Grades 5 to 8 Blackline Masters - Province of Manitoba · Students use combinations that add up to...
34
G RADE 8 M ATHEMATICS Grades 5 to 8 Blackline Masters
Transcript of Grades 5 to 8 Blackline Masters - Province of Manitoba · Students use combinations that add up to...
G r a d e 8 M a t h e M a t i c s
Grades 5 to 8 Blackline Masters
BLM 5–8.1: Observation Form
Students: Date: Activity:
Observation:
Possible Actions:
Students: Date: Activity:
Observation:
Possible Actions:
Students: Date: Activity:
Observation:
Possible Actions:
BLM
5–
8.2
: C
on
ce
pt
De
scrip
tio
n S
he
et
#1
C
hara
cter
istic
s
Exam
ples
N
on-E
xam
ples
D
iagr
ams/
Pict
ures
BLM 5–8.3: Concept Description Sheet #2
Concept Description
Example
Diagram
Non-Example
Concept Description
Example
Diagram
Non-Example
BLM 5–8.4: How I Worked in My Group Name ______________________________________________ Date ______________________________________________ Task ______________________________________________
Comments
I took turns
I participated
I encouraged others
I shared materials
I stayed with my group
I listened
I accomplished the task
BLM
5–8
.5:
Nu
mb
er C
ard
s
0
1
2
3
4
5
6
7
8
9
BLM 5–8.6: Blank Hundred Squares
BLM
5–
8.7
: P
lace
-V
alu
e C
ha
rt—
Wh
ole
Nu
mb
ers
hund
reds
te
ns
ones
hund
reds
te
ns
ones
hund
reds
te
ns
ones
Mill
ions
Thou
sand
s
One
s
BLM
5–
8.8
: M
en
tal
Ma
th S
tra
teg
ies
The
follo
win
g lis
t com
pile
s m
enta
l mat
h st
rate
gies
as
foun
d in
the
Kind
erga
rten
to G
rade
8 M
athe
mat
ics:
Man
itoba
Cu
rric
ulum
Fra
mew
ork
of O
utco
mes
. Not
e: T
his
reso
urce
is m
eant
for t
each
er in
form
atio
n, n
ot a
s a
list o
f str
ateg
ies
that
st
uden
ts s
houl
d m
emor
ize.
Gra
de 1
G
rade
2
Gra
de 3
G
rade
4
Gra
de 5
G
rade
6
Gra
de 7
1.
N.1
0.
2.
N.8
. 2.
N.1
0.
3.N
.6.
3.N
.7.
3.N
.10.
3.
N.1
1.
3.N
.12.
4.N
.4.
4.N
.5.
4.N
.6.
4.N
.11.
5.N
.2.
5.N
.3.
5.N
.4.
6.N
.8.
7.
N.2
.
Gra
de
Con
cept
St
rate
gy
Mea
ning
Ex
ampl
e 1
Add
ition
C
ount
ing
on
Stud
ents
beg
in w
ith a
num
ber a
nd c
ount
on
to
get t
he s
um. S
tude
nts
shou
ld b
egin
to
reco
gniz
e th
at b
egin
ning
with
the
larg
er o
f the
tw
o ad
dend
s is
gen
eral
ly m
ost e
ffici
ent.
for 3
+ 5
th
ink
5 +
1 +
1 +
1 is
8;
thin
k 5,
6, 7
, 8
1 Su
btra
ctio
n C
ount
ing
back
St
uden
ts b
egin
with
the
min
uend
and
cou
nt
back
to fi
nd th
e di
ffere
nce.
fo
r 6 –
2
thin
k 6
– 1
– 1
is 4;
th
ink
6, 5
, 4
1, 2
A
dditi
on
U
sing
one
m
ore
Star
ting
from
a k
now
n fa
ct a
nd a
ddin
g on
e m
ore.
fo
r 8 +
5 if
you
kno
w
8 +
4 is
12 a
nd o
ne m
ore
is 13
1,
2
Add
ition
Usi
ng o
ne le
ss
Star
ting
from
a k
now
n fa
ct a
nd ta
king
one
aw
ay.
for 8
+ 6
if y
ou k
now
8
+ 7
is 15
and
one
less
is
14
1, 2
, A
dditi
on
Subt
ract
ion
Mak
ing
10
Stud
ents
use
com
bina
tions
that
add
up
to te
n an
d ca
n ex
tend
this
to m
ultip
les
of te
n in
late
r gr
ades
.
4 +
____
is 1
0 7
+ __
__ is
10;
so
23
+ __
__ is
30 (c
ontin
ued)
BLM
5–
8.8
: M
en
tal
Ma
th S
tra
teg
ies (
Co
nti
nu
ed
)
Gra
de
Con
cept
St
rate
gy
Mea
ning
Ex
ampl
e 1
Add
ition
Su
btra
ctio
n St
artin
g fr
om
know
n do
uble
s
Stud
ents
nee
d to
wor
k to
kno
w th
eir d
oubl
es
fact
s. 2
+ 2
is 4
and
4 –
2 is
2
1, 2
, 3
Subt
ract
ion
Usi
ng
addi
tion
to
subt
ract
This
is a
form
of p
art-p
art-w
hole
re
pres
enta
tion.
Thi
nkin
g of
add
ition
as:
par
t + p
art =
who
le
Thin
king
of s
ubtr
actio
n as
:
who
le –
par
t = p
art
for 1
2 –
5 th
ink
5 +
____
= 1
2 so
12
– 5
is 7
2 A
dditi
on
Subt
ract
ion
The
zero
pr
oper
ty o
f ad
ditio
n
Kno
win
g th
at a
ddin
g 0
to a
n ad
dend
doe
s no
t ch
ange
its
valu
e, a
nd ta
king
0 fr
om a
min
uend
do
es n
ot c
hang
e th
e va
lue.
0 +
5 =
5;
11 –
0 =
11
2, 3
A
dditi
on
Subt
ract
ion
Usi
ng d
oubl
es
Stud
ents
lear
n do
uble
s, a
nd u
se th
is to
ext
end
fact
s:
usi
ng d
oubl
es
d
oubl
es p
lus
one
(or t
wo)
dou
bles
min
us o
ne (o
r tw
o)
for 5
+ 7
th
ink
6 +
6 is
12;
for 5
+ 7
th
ink
5 +
5 +
2 is
12
for 5
+ 7
th
ink
7 +
7 –
2 is
12
2, 3
A
dditi
on
Subt
ract
ion
Build
ing
on
know
n do
uble
s
Stud
ents
lear
n do
uble
s, a
nd u
se th
is to
ext
end
fact
s. fo
r 7 +
8
thin
k 7
+ 7
is 14
so
7 +
8 is
14
+ 1
is 15
3
Add
ition
Add
ing
from
le
ft to
righ
t U
sing
pla
ce v
alue
und
erst
andi
ng to
add
2-
digi
t num
eral
s. fo
r 25
+ 33
th
ink
20 +
30
and
5 +
3 is
50 +
8 o
r 58
(con
tinue
d)
BLM
5–
8.8
: M
en
tal
Ma
th S
tra
teg
ies (
Co
nti
nu
ed
)
Gra
de
Con
cept
St
rate
gy
Mea
ning
Ex
ampl
e 3
Add
ition
Su
btra
ctio
n M
akin
g 10
St
uden
ts u
se c
ombi
natio
ns th
at a
dd u
p to
ten
to c
alcu
late
oth
er m
ath
fact
s an
d ca
n ex
tend
th
is to
mul
tiple
s of
ten
in la
ter g
rade
s.
for 8
+ 5
th
ink
8 +
2 +
3 is
10 +
3 o
r 13
3 A
dditi
on
Subt
ract
ion
Com
pens
atio
n U
sing
oth
er k
now
n m
ath
fact
s an
d co
mpe
nsat
ing.
For
exa
mpl
e, a
ddin
g 2
to a
n ad
dend
and
taki
ng 2
aw
ay fr
om th
e su
m.
for 2
5 +
33
thin
k 25
+ 3
5 –
2 is
60
– 2
or 5
8 3
Add
ition
C
omm
utat
ive
prop
erty
Sw
itchi
ng th
e or
der o
f the
two
num
bers
bei
ng
adde
d w
ill n
ot a
ffect
the
sum
. 4
+ 3
is th
e sam
e as
3 +
4 3,
4
(dec
imal
s)
Add
ition
Su
btra
ctio
n C
ompa
tible
nu
mbe
rs
Com
patib
le n
umbe
rs a
re fr
iend
ly n
umbe
rs
(ofte
n as
soci
ated
with
com
patib
le n
umbe
rs to
5
or 1
0).
for 4
+ 3
stud
ents
may
th
ink
4 +
1 is
5 an
d 2
mor
e mak
es 7
3
Mul
tiplic
atio
n D
ivis
ion
Arr
ay
Usi
ng a
n or
dere
d ar
rang
emen
t to
show
m
ultip
licat
ion
or d
ivis
ion
(sim
ilar t
o ar
ea).
for 3
x 4
thin
k
fo
r 12
3 th
ink
3
Mul
tiplic
atio
n C
omm
utat
ive
prop
erty
Sw
itchi
ng th
e or
der o
f the
two
num
bers
bei
ng
mul
tiplie
d w
ill n
ot a
ffect
the
prod
uct.
4 x
5 is
the s
ame a
s 5
x 4
3 M
ultip
licat
ion
Sk
ip-c
ount
ing
Usi
ng th
e co
ncep
t of m
ultip
licat
ion
as a
ser
ies
of e
qual
gro
upin
g to
det
erm
ine
a pr
oduc
t. fo
r 4 x
2
thin
k 2,
4, 6
, 8
so 4
x 2
is 8
4
Mul
tiplic
atio
n Ze
ro p
rope
rty
of m
ultip
li-ca
tion
Mul
tiply
ing
a fa
ctor
by
zero
will
alw
ays
resu
lt in
zer
o.
30 x
0 is
0
0 x
15 is
0
(con
tinue
d)
BLM
5–
8.8
: M
en
tal
Ma
th S
tra
teg
ies (
Co
nti
nu
ed
)
Gra
de
Con
cept
St
rate
gy
Mea
ning
Ex
ampl
e 4
Mul
tiplic
atio
n D
ivis
ion
Mul
tiplic
ativ
e id
entit
y M
ultip
lyin
g (d
ivid
ing)
a fa
ctor
(div
iden
d) b
y on
e w
ill n
ot c
hang
e its
val
ue.
1 x
12 is
12
21
1 is
21
4. 5
M
ultip
licat
ion
D
ivis
ion
Skip
-cou
ntin
g fr
om a
kno
wn
fact
Sim
ilar t
o th
e co
untin
g on
str
ateg
y fo
r ad
ditio
n. U
sing
a k
now
n fa
ct a
nd s
kip
coun
ting
forw
ard
or b
ackw
ard
to d
eter
min
e th
e an
swer
.
for 3
x 8
th
ink
3 x
5 is
15 a
nd sk
ip
coun
t by
thre
es 1
5, 1
8,
21, 2
4 4,
5
Mul
tiplic
atio
n D
ivis
ion
Dou
blin
g or
ha
lvin
g U
sing
kno
wn
fact
s an
d do
ublin
g or
hal
ving
th
em to
det
erm
ine
the
answ
er.
for 7
x 4
, thi
nk th
e dou
ble
of 7
x 2
is 2
8 fo
r 48
6, t
hink
the
doub
le of
24
6 is
8
4 M
ultip
licat
ion
Div
isio
n U
sing
the
patte
rn fo
r 9s
Kno
win
g th
e fir
st d
igit
of th
e an
swer
is o
ne
less
than
the
non-
nine
fact
or a
nd th
e su
m o
f th
e pr
oduc
t’s d
igits
is n
ine.
for 7
x 9
thin
k on
e les
s th
an 7
is 6
and
6 p
lus 3
is
nine
, so
7 x
9 is
63
4, 5
M
ultip
licat
ion
Repe
ated
do
ublin
g C
ontin
ually
dou
blin
g to
get
to a
n an
swer
. fo
r 3 x
8, t
hink
3 x
2 is
6,
6 x
2 is
12, 1
2 x
2 is
24
4 D
ivis
ion
Usi
ng
mul
tiplic
atio
n to
div
ide
This
is a
form
of p
art-p
art-w
hole
re
pres
enta
tion.
Thi
nkin
g of
mul
tiplic
atio
n as
:
par
t x p
art =
who
le
Thin
king
of d
ivis
ion
as:
w
hole
p
art =
par
t
for 3
5
7
thin
k 7
x _
___
= 35
so
35
7 is
5
4, 5
M
ultip
licat
ion
Dis
trib
utiv
e pr
oper
ty
In a
rith
met
ic o
r alg
ebra
, whe
n yo
u di
stri
bute
a
fact
or a
cros
s th
e br
acke
ts:
a
x (b
+ c)
= a
x b
+ a
x c
(a
+ b
) x (c
+ d
) = a
c + a
d +
bc +
bd
for 2
x 1
54
thin
k 2
x 10
0 pl
us 2
x 5
0 pl
us 2
x 4
is 2
00 +
100
+
8 or
308
(con
tinue
d)
BLM
5–
8.8
: M
en
tal
Ma
th S
tra
teg
ies (
Co
nti
nu
ed
)
Gra
de
Con
cept
St
rate
gy
Mea
ning
Ex
ampl
e 5
Div
isio
n Re
peat
ed
halv
ing
Con
tinua
lly h
alvi
ng to
get
a n
umbe
r. fo
r 32
4, t
hink
32
2
is 16
and
16
2 is
8 so
32
4
is 8
5
Mul
tiplic
atio
n A
nnex
ing
zero
s W
hen
mul
tiply
ing
by a
fact
or o
f 10
(or a
pow
er
of te
n), t
akin
g of
f the
zer
os to
det
erm
ine
the
prod
uct a
nd a
ddin
g th
em b
ack
on.
for 4
x 7
00, t
hink
4 x
7 is
28
and
add
two
zero
s to
mak
e 280
0 5
Mul
tiplic
atio
n H
alvi
ng a
nd
doub
ling
Hal
ving
one
fact
or a
nd d
oubl
ing
the
othe
r. fo
r 24
x 4,
thin
k 48
x 2
is
96
6, 7
D
ivis
ion
Div
idin
g by
m
ultip
les
of
ten
Whe
n di
vidi
ng b
y 10
, 100
, etc
., th
e di
vide
nd
beco
mes
smal
ler b
y 1,
2, e
tc. p
lace
val
ue
posi
tions
.
for 7
6.3
10
thin
k 76
.3
shou
ld b
ecom
e sm
aller
by
one p
lace
val
ue p
ositi
on
so 7
6.3
10
is 7.
63
BLM 5–8.9: Centimetre Grid Paper
BLM 5–8.10: Base-Ten Grid Paper
BLM 5–8.11: Multiplication Table
× 0 1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 2 0 2 4 6 8 10 12 14 16 18 3 0 3 6 9 12 15 18 21 24 27 4 0 4 8 12 16 20 24 28 32 36 5 0 5 10 15 20 25 30 35 40 45 6 0 6 12 18 24 30 36 42 48 54 7 0 7 14 21 28 35 42 49 56 63 8 0 8 16 24 32 40 48 56 64 72 9 0 9 18 27 36 45 54 63 72 81
BLM 5–8.12: Fraction Bars
BLM 5–8.13: Clock Face
BLM 5–8.14: Spinner
BLM
5–
8.1
5:
Th
ou
sa
nd
Grid
BLM
5–
8.1
6:
Pla
ce
-V
alu
e M
at—
De
cim
al
Nu
mb
ers
One
s Te
nths
H
undr
edth
s Th
ousa
ndth
s
BLM
5–
8.1
7:
Nu
mb
er F
an
.
0
1
2
3
4
5
6
BLM
5–
8.1
7:
Nu
mb
er F
an
(C
on
tin
ue
d)
7
8
9
BLM
5–
8.1
8:
KW
L C
ha
rt
K W
L
Wha
t do
you
thin
k yo
u KN
OW a
bout
__
____
____
_?
Wha
t do
you
WAN
T to
kno
w a
bout
__
____
____
__?
Wha
t did
you
LEA
RN a
bout
__
____
____
___?
BLM 5–8.19: Double Number Line
BLM 5–8.20: Algebra Tiles
BLM 5–8.21: Isometric Dot Paper
BLM 5–8.22: Dot Paper
BLM 5–8.23: Understanding Words Chart What does it mean? Word Picture
Example
What does it mean? Word Picture
Example
B
LM
5–8
.24
: N
um
be
r L
ine
BLM
5–8
.25
: M
y S
ucce
ss w
ith
Ma
the
ma
tica
l P
ro
ce
sse
s
Nam
e __
____
____
____
____
____
____
____
____
____
____
____
____
____
Date
___
____
____
____
____
____
____
____
Ta
sk _
____
____
____
____
____
____
____
____
____
____
____
____
____
____
____
____
____
____
____
____
____
____
____
____
_
Wha
t are
the
mat
hem
atic
al
proc
esse
s?
How
do
I kno
w th
at I
have
bee
n su
cces
sful
?
How
hav
e I s
how
n m
y su
cces
ses?
Com
mun
icat
ion
I use
mat
hem
atic
al la
ngua
ge a
nd
sym
bols
that
I al
read
y kn
ow a
nd
that
I am
lear
ning
.
I use
real
thin
gs, p
ictu
res,
sy
mbo
ls, t
alki
ng, w
ritin
g, a
nd
thin
king
to c
omm
unic
ate.
Con
nect
ions
I con
nect
the
mat
h I a
m le
arni
ng
to m
ath
I alr
eady
kno
w.
I c
onne
ct th
e m
ath
I am
lear
ning
to
my
life.
Men
tal
Mat
hem
atic
s an
d Es
timat
ion
I c
an q
uick
ly fi
gure
out
the
answ
ers
to q
uest
ions
with
nu
mbe
rs b
y th
inki
ng a
bout
how
nu
mbe
rs w
ork
(and
I do
n’t n
eed
to w
rite
dow
n m
y st
eps)
.
I est
imat
e to
mak
e su
re m
y an
swer
mak
es s
ense
or w
hen
I do
n’t n
eed
an e
xact
ans
wer
or
mea
sure
men
t.
Prob
lem
So
lvin
g
I lis
ten
to o
ther
s, ta
lk w
ith
othe
rs, a
nd tr
y m
any
thin
gs
whe
n I a
m tr
ying
to a
nsw
er a
ki
nd o
f que
stio
n th
at I
have
ne
ver s
een
befo
re.
(con
tinue
d)
BLM
5–8
.25
: M
y S
ucce
ss w
ith
Ma
the
ma
tica
l P
ro
ce
sse
s
(co
nti
nu
ed
)
Wha
t are
the
mat
hem
atic
al
proc
esse
s?
How
do
I kno
w th
at I
have
bee
n su
cces
sful
?
How
hav
e I s
how
n m
y su
cces
ses?
Rea
soni
ng
W
hen
doin
g m
ath,
I se
e pa
ttern
s,
I use
wha
t I k
now
to h
elp
me
figur
e ou
t som
ethi
ng th
at I
don’
t kn
ow, a
nd I
thin
k ab
out m
y an
swer
s.
Tech
nolo
gy
I u
se c
alcu
lato
rs, c
ompu
ters
, and
ot
her t
echn
olog
y to
or
gani
ze a
nd s
how
my
wor
k
fig
ure
out p
atte
rns
chec
k so
met
hing
of w
hich
I am
un
sure
he
lp m
e le
arn
in n
ew w
ays
Vis
ualiz
atio
n
I can
mak
e up
, fig
ure
out,
expl
ain,
an
d lin
k to
geth
er d
iffer
ent p
ictu
res
and
3-di
men
sion
al o
bjec
ts.
W
hen
thin
king
abo
ut n
umbe
rs, I
im
agin
e th
em in
my
head
.
Whe
n m
easu
ring
, I k
now
that
so
met
imes
I ne
ed a
n ex
act n
umbe
r an
d so
met
imes
I ne
ed o
ne th
at is
cl
ose.
BLM 5–8.26: Percent Circle
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