ne
stu
den
t.
Teac
hing
& L
earn
ing
Plan
3: F
air T
rial
s w
ith
Two
Dic
e
© P
roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
w
ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
5
Stud
ent
Lear
ning
Tas
ks:
Teac
her
Inpu
tSt
uden
t Act
ivit
ies:
Pos
sibl
e an
d Ex
pect
ed R
espo
nses
Teac
her’s
Sup
port
and
A
ctio
nsCh
ecki
ng U
nder
stan
ding
Wh
y is
it n
ot
fair
? »
Stu
den
ts m
igh
t sa
y th
at 2
•
can
on
ly b
e g
ot
1 w
ay (
1+1)
w
her
eas
9 fo
r ex
amp
le c
an
be
go
t fr
om
(3+
6), (
4+5)
.
All
ou
tco
mes
are
no
t •
equ
ally
like
ly.
Giv
e st
ud
ents
a m
inu
te t
o
»th
ink
and
th
en a
sk o
ne
stu
den
t.
Do
stu
den
ts u
nd
erst
and
»
the
con
cep
t o
f fa
irn
ess?
Is t
he
ou
tco
me
4+5
the
»sa
me
as t
he
ou
tco
me
5+4?
No
, bec
ause
th
e fi
rst
tim
e •
4 is
fro
m d
ie 1
an
d t
he
seco
nd
tim
e it
’s f
rom
die
2.
Giv
e st
ud
ents
a m
inu
te t
o
»th
ink
and
th
en a
sk o
ne
stu
den
t.
In h
ow
man
y w
ays
cou
ld a
n
»o
utc
om
e o
f 9
be
ach
ieve
d?
4+5
•5+
4 •
3+6
•6+
3•
Giv
e st
ud
ents
a m
inu
te t
o
»th
ink
and
th
en a
sk o
ne
stu
den
t.
Co
uld
yo
u d
esig
n a
tab
le t
o
»sh
ow
yo
u a
ll th
e p
oss
ible
o
utc
om
es.
The
set
of
all t
he
po
ssib
le
»o
utc
om
es is
cal
led
th
e ‘S
amp
le S
pac
e’.
Try
this
fo
r a
few
min
ute
s. »
Som
e st
ud
ents
will
»
pro
bab
ly c
om
e u
p w
ith
th
e 2
way
tab
le a
nd
sh
ow
it t
o
the
clas
s.
Cir
cula
te lo
oki
ng
at
»st
ud
ent
sug
ges
tio
ns
and
g
ivin
g h
elp
ful h
ints
. On
fi
nd
ing
a s
uit
able
tab
le
ask
stu
den
ts t
o s
ho
w a
nd
ex
pla
in it
to
th
e cl
ass.
St
ud
ents
may
nee
d h
elp
d
esig
nin
g t
he
tab
le.
Ho
w m
any
of
the
stu
den
ts
»w
ere
able
to
co
me
up
wit
h
a su
itab
le t
able
?
Ind
ivid
ual
ly, fi
ll in
th
e »
2-w
ay t
able
fo
r th
e sa
mp
le
spac
e fo
r th
e su
m a
chie
ved
o
n t
hro
win
g 2
dic
e (S
tud
ent
Act
ivit
y 2A
).
Stu
den
ts fi
ll u
p t
he
tab
le
»as
per
exa
mp
le in
Stu
den
t A
ctiv
ity
2A.
Dis
trib
ute
»
Stu
den
t A
ctiv
ity
2.
Cir
cula
te t
o c
hec
k th
at
»st
ud
ents
un
der
stan
d h
ow
to
fill
it in
.
Are
all
stu
den
ts a
ble
to
fill
»in
th
e ta
ble
su
cces
sfu
lly
and
wit
h u
nd
erst
and
ing
?
Teac
hing
& L
earn
ing
Plan
3: F
air T
rial
s w
ith
Two
Dic
e
© P
roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
w
ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
6
Stud
ent
Lear
ning
Tas
ks:
Teac
her
Inpu
tSt
uden
t Act
ivit
ies:
Pos
sibl
e an
d Ex
pect
ed R
espo
nses
Teac
her’s
Sup
port
and
A
ctio
nsCh
ecki
ng U
nder
stan
ding
Ho
w m
any
po
ssib
le
»o
utc
om
es a
re t
her
e?
Stu
den
t A
ctiv
ity
2B.
36.
•C
ircu
late
an
d lo
ok
at t
he
»an
swer
s b
ein
g fi
lled
in,
aski
ng
qu
esti
on
s w
her
e n
eces
sary
.
Can
yo
u r
elat
e th
is b
ack
to
»th
e fu
nd
amen
tal p
rin
cip
le
of
cou
nti
ng
in a
pre
vio
us
less
on
?
If t
her
e ar
e 6
dif
fere
nt
•o
utc
om
es f
rom
die
1,
and
6 d
iffe
ren
t o
utc
om
es
fro
m d
ie 2
, th
en t
he
tota
l nu
mb
er o
f p
oss
ible
o
utc
om
es is
6x6
= 3
6.
Ask
th
e q
ues
tio
n a
nd
wai
t »
for
som
eon
e to
vo
lun
teer
an
an
swer
. If
it’s
th
e sa
me
per
son
an
swer
ing
all
the
tim
e, a
sk a
no
ther
stu
den
t,
lead
ing
th
em t
o t
he
answ
er if
th
ey d
on
’t k
no
w
it, b
y re
ferr
ing
bac
k to
an
ex
amp
le t
hey
did
wh
en
lear
nin
g t
he
fun
dam
enta
l p
rin
cip
le o
f co
un
tin
g.
Hav
e st
ud
ents
bee
n a
ble
»
to r
ecal
l an
d u
se t
he
fun
dam
enta
l pri
nci
ple
of
cou
nti
ng
?
Go
ing
bac
k to
th
e ru
les
of
»th
e g
ame,
fo
r h
ow
man
y o
utc
om
es w
ill p
laye
r A
w
in a
nd
fo
r h
ow
man
y o
utc
om
es w
ill p
laye
r B
w
in?
Stu
den
t A
ctiv
ity
2C.
12 o
f th
e 36
ou
tco
mes
giv
e •
a w
in f
or
A w
her
eas
24 o
f th
e o
utc
om
es g
ive
a w
in
for
B.
Go
bac
k to
yo
ur
pre
dic
tio
n
»ag
ain
, Stu
den
t A
ctiv
ity
1C,
and
if it
was
no
t co
nsi
sten
t w
ith
th
e o
utc
om
e w
rite
d
ow
n w
hy
it w
as d
iffe
ren
t.
Stu
den
ts a
rtic
ula
te t
hei
r »
mis
con
cep
tio
ns.
Cir
cula
te a
nd
no
te
»m
isco
nce
pti
on
s, a
nd
ask
a
sele
ctio
n o
f st
ud
ents
wh
o
tho
ug
ht
A w
ou
ld w
in t
o
exp
lain
wh
y th
ey t
ho
ug
ht
that
an
d w
hy
they
no
w
thin
k d
iffe
ren
tly.
Are
stu
den
ts a
ble
to
»
un
der
stan
d in
cas
es w
her
e th
eir
pre
dic
tio
ns
wer
e in
er
ror
wh
y th
is w
as s
o?
Teac
hing
& L
earn
ing
Plan
3: F
air T
rial
s w
ith
Two
Dic
e
© P
roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
w
ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
7
Stud
ent
Lear
ning
Tas
ks: T
each
er In
put
Stud
ent A
ctiv
itie
s:
Poss
ible
and
Exp
ecte
d Re
spon
ses
Teac
her’s
Sup
port
and
A
ctio
nsCh
ecki
ng U
nder
stan
ding
Wri
te d
ow
n n
ew r
ule
s fo
r th
e g
ame,
»
Stu
den
t A
ctiv
ity
2D, w
hic
h w
ill m
ake
it f
air
and
an
exp
lan
atio
n o
f w
hy
it is
n
ow
fai
r.
Is m
ore
th
an o
ne
set
of
rule
s p
oss
ible
? »
Dif
fere
nt
gro
up
s »
pre
sen
t th
eir
new
ru
les
for
clas
s ap
pro
val.
For
exam
ple
. Pla
yer
A
•w
ins
if t
he
ou
tco
me
is
2, 3
, 4, 5
, 8 o
r 10
an
d B
w
ins
if t
he
ou
tco
me
is
6, 7
, 9, 1
1 o
r 12
.
Cir
cula
te a
nd
wh
en
»g
rou
ps
are
fin
ish
ed a
sk
a co
up
le o
f g
rou
ps
to
exp
lain
th
eir
new
ru
les.
Are
stu
den
ts a
ble
to
»
mak
e u
p m
ore
th
an o
ne
set
of
rule
s sa
tisf
yin
g
the
crit
erio
n f
or
a fa
ir
gam
e?
The
app
roac
h in
Tea
chin
g &
Lea
rnin
g
»Pl
an 2
, an
d a
bo
ve in
Stu
den
t A
ctiv
ity
1B, i
s kn
ow
n a
s th
e ‘e
xper
imen
tal’
or
‘em
pir
ical
’ ap
pro
ach
to
cal
cula
tin
g
pro
bab
iliti
es. I
n t
his
cas
e th
e pr
obab
ility
of
an e
ven
t is
th
e va
lue
that
th
e re
lati
ve f
req
uen
cy t
end
s to
in a
n
infi
nit
e n
um
ber
of
tria
ls.
In t
he
theo
reti
cal a
pp
roac
h, w
hen
»
thro
win
g a
die
, th
ere
are
six
po
ssib
le
ou
tco
mes
wh
ich
are
all
equa
lly li
kely
to
ap
pea
r d
ue
to t
he
sym
met
ry o
f th
e d
ie, a
nd
giv
en t
hat
it is
a f
air
die
(n
ot
load
ed)
so w
e h
ave
no
rea
son
to
as
sum
e th
at a
ny
nu
mb
er w
ill a
pp
ear
mo
re o
ften
th
an a
no
ther
. A2
is o
ne
of
the
6 p
oss
ible
ou
tco
mes
, so
th
e lik
elih
oo
d o
f it
tu
rnin
g u
p is
1 o
ut
of
6.
Teac
hing
& L
earn
ing
Plan
3: F
air T
rial
s w
ith
Two
Dic
e
© P
roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
w
ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
8
Stud
ent
Lear
ning
Tas
ks:
Teac
her
Inpu
tSt
uden
t Act
ivit
ies:
Pos
sibl
e an
d Ex
pect
ed R
espo
nses
Teac
her’s
Sup
port
and
A
ctio
nsCh
ecki
ng U
nder
stan
ding
Wh
at is
th
e re
lati
on
ship
»
bet
wee
n t
he
exp
erim
enta
l ap
pro
ach
to
cal
cula
tin
g
pro
bab
ility
an
d t
he
theo
reti
cal a
pp
roac
h?
As
the
nu
mb
er o
f tr
ials
•
incr
ease
s th
e re
lati
ve
freq
uen
cy b
eco
mes
alm
ost
eq
ual
to
th
e th
eore
tica
l p
rob
abili
ty.
Ask
s st
ud
ents
to
rec
all a
nd
»
then
aft
er a
sh
ort
pau
se
asks
an
ind
ivid
ual
.
Can
stu
den
ts r
ecal
l ho
w t
o
»ca
lcu
late
pro
bab
ility
fo
r eq
ual
ly li
kely
ou
tco
mes
?
Ho
w d
o w
e ca
lcu
late
th
e »
theo
reti
cal p
rob
abili
ty
of
each
ou
tco
me
in t
his
sa
mp
le s
pac
e?
Ho
w m
any
tim
es it
•
occ
urs
div
ided
by
the
tota
l nu
mb
er o
f p
oss
ible
o
utc
om
es.
Wh
at a
ssu
mp
tio
n a
re w
e »
mak
ing
?A
ll o
utc
om
es a
re e
qu
ally
•
likel
y.
Are
all
36 o
utc
om
es e
qu
ally
»
likel
y h
ere?
Yes
.•
Co
nst
ruct
a p
rob
abili
ty
»ta
ble
(St
ud
ent
Act
ivit
y 3)
fo
r th
e su
m o
f 2
dic
e u
sin
g
Stu
den
t A
ctiv
ity
2A.
Wal
k ar
ou
nd
ob
serv
ing
»
stu
den
ts a
s th
ey fi
ll o
ut
the
pro
bab
ility
tab
le.
Did
stu
den
ts fi
ll o
ut
the
»ta
ble
co
rrec
tly?
Ass
um
ing
th
at b
oth
of
the
»d
ice
are
fair,
an
d a
ll 36
o
utc
om
es a
re e
qu
ally
like
ly,
wh
at is
th
e p
rob
abili
ty o
f th
e su
m b
ein
g 5
?
Usi
ng
th
e 2
way
tab
le
•(S
tud
ent
Act
ivit
y 2A
) sh
ow
ing
th
e sa
mp
le s
pac
e co
nst
ruct
ed f
or
the
gam
e,
ther
e ar
e 4
ou
tco
mes
fo
r 5,
so
th
e p
rob
abili
ty o
f g
etti
ng
a 5
is 4
/36.
Wh
at is
th
e su
m o
f th
e »
pro
bab
iliti
es f
or
the
sam
ple
sp
ace?
1•
Ask
stu
den
ts if
th
ey
»re
mem
ber
th
is h
app
enin
g
in t
he
last
less
on
wit
h
ou
tco
mes
fro
m 1
die
?
Did
all
stu
den
ts g
et 1
? »
Teac
hing
& L
earn
ing
Plan
3: F
air T
rial
s w
ith
Two
Dic
e
© P
roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
w
ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
9
Stud
ent
Lear
ning
Tas
ks:
Teac
her
Inpu
tSt
uden
t Act
ivit
ies:
Pos
sibl
e an
d Ex
pect
ed R
espo
nses
Teac
her’s
Sup
port
and
A
ctio
nsCh
ecki
ng U
nder
stan
ding
If t
he
pro
bab
ility
of
get
tin
g
»a
3 is
2/3
6, w
hat
is t
he
pro
bab
ility
of
no
t g
etti
ng
a
3 w
ith
ou
t ad
din
g u
p a
ll th
e o
ther
pro
bab
iliti
es?
Wri
te
do
wn
th
e an
swer
.
1-2/
36=
34/3
6•
If a
stu
den
t ca
nn
ot
get
th
e »
answ
er w
ith
ou
t ad
din
g u
p
all t
he
oth
er p
rob
abili
ties
, te
ll th
em t
o d
o t
hat
firs
t an
d t
hen
see
if t
hey
can
th
en fi
nd
th
e o
ther
way
by
insp
ecti
ng
th
eir
answ
er.
Ho
w m
any
stu
den
ts g
ot
»th
e co
rrec
t an
swer
wit
ho
ut
hav
ing
to
ad
d u
p a
ll th
e o
ther
pro
bab
iliti
es?
Go
ing
bac
k to
th
e o
rig
inal
»
rule
s fo
r th
e g
ame,
wh
at
is t
he
pro
bab
ility
th
at A
w
ins?
Fill
in a
nsw
er o
n
»St
ud
ent
Act
ivit
y 3.
12/3
6=1/
3•
For
stu
den
ts w
ho
hav
e »
dif
ficu
lty:
ask
th
em t
o
cou
nt
ho
w m
any
of
the
ou
tco
mes
giv
e A
a w
in, a
nd
h
ow
man
y o
utc
om
es a
re
ther
e in
to
tal.
Use
th
e p
rob
abili
ty t
hat
»
A w
ins
to c
alcu
late
th
e p
rob
abili
ty t
hat
B w
ins,
w
ith
ou
t ad
din
g.
Fill
in a
nsw
er o
n
»St
ud
ent
Act
ivit
y 3.
1-1/
3=2/
3•
If a
stu
den
t ca
nn
ot
get
th
e »
answ
er w
ith
ou
t ad
din
g u
p
all t
he
oth
er p
rob
abili
ties
, te
ll th
em t
o d
o t
hat
firs
t an
d t
hen
see
if t
hey
can
th
en fi
nd
th
e o
ther
way
by
insp
ecti
ng
th
eir
answ
er.
Do
stu
den
ts u
nd
erst
and
»
the
rela
tio
nsh
ip b
etw
een
an
eve
nt
and
its
com
ple
men
t?
Co
mp
are
this
wit
h
»ex
per
imen
tal r
esu
lt f
or
rela
tive
fre
qu
ency
.
Fill
in a
nsw
er o
n
»St
ud
ent
Act
ivit
y 3.
They
are
ver
y cl
ose
an
d t
he
•re
lati
ve f
req
uen
cy b
eco
mes
cl
ose
r to
th
e th
eore
tica
l p
rob
abili
ty a
s th
e n
um
ber
o
f g
ames
incr
ease
s.
Cir
cula
te c
hec
kin
g t
hat
»
Stu
den
t A
ctiv
ity
3 is
b
ein
g c
om
ple
ted
, ask
ing
q
ues
tio
ns
of
stu
den
ts w
ho
ar
e h
avin
g d
iffi
cult
y.
Do
stu
den
ts s
ee t
hat
»
the
exp
erim
enta
l res
ult
s ap
pro
ach
th
e th
eore
tica
l va
lues
fo
r p
rob
abili
ty a
s th
e n
um
ber
of
gam
es
incr
ease
s?
Teac
hing
& L
earn
ing
Plan
3: F
air T
rial
s w
ith
Two
Dic
e
© P
roje
ct M
aths
Dev
elop
men
t Tea
m 2
009
w
ww
.pro
ject
mat
hs.ie
KE
Y:
» n
ext
step
•
stud
ent
answ
er/r
espo
nse
10
Stud
ent
Lear
ning
Tas
ks:
Teac
her
Inpu
tSt
uden
t Act
ivit
ies:
Pos
sibl
e an
d Ex
pect
ed R
espo
nses
Teac
her’s
Sup
port
and
A
ctio
nsCh
ecki
ng U
nder
stan
ding
If t
he
pro
bab
ility
of
a su
m
»o
f 7
occ
urr
ing
is 6
/36=
1/6,
h
ow
man
y 7’
s w
ou
ld y
ou
ex
pec
t to
get
if t
he
dic
e ar
e to
ssed
100
tim
es?
100x
1/6
i.e. a
pp
rox
17
•(1
/6 o
f th
e ti
me
you
exp
ect
a 7.
)
Emp
has
ise
that
yo
u a
re
»d
ealin
g w
ith
eq
ual
ly li
kely
o
utc
om
es.
Can
stu
den
ts c
alcu
late
an
»
exp
ecte
d v
alu
e fo
r a
larg
e n
um
ber
of
tria
ls?
Refle
ctio
n
Wri
te d
ow
n 3
th
ing
s yo
u
»le
arn
ed a
bo
ut
pro
bab
ility
to
day
. W
rite
do
wn
an
yth
ing
yo
u
»fo
un
d d
iffi
cult
.
Wri
te d
ow
n a
ny
qu
esti
on
s »
you
may
hav
e.
Ho
w t
o:
•lis
t al
l po
ssib
le o
utc
om
es
1.
(sam
ple
sp
ace)
fo
r th
row
ing
2 d
ice
use
th
e lis
t o
f al
l po
ssib
le
2.
ou
tco
mes
to
jud
ge
fair
nes
sco
nst
ruct
a p
rob
abili
ty
3.
tab
leca
lcu
late
th
e co
mp
lem
ent
4.
of
an e
ven
tca
lcu
late
exp
ecte
d v
alu
e 5.
fo
r a
larg
e n
um
ber
of
tria
ls.
Cir
cula
te a
nd
tak
e »
no
te p
arti
cula
rly
of
any
qu
esti
on
s st
ud
ents
hav
e an
d h
elp
th
em t
o a
nsw
er
them
.
Hav
e al
l stu
den
ts le
arn
ed
»an
d u
nd
erst
oo
d t
hes
e it
ems?
Are
th
ey u
sin
g t
he
»te
rmin
olo
gy
wit
h
un
der
stan
din
g a
nd
co
mm
un
icat
ing
wit
h e
ach
o
ther
usi
ng
th
ese
term
s?
Teaching & Learning Plan 3: Fair Trials with Two Dice
© Project Maths Development Team 2009 www.projectmaths.ie 11
Game Sheet 1A wins A wins A wins B wins B wins B wins B wins B wins A wins A wins A wins
1 2 3 4 5 6 7 8 9 10 11 12
Teaching & Learning Plan 3: Fair Trials with Two Dice
© Project Maths Development Team 2009 www.projectmaths.ie 12
Student Activity 1
Student Activity 1A Prediction
Player _____ will win most often because:
Student Activity 1B Play the game and record the results below:
Use Tally Marks to Help You Keep a Score
Total (Frequency) Relative Frequency (total no. of wins/total no. of games)
Player A Wins
Player B Wins
Totals
Student Activity 1C Did your predicted results agree with your actual results?
Teaching & Learning Plan 3: Fair Trials with Two Dice
© Project Maths Development Team 2009 www.projectmaths.ie 13
Master Sheet 1 (Results from the Whole Class)
Play the game and record the results below:
Use Tally Marks to Help You Keep a Score
Total (Frequency) Relative Frequency (total no. of wins/total no. of games)
Player A Wins 2+3+...
Player B Wins
Totals
Teaching & Learning Plan 3: Fair Trials with Two Dice
© Project Maths Development Team 2009 www.projectmaths.ie 14
Student Activity 2
Student Activity 2B
How many possible outcomes are there?__________________
Student Activity 2A
Complete the table to show all of the possible outcomes. Two way table showing the sample space.
Number thrown
1 2 3 4 5 6
1 1+1=2
2
3
4
5 5+2=7
6
Student Activity 2COriginal Rules: Player A wins when the sum is 2, 3, 4, 10, 11 or 12.
Player B wins when the sum is 5, 6, 7, 8 or 9.
For how many outcomes will player A win?__________________
For how many outcomes will player B win?__________________
Student Activity 2DNew Rules: Player A wins when the sum is __________________________
Player B wins when the sum is __________________________
Why I chose these new rules:
Teaching & Learning Plan 3: Fair Trials with Two Dice
© Project Maths Development Team 2009 www.projectmaths.ie 15
Student Activity 3Sum Frequency Probability
=
2 1
3
4
5
6
7
8
9
10
11
12
no. of outcomes in the event no. of outcomes in the sample event
1 36
