Embed Size (px)
Citation preview
Teaching & Learning PlansPlan 1: Introduction to Probability
Junior Certificate Syllabus
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 1: Introduction to Probability
AimsTo familiarise students with the ways in which we talk about uncertainty •and look at everyday situations in which probability arises
To engage students in activities that will give them contact with the main •ideas of probability
To rehearse the language and patterns associated with probability•
Prior Knowledge Prior knowledge and experience of handling fractions and percentages is required.
Students have prior knowledge of some of the ideas and language patterns of the topic of probability from the primary school curriculum, third class upwards, but the topic may need to be revisited to ensure that all students know the basics. Students may have certain ‘misconceptions’ based on intuition and personal experience. Experimentation is required, where students count and analyse outcomes, thereby constructing their own meanings by connecting the new information to what they already believe. Students accept new ideas only when they see that their old ideas do not work: for example, finding out experimentally that 6 is not the hardest number to get when throwing a fair die, and that all outcomes of such a throw are equally likely.
When working together cooperatively in small groups, to test a hypothesis for example, students will be using the language of the topic thus improving their ability to communicate effectively using correct terminology. They can then move on from the experimental approach, where they calculate the relative frequency of an event, which tends towards the probability for an infinite sequence of trials, to the theoretical approach, which is based on logical reasoning.
Learning OutcomesAs a result of studying this topic, students will be able to
distinguish certain from uncertain events•
describe events as being more or less likely from experience•
order events from least likely to most likely and justify their choice•
use a scale from 0 to 1 to informally place everyday chance-related events•
represent and interpret probabilities as fractions, decimals and percentages•
represent the probability of an event as a fraction or decimal between 0 •and 1 or as a percentage
list all possible outcomes for practical experiments such as rolling one die•
determine the probability of an event using the results of an experiment•
Teaching & Learning Plan 1: Introduction to Probability
© Project Maths Development Team 2009 www.projectmaths.ie 2
Relationship to Junior Certificate SyllabusSub-topics Ordinary Level1.5 Counting Listing outcomes of experiments in a
systematic way
1.6 Concepts of probability The probability of an event occurring: students progress from informal to formal descriptions of probability.
Predicting and determining probabilities
Decide whether an everyday event is likely or unlikely to occur.
Relationship to Leaving Certificate Syllabus
Sub-topics Foundation Level Ordinary Level1.2 Concepts of
probabilityDecide whether an everyday event is likely or unlikely to occur.
Recognise that probability is a measure on a scale of 0-1 of how likely an event is to occur.
Estimate probabilities from experimental data.
Associate the probability of an event with its long-run, relative frequency.
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.
Teaching & Learning Plan 1: Introduction to Probability
© Project Maths Development Team 2009 www.projectmaths.ie 3
Introducing the TopicStudents need to get into a frame of mind for learning probability by looking at the language of uncertainty and then trying to order phrases used to describe uncertainty, leading to being able to quantifying it.
The following examples could be used to explore misconceptions:
What is the most difficult number to get when throwing a fair die?•
Random events should have outcomes which appear random; for example, •in the lotto theory tells us that any of the six numbers is equally likely to turn up, yet more people choose randomly spaced numbers than numbers which form a pattern like 1,2,3,4,5,6 etc.
The likelihood of 2 consecutive numbers appearing in any Lotto draw •(which is > 50%) could easily be investigated by reference to a number of recent draws.
Real Life ContextThe following examples could be used to explore real life contexts.
Looking at statistics from the Census, questions like:
How long will I live? •
Will I get married? •
How many children will I have?•
These questions can be answered with some degree of certainty based on population statistics.
Life assurance companies work out how much to charge for their premiums based on tables of life expectancy. Why are some premiums cheaper than others?
Teac
hing
& L
earn
ing
Plan
1: I
ntro
duct
ion
to P
roba
bilit
y
© 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
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 t
his
less
on
we
will
be
»in
vest
igat
ing
idea
s ab
ou
t u
nce
rtai
nty
or
chan
ce o
r p
rob
abili
ty.
Wh
en, i
n o
ur
ever
yday
»
lives
, wo
uld
kn
ow
ing
th
e ch
ance
or
likel
iho
od
of
an
even
t o
ccu
rrin
g a
ffec
t o
ur
acti
on
s? D
o y
ou
hav
e an
y su
gg
esti
on
s?
Bet
tin
g o
n a
ho
rse
– •
kno
win
g t
he
od
ds.
Taki
ng
a n
ew d
rug
– w
hat
•
are
the
chan
ces
of
it c
uri
ng
th
e d
isea
se?
Flyi
ng
wit
h a
par
ticu
lar
•ai
rlin
e –
wh
at is
its
safe
ty
reco
rd t
o d
ate?
Car
insu
ran
ce c
om
pan
ies
•ch
arg
e p
rem
ium
s b
ased
on
th
e p
rob
abili
ty t
hat
yo
u
will
hav
e an
acc
iden
t.
Hea
lth
insu
ran
ce p
rem
ium
s •
are
less
if y
ou
do
n’t
sm
oke
an
d h
ave
no
dia
gn
ose
d
seri
ou
s ill
nes
ses
sin
ce t
he
pro
bab
ility
of
you
bei
ng
si
ck is
less
.
Did
stu
den
ts c
om
e u
p w
ith
»
seve
ral v
arie
d s
ug
ges
tio
ns?
Teac
hing
& L
earn
ing
Plan
1: I
ntro
duct
ion
to P
roba
bilit
y
© 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
We
will
beg
in b
y lo
oki
ng
»
at t
he
lan
gu
age
use
d in
u
nce
rtai
nty
an
d c
han
ce,
and
mo
ve o
n t
o h
ow
n
um
ber
s ar
e as
sig
ned
to
u
nce
rtai
nty
.
Dis
trib
ute
»
Stu
den
t A
ctiv
ity
1.
Div
ide
clas
s in
to s
mal
l »
gro
up
s. E
ach
mem
ber
of
the
gro
up
sh
ou
ld h
ave
a cl
ear
task
. Mak
e su
re
ther
e is
a t
ime
limit
on
th
e ac
tivi
ty.
Stu
den
t A
ctiv
ity
1A,
» fi
ll in
:
3 ev
ents
wh
ich
are
cer
tain
»
to h
app
en.
3 ev
ents
wh
ich
are
cer
tain
»
no
t to
hap
pen
or
to h
ave
hap
pen
ed.
(in
th
e ar
ea m
arke
d
»u
nce
rtai
nty
) 3
even
ts
wh
ich
mig
ht
or
mig
ht
no
t h
app
en.
Dep
end
ing
on
th
e ev
ent,
»
pla
ce t
he
un
cert
ain
on
es
nea
rer
the
“cer
tain
to
h
app
en”
or
“cer
tain
no
t to
hap
pen
” si
de
of
the
dia
gra
m.
Wal
k ar
ou
nd
to
see
wh
at
»st
ud
ents
are
wri
tin
g d
ow
n;
if t
hey
are
str
ug
glin
g, a
sk
qu
esti
on
s w
hic
h w
ill g
ive
them
a h
int
of
an e
xam
ple
.
Take
sel
ecti
on
s fr
om
eac
h
»g
rou
p a
nd
pu
t th
ese
on
th
e b
oar
d.
Did
stu
den
ts c
om
e u
p w
ith
»
seve
ral v
arie
d s
ug
ges
tio
ns?
Teac
hing
& L
earn
ing
Plan
1: I
ntro
duct
ion
to P
roba
bilit
y
© 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
Cer
tain
to
hap
pen
/hav
e •
hap
pen
ed:
I hav
e b
een
bo
rn.
1.
The
sun
ro
se t
his
mo
rnin
g.
2.
Ther
e is
a C
hin
ese
3.
Oly
mp
ian
wh
o is
6’ 7
”.
Cer
tain
no
t to
hap
pen
/hav
e •
hap
pen
ed/im
po
ssib
le:
1.
Irel
and
will
no
t h
ost
th
e n
ext
Oly
mp
ics.
2.
Fin
din
g a
tri
ang
le w
ith
4
sid
es.
3.
Som
eon
e in
ou
r cl
ass
was
b
orn
du
rin
g t
he
Firs
t W
orl
d
War
.4.
M
ich
ael J
acks
on
is s
till
aliv
e.
Mig
ht/
mig
ht
no
t h
app
en• 1.
Ir
elan
d w
ill w
in a
go
ld
med
al in
th
e n
ext
Oly
mp
ics.
2.
It w
ill r
ain
to
mo
rro
w.
3.
Ro
y K
ean
e w
ill m
anag
e th
e Ir
ish
so
ccer
sq
uad
(st
ud
ents
b
asin
g t
hei
r co
nvi
ctio
ns
on
ex
per
ien
ce o
r in
tuit
ion
).
Wal
k ar
ou
nd
to
see
wh
at
»st
ud
ents
are
wri
tin
g d
ow
n;
if t
hey
are
str
ug
glin
g, a
sk
qu
esti
on
s w
hic
h w
ill g
ive
them
a h
int
of
an e
xam
ple
.
Take
sel
ecti
on
s fr
om
eac
h
»g
rou
p a
nd
pu
t th
ese
on
th
e b
oar
d.
Did
stu
den
ts c
om
e u
p w
ith
»
seve
ral v
arie
d s
ug
ges
tio
ns?
Teac
hing
& L
earn
ing
Plan
1: I
ntro
duct
ion
to P
roba
bilit
y
© 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:
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
Wo
rkin
g in
pai
rs,
»b
rain
sto
rm p
hra
ses
use
d
to d
escr
ibe
the
pro
bab
ility
o
r ch
ance
of
an e
ven
t o
ccu
rrin
g o
n a
sca
le f
rom
ab
solu
te c
erta
inty
to
no
ch
ance
at
all.
Wri
te d
ow
n a
t le
ast
5 »
ph
rase
s o
n t
he
bo
tto
m o
f St
ud
ent
Act
ivit
y 1B
.
Stu
den
ts w
ill fi
ll o
ut
»p
hra
ses
on
Stu
den
t A
ctiv
ity
1B:
a d
ead
cer
t•
a ve
ry g
oo
d c
han
ce•
likel
y•
alm
ost
cer
tain
•n
o c
han
ce•
mo
re t
han
like
ly•
extr
emel
y lik
ely
•50
/50
•a
smal
l ch
ance
•ex
trem
ely
un
likel
y•
nev
er•
no
t in
a m
on
th o
f Su
nd
ays
•fa
irly
like
ly•
Ch
eck
if e
very
on
e »
un
der
stan
ds
the
task
.
Wal
k ar
ou
nd
to
see
wh
at
»st
ud
ents
are
wri
tin
g d
ow
n.
If a
nyo
ne
is s
tru
gg
ling
, ask
q
ues
tio
ns
wh
ich
will
giv
e th
em a
hin
t o
f an
exa
mp
le.
Take
sel
ecti
on
s fr
om
eac
h
»g
rou
p a
nd
rec
ord
th
em o
n
the
bo
ard
/flip
char
t/la
pto
p.
Did
stu
den
ts h
ave
lots
of
»d
iffe
ren
t su
gg
esti
on
s o
nce
th
ey u
nd
erst
oo
d t
he
task
?
Take
do
wn
th
e se
lect
ion
»
of
clas
s p
hra
ses
fro
m t
he
bo
ard
into
th
e ta
ble
on
St
ud
ent
Act
ivit
y 2A
.
Stu
den
ts c
op
y fr
om
»
the
bo
ard
th
e se
lect
ion
o
f p
hra
ses
(ab
ou
t 12
) su
gg
este
d b
y cl
ass.
Dis
trib
ute
»
Stu
den
t A
ctiv
ity
2.
Teac
hing
& L
earn
ing
Plan
1: I
ntro
duct
ion
to P
roba
bilit
y
© 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
Fro
m t
his
list
of
ph
rase
s »
iden
tify
an
eve
nt
wh
ich
can
b
est
be
des
crib
ed b
y ea
ch
of
thes
e te
rms.
Stu
den
ts t
hen
fill
in o
ne
»ev
ent
for
each
ph
rase
on
St
ud
ent
Act
ivit
y 2B
.
Ch
eck
if e
very
on
e »
un
der
stan
ds
the
task
.
Wal
k ar
ou
nd
to
see
wh
at
»st
ud
ents
are
wri
tin
g d
ow
n;
if t
hey
are
str
ug
glin
g, a
sk
qu
esti
on
s w
hic
h w
ill g
ive
them
a h
int
of
an e
xam
ple
.
Take
sel
ecti
on
s fr
om
eac
h
»g
rou
p a
nd
pu
t o
n t
he
bo
ard
. In
vite
stu
den
ts t
o
agre
e o
r d
isag
ree,
bu
t ex
pla
in t
hat
th
ey m
ust
h
ave
a va
lid r
easo
n f
or
do
ing
so
.
Wer
e th
ere
man
y an
d
»va
ried
su
gg
esti
on
s an
d
wer
e th
ey a
pp
rop
riat
e to
th
e p
hra
ses?
No
w t
hin
k in
ter
ms
of
»h
ow
yo
u m
igh
t in
terp
ret
this
lack
of
pre
cisi
on
in
dif
fere
nt
situ
atio
ns,
fo
r ex
amp
le t
he
pla
ne
you
’re
on
pro
bab
ly w
on
’t c
rash
vs
. it
pro
bab
ly w
on
’t r
ain
to
mo
rro
w. W
ou
ld y
ou
be
hap
py
wit
h t
he
ph
rase
“p
rob
ably
wo
n’t
” in
bo
th
situ
atio
ns?
Stu
den
ts w
ill b
e lo
oki
ng
fo
r »
mo
re p
reci
sio
n in
th
e ca
se
of
a p
lan
e n
ot
cras
hin
g –
in
th
e fo
rm o
f a
nu
mer
ic
rep
rese
nta
tio
n o
f th
e p
hra
se “
pro
bab
ly w
on
’t”.
Do
stu
den
ts r
eco
gn
ise
»th
e n
eed
fo
r a
nu
mer
ic
rep
rese
nta
tio
n o
f th
e p
hra
se “
pro
bab
ly w
on
’t”?
Teac
hing
& L
earn
ing
Plan
1: I
ntro
duct
ion
to P
roba
bilit
y
© 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
Let’
s tr
y to
get
mo
re
»p
reci
sio
n b
y u
sin
g
per
cen
tag
es.
In t
erm
s o
f p
erce
nta
ges
, »
ho
w w
ou
ld y
ou
des
crib
e a
“dea
d c
ert”
, or
som
eth
ing
w
hic
h w
as d
efin
itel
y g
oin
g
to h
app
en?
100%
•
Dis
trib
ute
»
Stu
den
t A
ctiv
ity
3. Ask
th
e cl
ass
and
giv
e th
em
»a
mo
men
t to
th
ink
bef
ore
as
kin
g o
ne
stu
den
t.
Wri
te t
his
in a
t th
e co
rrec
t »
po
siti
on
on
‘Th
e Pr
ob
abili
ty
Scal
e (S
tud
ent
Act
ivit
y 3A
).
In t
erm
s o
f p
erce
nta
ges
, »
ho
w w
ou
ld y
ou
des
crib
e so
met
hin
g w
hic
h h
ad n
o
chan
ce o
f h
app
enin
g?
Wri
te t
his
in o
n ‘T
he
Pro
bab
ility
Sca
le’ (
Stu
den
t A
ctiv
ity
3A).
0%•
Emp
has
ise
no
ch
ance
. »
Are
stu
den
ts g
etti
ng
th
e »
idea
of
limit
s o
f 0%
an
d
100%
fo
r th
e ra
ng
e o
f p
rob
abili
ties
of
an e
ven
t.
Say
that
so
met
hin
g
»p
rob
ably
will
hap
pen
, th
at
it is
no
t a
“dea
d c
ert”
bu
t th
at it
has
a v
ery
go
od
ch
ance
; can
yo
u a
ssig
n a
p
erce
nta
ge
to t
his
eve
nt?
Wh
at is
th
e ra
ng
e o
f th
e »
answ
ers?
May
be
70%
, 80
% b
ut
•g
reat
er t
han
50%
>
50%
•
Emp
has
ise
the
idea
of
a »
po
ssib
ility
of
a ra
ng
e o
f an
swer
s b
ut
no
te t
hat
all
answ
ers
are
gre
ater
th
an
50%
.
Hav
e st
ud
ents
un
der
sto
od
»
that
ph
rase
s lik
e “h
as a
g
oo
d c
han
ce”
are
imp
reci
se
bu
t ye
t h
ave
a b
ias
tow
ard
s th
e u
pp
er e
nd
of
the
scal
e?
Teac
hing
& L
earn
ing
Plan
1: I
ntro
duct
ion
to P
roba
bilit
y
© 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
Ass
ign
an
est
imat
ed
»p
erce
nta
ge
to t
he
ph
rase
“p
rob
ably
wo
n’t
h
app
en?”
(sn
ow
on
St.
Pa
tric
k’s
day
).
Wh
at is
th
e ra
ng
e o
f th
e »
answ
ers?
May
be
20%
, 10%
•
<50
%•
Ag
ain
, hav
e st
ud
ents
»
un
der
sto
od
th
e id
ea o
f a
po
ssib
ility
of
a ra
ng
e o
f an
swer
s b
ut
all l
ess
than
50
%?
Wh
at r
ang
e o
f p
erce
nta
ges
»
can
we
use
to
rep
rese
nt
the
chan
ce o
r lik
elih
oo
d o
f so
met
hin
g h
app
enin
g, t
o
cove
r al
l po
ssib
iliti
es?
0% t
o 1
00%
•A
sk t
he
clas
s; w
ait
a sh
ort
»
wh
ile a
nd
th
en a
sk a
n
ind
ivid
ual
stu
den
t. If
st
ud
ents
can
’t a
nsw
er, t
ake
them
bac
k th
rou
gh
th
e p
revi
ou
s q
ues
tio
ns.
Do
stu
den
ts u
nd
erst
and
»
that
ch
ance
can
be
rep
rese
nte
d b
y a
ran
ge
fro
m 0
% t
o 1
00%
?
Co
nsi
der
a w
ho
le b
ar
»o
f ch
oco
late
– w
hat
p
erce
nta
ge
of
the
bar
are
w
e lo
oki
ng
at?
100%
•
If w
e to
ss a
co
in, w
hat
is
»th
e ch
ance
of
get
tin
g a
‘t
ail’?
Wh
at is
an
oth
er w
ay o
f »
exp
ress
ing
th
is c
han
ce?
50%
•
½•
Lead
th
e cl
ass
to t
he
idea
»
of
a fr
acti
on
as
exp
ress
ing
th
e ch
ance
of
som
eth
ing
h
app
enin
g.
If s
tud
ents
are
co
mfo
rtab
le
»w
ith
th
e id
ea o
f fr
acti
on
s,
it m
ay b
e p
oss
ible
to
ex
plo
re t
he
rolli
ng
of
a fa
ir
die
.
Teac
hing
& L
earn
ing
Plan
1: I
ntro
duct
ion
to P
roba
bilit
y
© 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
11
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
Inst
ead
of
giv
ing
0%
as
»th
e ch
ance
of
som
eth
ing
h
app
enin
g w
hat
nu
mb
er
cou
ld w
e u
se?
No
w w
rite
th
is in
on
‘Th
e »
Pro
bab
ility
Sca
le (
Stu
den
t A
ctiv
ity
3A).
0•
Ask
th
e cl
ass;
th
en s
elec
t »
an in
div
idu
al s
tud
ent
to
answ
er.
Are
stu
den
ts a
sso
ciat
ing
»
a 0%
ch
ance
wit
h t
he
nu
mb
er 0
?
Bet
wee
n w
hat
ran
ges
of
»n
um
ber
s ca
n I
rep
rese
nt
the
chan
ce o
f so
met
hin
g
hap
pen
ing
to
co
ver
all
po
ssib
iliti
es?
0 to
1
•A
sk t
he
clas
s; t
hen
sel
ect
»an
ind
ivid
ual
stu
den
t to
an
swer
.
Do
stu
den
ts u
nd
erst
and
»
that
pro
bab
ility
can
be
rep
rese
nte
d o
n a
sca
le o
f 0
to 1
as
wel
l as
fro
m 0
% t
o
100%
?
So n
ow
yo
u h
ave
two
way
s »
of
rep
rese
nti
ng
a s
cale
of
pro
bab
iliti
es. W
hat
are
th
ey?
0% t
o 1
00%
• o
r 0 to
1
•
Ask
th
e cl
ass;
th
en s
elec
t »
an in
div
idu
al s
tud
ent
to
answ
er.
Giv
e ex
amp
les
of
nu
mb
ers
»w
hic
h c
an r
epre
sen
t th
e p
oss
ibili
ty o
f so
met
hin
g
hap
pen
ing
?
Posi
tio
n t
hem
on
‘Th
e »
Pro
bab
ility
Sca
le1
on
St
ud
ent
Act
ivit
y 3A
.
Sho
w m
e w
her
e 5/
8 w
ou
ld
»b
e p
lace
d. H
as a
nyo
ne
anyt
hin
g d
iffe
ren
t?
0.9,
1, 0
, .5,
.3, ¾
, 0.7
5•
1 =
dea
d c
ert
•0
= n
ever
•0.
5 =
eve
ns
•0.
8 =
qu
ite
likel
y•
0.1
=ve
ry u
nlik
ely
•0.
2 =
qu
ite
un
likel
y•
0.4
= n
ot
a g
oo
d c
han
ce•
Ask
mo
st s
tud
ents
in t
he
»cl
ass,
eac
h t
ime
aski
ng
th
e cl
ass
to v
erif
y if
th
ey a
re
corr
ect,
an
d w
hy.
Wri
te u
p c
orr
ect
valu
es o
n
»th
e b
oar
d.
No
te: (
Ensu
re t
hat
a go
od
sele
ctio
n of
pro
per
frac
tions
and
de
cim
als
are
incl
uded
). N
ote
that
, by
con
tras
t w
ith “
likel
y”, w
e ca
n al
l agr
ee w
ith t
he p
laci
ng o
f th
ese
valu
es.
Can
stu
den
ts a
pp
ly w
hat
»
they
hav
e le
arn
ed a
bo
ut
the
pro
bab
ility
sca
le a
nd
ca
n s
tud
ents
giv
e a
ran
ge
of
nu
mb
ers
incl
ud
ing
bo
th
dec
imal
s an
d f
ract
ion
s?
Teac
hing
& L
earn
ing
Plan
1: I
ntro
duct
ion
to P
roba
bilit
y
© 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
12
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 I
say
that
th
e ch
ance
of
it
»ra
inin
g t
om
orr
ow
is 2
.5 –
is
this
po
ssib
le?
If I
say
that
th
e p
rob
abili
ty
»o
f o
ne
of
you
flyi
ng
to
M
ars
tom
orr
ow
is 3
– is
th
is
po
ssib
le?
No
, bec
ause
th
e ch
ance
of
•so
met
hin
g h
app
enin
g m
ust
b
e a
nu
mb
er b
etw
een
0 a
nd
1.
Ask
th
e cl
ass;
th
en s
elec
t »
an in
div
idu
al s
tud
ent
to
answ
er.
Can
stu
den
ts a
pp
ly w
hat
»
they
hav
e le
arn
ed a
bo
ut
the
pro
bab
ility
sca
le?
Can
yo
u g
ive
exam
ple
s »
of
nu
mb
ers
wh
ich
can
no
t re
pre
sen
t th
e ch
ance
of
som
eth
ing
hap
pen
ing
?
-1•
5, 7
, •
2000
,•
23.6
,•
9/8
•
Ask
mo
st s
tud
ents
in t
he
»cl
ass.
Th
en a
sk t
he
clas
s to
ve
rify
if t
he
answ
ers
are
corr
ect,
an
d w
hy.
Sug
ges
t fr
acti
on
s an
d
»n
egat
ive
nu
mb
ers.
Can
stu
den
ts g
ive
a »
ran
ge
of
nu
mb
ers
incl
ud
ing
neg
ativ
e n
um
ber
s?
Usi
ng
a r
ule
r, d
raw
in y
ou
r »
cop
y ‘T
he
Pro
bab
ility
Sca
le’
line
seg
men
t fr
om
Stu
den
t A
ctiv
ity
3A.
Lab
el t
his
“Th
e Pr
ob
abili
ty
»Sc
ale”
. Mar
k in
th
e n
um
ber
s lis
ted
on
th
e b
oar
d.
Stu
den
ts d
raw
th
e lin
e an
d
»fi
ll in
th
e n
um
ber
s.C
ircu
late
, su
pp
ort
ing
»
stu
den
ts w
ho
hav
e d
iffi
cult
y w
ith
th
e ta
sk.
Hav
e al
l stu
den
ts b
een
»
succ
essf
ul i
n d
raw
ing
an
d
mar
kin
g t
he
scal
e?
The
line
on
»
Stu
den
t A
ctiv
ity
3B r
epre
sen
ts a
sc
ale
fro
m 0
to
1. W
ork
ing
in
pai
rs w
rite
in e
ach
item
fr
om
Bo
x A
at
the
mo
st
app
rop
riat
e p
osi
tio
n o
n t
he
line.
(U
se a
rro
ws.
)
Stu
den
ts w
rite
in e
ach
»
ph
rase
or
nu
mb
er o
nto
th
e ap
pro
pri
ate
spo
t o
n t
he
scal
e.
Stu
den
ts m
igh
t st
art
wit
h
»p
erce
nta
ges
, wh
ich
th
ey
are
mo
st f
amili
ar w
ith
, an
d
pro
ceed
to
ph
rase
s an
d t
hen
fr
acti
on
s.
Pin
a la
rge
scal
e o
nto
th
e »
bo
ard
an
d h
ave
card
s w
ith
th
e va
rio
us
op
tio
ns
wri
tten
o
n t
hem
(o
r d
raw
in o
n t
he
bo
ard
).
Ch
eck
if e
very
on
e »
un
der
stan
ds
the
task
.
Are
th
ere
man
y »
stu
den
ts h
avin
g
dif
ficu
lty
un
der
stan
din
g
per
cen
tag
es e
tc?
Teac
hing
& L
earn
ing
Plan
1: I
ntro
duct
ion
to P
roba
bilit
y
© 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
13
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
To k
eep
th
e d
iag
ram
»
clea
r yo
u c
ou
ld p
ut
all
per
cen
tag
es in
a li
ne,
fr
acti
on
s u
nd
ern
eath
on
an
oth
er li
ne
and
th
en
ph
rase
s o
n a
no
ther
lin
e.
Stu
den
ts m
ay le
ave
the
»p
hra
ses
un
til l
ast
as t
hey
ar
e im
pre
cise
.
Wal
k ar
ou
nd
to
see
wh
at
»st
ud
ents
are
wri
tin
g d
ow
n.
Som
e st
ud
ents
may
hav
e d
iffi
cult
y h
ere
chan
gin
g
per
cen
tag
es o
r d
ecim
als
to f
ract
ion
s o
r vi
ce v
ersa
, an
d a
s yo
u w
alk
aro
un
d
iden
tify
an
d g
uid
e th
ose
st
ud
ents
.
Has
eve
ryo
ne
com
ple
ted
»
the
task
?
Att
ach
th
e p
hra
ses
to t
he
»la
rge
scal
e o
n t
he
bo
ard
. (o
r w
rite
in o
n t
he
bo
ard
).
Do
es e
very
on
e ag
ree
wit
h
»th
ese
pla
cem
ents
?
Do
es a
nyo
ne
thin
k th
ey
»sh
ou
ld b
e ch
ang
ed?
Has
an
yon
e an
yth
ing
»
dif
fere
nt?
Wh
y d
o y
ou
th
ink
it s
ho
uld
»
be
chan
ged
?
Wh
en e
very
on
e is
fin
ish
ed
»a
volu
nte
er s
tud
ent
fills
in
the
ph
rase
s o
n t
he
bo
ard
.
Than
k st
ud
ent
wh
o d
oes
»
bo
ard
wo
rk.
If a
stu
den
t d
isag
rees
th
ey
»m
ust
giv
e a
reas
on
. Bri
ef
clas
s d
iscu
ssio
n t
o a
chie
ve
con
sen
sus.
Is t
he
stu
den
t b
od
y in
»
agre
emen
t w
ith
th
e p
lace
men
t o
f th
e p
hra
ses?
Teac
hing
& L
earn
ing
Plan
1: I
ntro
duct
ion
to P
roba
bilit
y
© 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
14
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
For
each
of
»th
e n
um
eric
al
rep
rese
nta
tio
ns
of
pro
bab
ility
in B
ox
A w
rite
it in
th
e tw
o o
ther
po
ssib
le
form
s, f
or
exam
ple
as
a f
ract
ion
/dec
imal
/p
erce
nta
ge.
¾=
75%
=0.
75•
0.37
5=3/
8=37
.5%
•87
.5%
=7/
8=0.
875
•0.
125=
1/8=
12.5
%•
0.25
=1/
4=25
%•
Plac
e st
ud
ents
wh
o c
an
»d
o t
his
co
mp
eten
tly
wit
h s
tud
ents
wh
o h
ave
dif
ficu
lty.
Th
e b
ette
r st
ud
ent
can
hav
e a
sup
po
rtin
g r
ole
wh
en t
he
oth
er s
tud
ent
is a
sked
to
ex
pla
in h
is/h
er a
nsw
er.
Ask
a s
tud
ent
wh
o w
as
»p
revi
ou
sly
un
sure
to
cal
l o
ut
and
exp
lain
ho
w h
e/sh
e d
id t
he
con
vers
ion
s fr
om
on
e fo
rm t
o a
no
ther
.
Refl
ecti
on
No
w t
hin
k h
ow
yo
u
»h
ave
rep
rese
nte
d
pro
bab
ility
n
um
eric
ally
.
Giv
e 3
nu
mer
ical
»
rep
rese
nta
tio
ns
of
a 50
/50
chan
ce?
No
w w
rite
do
wn
»
thre
e id
eas
you
h
ave
lear
ned
ab
ou
t p
rob
abili
ty a
nd
at
leas
t o
ne
qu
esti
on
.
%, f
ract
ion
s an
d d
ecim
als
•b
etw
een
0 a
nd
1
0.5,
1/2
, 50%
•
Are
stu
den
ts a
war
e o
f th
ese
idea
s?
»
Pro
bab
ility
is a
bo
ut
un
cert
ain
ty
1.
and
ho
w t
o a
ssig
n n
um
ber
s to
u
nce
rtai
nty
(p
hra
ses
bei
ng
to
o
imp
reci
se)
giv
en s
om
e in
form
atio
n
abo
ut
the
par
ticu
lar
situ
atio
n.
The
Pro
bab
ility
sca
le is
bet
wee
n 0
2.
an
d 1
.
Pro
bab
ility
can
be
rep
rese
nte
d b
y 3.
a
frac
tio
n o
r a
dec
imal
bet
wee
n
0 an
d 1
or
by
a p
erce
nta
ge
e.g
.½,
0.5,
50%
.
No
t ev
eryt
hin
g in
mat
hem
atic
s is
4.
ce
rtai
n!
Teaching & Learning Plan 1: Introduction to Probability
© Project Maths Development Team 2009 www.projectmaths.ie 15
Student Activity 1
Certain not to happen
1.
2.
3.
Certain to happen
1.
2.
3.
Area of Uncertainty
Student Activity 1B Phrases used to describe uncertainty
1.
2.
3.
4.
5.
Student Activity 1A
Teaching & Learning Plan 1: Introduction to Probability
© Project Maths Development Team 2009 www.projectmaths.ie 16
Student Activity 2
Student Activity 2A
Phrases used to describe uncertainty(examples from the class)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Student Activity 2B
An event associated with each phrase(examples from the class)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Student Activity 2C
Order the above phrases on the scaled line segment below – from least likely to most likely.
Teaching & Learning Plan 1: Introduction to Probability
© Project Maths Development Team 2009 www.projectmaths.ie 17
Student Activity 3
Student Activity 3A
The Probability Scale
Student Activity 3B
The Probability Scale
Box A0 1
Place the above phrases, numbers and percentages at the correct position on the probability scale.
Find and write down instances from TV, radio, or in the newspaper which illustrate how probability affects people’s lives.
Extremely unlikely
0.25
1
¾
87.5%
3/8
Extremely likely
0
Equally likely Impossible
0.125
50:501/2
75%
Certain
1 in 4 chance
Probability of getting an odd number when rolling a die
1/4
