®
© Big Ideas Learning, LLC
Materials: • Student directions (one for each group) • Group 1 (cylinder)
• Group 2 (rectangular pyramid)• Group 3 (rectangular prism)• Group 4 (hexagonal pyramid)• Group 5 (triangular pyramid)• Group 6 (pentagonal prism)• Group 7 (triangular prism)• Group 8 (cone)
• Review cards (Fold each card vertically so the crease is on the right. Then fold each card horizontally so the crease is on the top.)
• 8 sets (one for each group)• 2 decoy sets
• Solution I (the last solution, which is the same for all groups) • Lined paper • Calculators
Directions: Divide the students into 8 groups. The students will work in these groups to solve 9 problems.
As the students work, be sure each student shows all work on lined paper. The fi rst question is on the directions page. From there, the students are able to fi nd the next card based on the answer. Once they have checked their answer, they can solve the next problem. The solid assigned to each group from the directions page will appear on each solution for that group. In each group, there should be a time keeper, messenger and a researcher. The time keeper watches the clock to make sure the group fi nishes the problem within the time given on the card. It is also their job to keep the group on task. The messenger is responsible for retrieving the next card and checking the group’s solution on the card. Each student is responsible for showing all work on lined paper. The researcher is responsible for looking up how to solve the problem if the students cannot fi gure it out as a group. The activity is complete when each group has completed all questions correctly. If the students solve the problems within the time limit given on each card, this activity should take about 30 minutes.
Scavenger Hunt
Back
Front
Opened card
Your next card will look like this.
Big Ideas Math®
Game Closet
Back-to-School Review Game Blue
Objectives: This is a back-to-school review game. Use it before you start the Blue Book. The student will • identify a given solid.
• construct a stem-and-leaf plot.• write and solve a proportion.• evaluate an expression involving exponents and absolute value.• write and solve a two-step equation.• graph two points and fi nd the slope of the line.• write and simplify an expression involving fractions.• convert between systems of measurement and calculate the surface area of a solid.• graph fi gures in a coordinate plane and determine which two fi gures are similar.
®
© Big Ideas Learning, LLC
Materials: • Lined paper • Review cards • Calculators
Directions: Decide who in the group will be the researcher, timekeeper, and messenger. There are Key Ideas on the
back of each card, but if your group gets stuck, the researcher is responsible for looking in a book to help your group fi nd the solution. The timekeeper makes sure that your group fi nds the solution in the time limit given. Once each group member has shown all work on the lined paper, and arrived at the same solution, the messenger retrieves the next card by using your group’s solution. Once you have completed all the cards, your group is fi nished!
Start by solving the problem below.
Scavenger HuntStudent Directions
Group 1
Sketch a cylinder.
“Name these shapes.”
1min
Your first card will look like this.
Big Ideas Math®
Game Closet
Scavenger HuntStudent Directions
Group 2
Sketch a rectangular pyramid.
“Name these shapes.”
1min
Your first card will look like this.
Materials: • Lined paper • Review cards • Calculators
Directions: Decide who in the group will be the researcher, timekeeper, and messenger. There are Key Ideas on the
back of each card, but if your group gets stuck, the researcher is responsible for looking in a book to help your group fi nd the solution. The timekeeper makes sure that your group fi nds the solution in the time limit given. Once each group member has shown all work on the lined paper, and arrived at the same solution, the messenger retrieves the next card by using your group’s solution. Once you have completed all the cards, your group is fi nished!
Start by solving the problem below.
Big Ideas Math®
Game Closet
Scavenger HuntStudent Directions
Group 3
Sketch a rectangular prism.
“Name these shapes.”
1min
Your first card will look like this.
Materials: • Lined paper • Review cards • Calculators
Directions: Decide who in the group will be the researcher, timekeeper, and messenger. There are Key Ideas on the
back of each card, but if your group gets stuck, the researcher is responsible for looking in a book to help your group fi nd the solution. The timekeeper makes sure that your group fi nds the solution in the time limit given. Once each group member has shown all work on the lined paper, and arrived at the same solution, the messenger retrieves the next card by using your group’s solution. Once you have completed all the cards, your group is fi nished!
Start by solving the problem below.
Big Ideas Math®
Game Closet
Scavenger HuntStudent Directions
Group 4
Sketch a hexagonal pyramid.
“Name these shapes.”
1min
Your first card will look like this.
Materials: • Lined paper • Review cards • Calculators
Directions: Decide who in the group will be the researcher, timekeeper, and messenger. There are Key Ideas on the
back of each card, but if your group gets stuck, the researcher is responsible for looking in a book to help your group fi nd the solution. The timekeeper makes sure that your group fi nds the solution in the time limit given. Once each group member has shown all work on the lined paper, and arrived at the same solution, the messenger retrieves the next card by using your group’s solution. Once you have completed all the cards, your group is fi nished!
Start by solving the problem below.
Big Ideas Math®
Game Closet
Scavenger HuntStudent Directions
Group 5
Sketch a triangular pyramid.
“Name these shapes.”
1min
Your first card will look like this.
Materials: • Lined paper • Review cards • Calculators
Directions: Decide who in the group will be the researcher, timekeeper, and messenger. There are Key Ideas on the
back of each card, but if your group gets stuck, the researcher is responsible for looking in a book to help your group fi nd the solution. The timekeeper makes sure that your group fi nds the solution in the time limit given. Once each group member has shown all work on the lined paper, and arrived at the same solution, the messenger retrieves the next card by using your group’s solution. Once you have completed all the cards, your group is fi nished!
Start by solving the problem below.
Big Ideas Math®
Game Closet
Scavenger HuntStudent Directions
Group 6
Sketch a pentagonal prism.
“Name these shapes.”
1min
Your first card will look like this.
Materials: • Lined paper • Review cards • Calculators
Directions: Decide who in the group will be the researcher, timekeeper, and messenger. There are Key Ideas on the
back of each card, but if your group gets stuck, the researcher is responsible for looking in a book to help your group fi nd the solution. The timekeeper makes sure that your group fi nds the solution in the time limit given. Once each group member has shown all work on the lined paper, and arrived at the same solution, the messenger retrieves the next card by using your group’s solution. Once you have completed all the cards, your group is fi nished!
Start by solving the problem below.
Big Ideas Math®
Game Closet
Scavenger HuntStudent Directions
Group 7
Sketch a triangular prism.
“Name these shapes.”
1min
Your first card will look like this.
Materials: • Lined paper • Review cards • Calculators
Directions: Decide who in the group will be the researcher, timekeeper, and messenger. There are Key Ideas on the
back of each card, but if your group gets stuck, the researcher is responsible for looking in a book to help your group fi nd the solution. The timekeeper makes sure that your group fi nds the solution in the time limit given. Once each group member has shown all work on the lined paper, and arrived at the same solution, the messenger retrieves the next card by using your group’s solution. Once you have completed all the cards, your group is fi nished!
Start by solving the problem below.
Big Ideas Math®
Game Closet
Scavenger HuntStudent Directions
Group 8
Sketch a cone.
“Name these shapes.”
1min
Your first card will look like this.
Materials: • Lined paper • Review cards • Calculators
Directions: Decide who in the group will be the researcher, timekeeper, and messenger. There are Key Ideas on the
back of each card, but if your group gets stuck, the researcher is responsible for looking in a book to help your group fi nd the solution. The timekeeper makes sure that your group fi nds the solution in the time limit given. Once each group member has shown all work on the lined paper, and arrived at the same solution, the messenger retrieves the next card by using your group’s solution. Once you have completed all the cards, your group is fi nished!
Start by solving the problem below.
Big Ideas Math®
Game Closet
Solu
tion:
A cylin
der is a
solid th
at h
as tw
o para
llel,
congru
ent circu
lar ba
ses. S
o, the solid
show
n is a
cylind
er.
Make
a ste
m-a
nd
-leaf plot of th
e n
um
ber
of songs d
ownloa
ded
.
4min
Your next card will look like this.
Each
card
for your
grou
p shou
ld h
ave
th
is solid. If you
do
not se
e a
cylind
er,
go ba
ck and
try again
.
Key Id
ea
A s
tem
-and
-leaf plot
use
s the d
igits of d
ata
valu
es to org
anize
a d
ata
set. E
ach
data
valu
e is
broken in
to a ste
m (d
igit
or dig
its on th
e le
ft) and
a le
af (d
igit or d
igits on
the rig
ht).
Songs Downloaded
204516
142512
52031
34189
Rem
ind
er
Solu
tion:
To make
a ste
m-a
nd
-leaf plot:
1.) O
rder th
e d
ata
.
2.) C
hoose
the ste
ms a
nd
the le
ave
s. B
eca
use
the
data
valu
es ra
nge from
5 to 4
5, u
se th
e tens d
igits
for the ste
ms a
nd
the ones d
igits for th
e le
ave
s.
3
.) Write
the ste
ms to th
e left of th
e ve
rtical lin
e.
4.) W
rite th
e le
ave
s for each
stem
to the right
of the ve
rtical lin
e.
5.) C
reate
a title
and
a ke
y.
It costs $3
7.50
for 5 ticke
ts to the m
ovies.
Write
and
solve a
proportion to d
ete
rmin
e
how
much
8 ticke
ts cost.
3min
Your next card will look like this.
Rem
ind
er
Key:
1 | 4
= 1
4 s
ongs
Songs Downloaded
Stem
Leaf
0 1 2 3 4
5 9
2 4 6 8
0 0 5
1 4
5
Key Id
eas
propo
rtion is a
n e
quation
sta
ting th
at tw
o ratios a
re
equiva
lent.
th
e M
ultiplica
tion P
rope
rty
of E
quality or th
e C
ross
P
roducts
Pro
perty.
Solu
tion:
Write
and
solve a
proportion.
—
= —
dollars
tickets
3
8 =
5 Cross Products Property
3
00
=Multiply.
6
0 =
Divide.
It costs $6
0 for 8
tickets to th
e m
ovies.
when x =
- 3 a
nd
y = 1.
3min
Your next card will look like this.
Rem
ind
er
$60.00
Key Id
ea
Use
the o
rder o
f
ope
ration
s w
hen
eva
luatin
g a
n
x2 —
| y — 2 | +
— 12x
37.5
0
5
x8
Solu
tion:
Substitu
te - 3
for x and
1 for y. Then sim
plify.
x2 —
| y — 2 | +
—
= (- 3
)2 —
| 1 — 2 | +
—
= 9
— | -1 | +
(-4)
= 9
— 1 +
(-4)
= 9
+ (-1) +
(-4)
= 4
The pe
rimete
r of the tra
pezoid
is 40
.
What is th
e va
lue of x?
4min
Your next card will look like this.
x 5 x 3
x + 5x + 5
Rem
ind
er
4
Key Id
eas
perim
ete
r of a fig
ure
is th
e su
m of th
e sid
e le
ngth
s.
Solvin
g a
n e
quation
1. C
ombin
e like
term
s.
2. U
nd
o ad
dition
and
subtra
ction.
3
. Und
o multiplica
tion a
nd
d
ivision.
12x12- 3
Solu
tion:
P
= S
um
of side le
ngth
s
40
= (x +
5) +
3x + (x +
5) +
5x
40
= 10x +
10 —
10
— 10
3
0 =
10x
30
= 10x
10
10
3
= x
The va
lue of x is 3
.
Gra
ph th
e lin
e th
at pa
sses th
rough th
e tw
o points
(-2, 2) and
(4, 6
). Then fin
d th
e slope
of the lin
e.
3min
Your next card will look like this.
Rem
ind
er
3
Key Id
eas
ord
ere
d pa
ir (x, y) is a pa
ir of
num
bers th
at is u
sed
to locate
a
poin
t in a
coordin
ate
plane.
Slo
pe is th
e ra
te of ch
ange
be
tween a
ny tw
o points on
a lin
e.
To find
the slope
of a lin
e, fin
d
th
e ra
tio of the ve
rtical ch
ange
to th
e h
orizonta
l change.
Solu
tion:
What is th
e d
iffere
nce
of 1— a
nd
- 3—
?
2min
Your next card will look like this.
Rem
ind
er
2 3
Key Id
eas
ad
d its o
pposite
.
LC
D
.
45
310
——
—.
yx46
23
23
y
x2
4
2 4 6
-2-4
Solu
tion:
1— —
( - 3—)
= 1—
+ 3
—
= —
+ —
= —
+ —
= —
= 5
—
The d
iffere
nce
is 5—
.
Fin
d th
e su
rface
are
a of th
e cylin
der in
square
inch
es. R
ound
your a
nsw
er to th
e n
eare
st tenth
.
5min
Your next card will look like this.
Rem
ind
er
1 105
45
310
45
310
9551
10
110
110
3310
18103
310
15.24 cm
1 in. ≈ 2.54 cm
9 in.
Key Id
ea
The su
rface
are
a of a
cylind
er is th
e
sum
of the a
reas of th
e ba
ses a
nd
the
late
ral su
rface
.
Surfa
ce A
rea: S
= 2
r2 +
2rh
r
h
Base
Lateral surface
rr
h
Base
r2
Solu
tion:
First, con
vert 15
.24 ce
ntim
ete
rs to inch
es.
15.24
cm x —
≈ 6 in
.
Then, fin
d th
e su
rface
are
a.
S =
2r
2 + 2
rh
= 2
(6)
2 + 2
(6)(9
)
= 72
+ 10
8
= 18
0
≈
56
5.2 in
. 2
The su
rface
are
a is a
bout 5
65.2 sq
uare
inch
es.
In a
coordin
ate
plane, d
raw
the fig
ure
s with
the g
iven
vertice
s. W
hich
figure
s are
simila
r? Expla
in you
r reason
ing
.
5min
Congratulations!Once you have checked
the solution with your teacher,
your group is all done!
565.2 in.2
1 in.
2.54 cm
Rem
ind
er
Key Id
eas
sh
ape
but n
ot nece
ssarily th
e
sa
me size
are
calle
d s
imila
r
fig
ure
s.
sim
ilar if
corre
spond
ing sid
e le
ngth
s are
proportion
al, a
nd
correspon
din
g
angle
s have
the sa
me m
easu
re.
Triangle A: (0, 0), (9, 0), (0, 9)
Triangle B: (0, 0), (6, 0), (0, 9)
Triangle C: (0, 0), (6, 0), (0, 6)
Solu
tion:
A re
ctangula
r pyram
id is a
solid th
at h
as
one re
ctangula
r base
and
four tria
ngula
r
late
ral fa
ces. S
o, the solid
show
n is a
recta
ngula
r pyram
id.
Make
a ste
m-a
nd
-leaf plot of th
e n
um
ber
of songs d
ownloa
ded
.
4min
Your next card will look like this.
Each
card
for your
grou
p shou
ld h
ave
this
solid. If you
do n
ot see
a re
ctangula
r pyram
id,
go ba
ck and
try again
.
Key Id
ea
A s
tem
-and
-leaf plot
use
s the d
igits of d
ata
valu
es to org
anize
a d
ata
set. E
ach
data
valu
e is
broken in
to a ste
m (d
igit
or dig
its on th
e le
ft) and
a le
af (d
igit or d
igits on
the rig
ht).
Songs Downloaded
26456
14621
52019
34349
Rem
ind
er
Solu
tion:
To make
a ste
m-a
nd
-leaf plot:
1.) O
rder th
e d
ata
.
2.) C
hoose
the ste
ms a
nd
the le
ave
s. B
eca
use
the
data
valu
es ra
nge from
5 to 4
5, u
se th
e tens d
igits
for the ste
ms a
nd
the ones d
igits for th
e le
ave
s.
3
.) Write
the ste
ms to th
e left of th
e ve
rtical lin
e.
4.) W
rite th
e le
ave
s for each
stem
to the right
of the ve
rtical lin
e.
5.) C
reate
a title
and
a ke
y.
It costs $3
7.50
for 5 ticke
ts to the m
ovies.
Write
and
solve a
proportion to d
ete
rmin
e
how
much
3 ticke
ts cost.
3min
Your next card will look like this.
Key Id
eas
propo
rtion is a
n e
quation
sta
ting th
at tw
o ratios a
re
equiva
lent.
th
e M
ultiplica
tion P
rope
rty
of E
quality or th
e C
ross
P
roducts
Pro
perty.
Rem
ind
er
Key:
1 | 4
= 1
4 s
ongs
Songs Downloaded
Stem
Leaf
0 1 2 3 4
5 6 6 9
4 9
0 1 6
4 4
5
Solu
tion:
Write
and
solve a
proportion.
—
= —
dollars
tickets
3
3 =
5 Cross Products Property
112
.5 =
Multiply.
22
.5 =
Divide.
It costs $22
.50
for 3 ticke
ts to the m
ovies.
when x =
2 and
y = -1.
3min
Your next card will look like this.
Rem
ind
er
$22.50
Key Id
ea
Use
the o
rder o
f
ope
ration
s w
hen
eva
luatin
g a
n
x2 —
| y — 2 | +
— 12x
37.5
0
5
x3
Solu
tion:
Substitu
te 2 for x a
nd
-1 for y. Then sim
plify.
x2 —
| y — 2 | +
—
= 2
2 — | -1 —
2 | + —
= 4
— | - 3
| + 6
= 4
— 3
+ 6
= 4
+ (- 3
) + 6
= 7
The pe
rimete
r of the tra
pezoid
is 30
.
What is th
e va
lue of x?
4min
Your next card will look like this.
x 5 x 3
x + 5x + 5
Rem
ind
er
7
12x122
Key Id
eas
perim
ete
r of a fig
ure
is th
e su
m of th
e sid
e le
ngth
s.
Solvin
g a
n e
quation
1. C
ombin
e like
term
s.
2. U
nd
o ad
dition
and
subtra
ction.
3
. Und
o multiplica
tion a
nd
d
ivision.
Solu
tion:
P
= S
um
of side le
ngth
s
3
0 =
(x + 5
) + 3x +
(x + 5
) + 5x
3
0 =
10x + 10
— 10
—
10
20
= 10x
20
= 10x
10
10
2 =
xTh
e va
lue of x is 2
.
Gra
ph th
e lin
e th
at pa
sses th
rough th
e tw
o points
(-2, 2) and
(0, 3
). Then fin
d th
e slope
of the lin
e.
3min
Your next card will look like this.
Rem
ind
er
2
Key Id
eas
ord
ere
d pa
ir (x, y) is a pa
ir of
num
bers th
at is u
sed
to locate
a
poin
t in a
coordin
ate
plane.
Slo
pe is th
e ra
te of ch
ange
be
tween a
ny tw
o points on
a lin
e.
To find
the slope
of a lin
e, fin
d
th
e ra
tio of the ve
rtical ch
ange
to th
e h
orizonta
l change.
Solu
tion:
What is th
e d
iffere
nce
of 1— a
nd
-2—?
2min
Your next card will look like this.
Rem
ind
er
1 2
Key Id
eas
ad
d its o
pposite
.
LC
D
.
45310
— —
.
yx12
12
y
x2
4
2 4 6
-2-4
3
Solu
tion:
1— —
( -2—) = 1—
+ 2—
= —
+ —
= —
+ —
= —
= 4
—
The d
iffere
nce
is 4—
.
Fin
d th
e su
rface
are
a of th
e cylin
der in
square
inch
es. R
ound
your a
nsw
er to th
e n
eare
st tenth
.
5min
Your next card will look like this.
Rem
ind
er
1 104
45
310
45
310
1 31041
10
110
110
145
1 310
2810
17.78 cm
1 in. ≈ 2.54 cm
9 in.
Key Id
ea
The su
rface
are
a of a
cylind
er is th
e
sum
of the a
reas of th
e ba
ses a
nd
the
late
ral su
rface
.
Surfa
ce A
rea: S
= 2
r2 +
2rh
r
h
Base
Lateral surface
rr
h
Base
r2
Solu
tion:
First, con
vert 17.78
centim
ete
rs to inch
es.
17.78 cm
x — ≈ 7 in
.
Then, fin
d th
e su
rface
are
a.
S =
2r
2 + 2
rh
= 2
(7)
2 + 2
(7)(9
)
= 9
8 +
126
= 224
≈
703
.4 in
. 2
The su
rface
are
a is a
bout 70
3.4
square
inch
es.
In a
coordin
ate
plane, d
raw
the fig
ure
s with
the g
iven
vertice
s. W
hich
figure
s are
simila
r? Expla
in you
r reason
ing
.
5min
Congratulations!Once you have checked
the solution with your teacher,
your group is all done!
703.4 in.2
1 in.
2.54 cm
Rem
ind
er
Key Id
eas
sh
ape
but n
ot nece
ssarily th
e
sa
me size
are
calle
d s
imila
r
fig
ure
s.
sim
ilar if
corre
spond
ing sid
e le
ngth
s are
proportion
al, a
nd
correspon
din
g
angle
s have
the sa
me m
easu
re.
Triangle A: (0, 0), (9, 0), (0, 9)
Triangle B: (0, 0), (6, 0), (0, 9)
Triangle C: (0, 0), (6, 0), (0, 6)
Solu
tion:
A re
ctangula
r prism
is a solid
that h
as tw
o para
llel,
congru
ent re
ctangula
r base
s. Th
e oth
er fa
ces a
re
para
llelog
ram
s. S
o , the solid
show
n is a
recta
ngula
r prism.
Make
a ste
m-a
nd
-leaf plot of th
e n
um
ber
of songs d
ownloa
ded
.
4min
Your next card will look like this.
Each
card
for your
grou
p shou
ld h
ave
this
solid. If you
do n
ot see
a re
ctangula
r prism,
go ba
ck and
try again
.
Key Id
ea
A s
tem
-and
-leaf plot
use
s the d
igits of d
ata
valu
es to org
anize
a d
ata
set. E
ach
data
valu
e is
broken in
to a ste
m (d
igit
or dig
its on th
e le
ft) and
a le
af (d
igit or d
igits on
the rig
ht).
Songs Downloaded
74539
142713
52045
34229
Rem
ind
er
Solu
tion:
To make
a ste
m-a
nd
-leaf plot:
1.) O
rder th
e d
ata
.
2.) C
hoose
the ste
ms a
nd
the le
ave
s. B
eca
use
the
data
valu
es ra
nge from
5 to 4
5, u
se th
e tens d
igits
for the ste
ms a
nd
the ones d
igits for th
e le
ave
s.
3
.) Write
the ste
ms to th
e left of th
e ve
rtical lin
e.
4.) W
rite th
e le
ave
s for each
stem
to the right
of the ve
rtical lin
e.
5.) C
reate
a title
and
a ke
y.
It costs $3
7.50
for 5 ticke
ts to the m
ovies.
Write
and
solve a
proportion to d
ete
rmin
e
how
much
9 ticke
ts cost.
3min
Your next card will look like this.
Key Id
eas
propo
rtion is a
n e
quation
sta
ting th
at tw
o ratios a
re
equiva
lent.
th
e M
ultiplica
tion P
rope
rty
of E
quality or th
e C
ross
P
roducts
Pro
perty.
Rem
ind
er
Key:
1 | 4
= 1
4 s
ongs
Songs Downloaded
Stem
Leaf
0 1 2 3 4
5 7 9
3 4
0 2 7
4 9
5 5
Solu
tion:
Write
and
solve a
proportion.
—
= —
dollars
tickets
3
9 =
5 Cross Products Property
3
37.5
=Multiply.
6
7.5 =
Divide.
It costs $6
7.50
for 9 ticke
ts to the m
ovies.
when x =
3 a
nd
y = -1.
3min
Your next card will look like this.
Rem
ind
er
$67.50
Key Id
ea
Use
the o
rder o
f
ope
ration
s w
hen
eva
luatin
g a
n
x2 —
| y — 2 | +
— 12x
37.5
0
5
x9
Solu
tion:
Substitu
te 3 for x a
nd
-1 for y. Then sim
plify.
x2 —
| y — 2 | +
—
= 3
2 — | -1 —
2 | + —
= 9
— | - 3
| + 4
= 9
— 3
+ 4
= 9
+ (- 3
) + 4
= 10
The pe
rimete
r of the tra
pezoid
is 60
.
What is th
e va
lue of x?
4min
Your next card will look like this.
x 5 x 3
x + 5x + 5
Rem
ind
er
10
12x123
Key Id
eas
perim
ete
r of a fig
ure
is th
e su
m of th
e sid
e le
ngth
s.
Solvin
g a
n e
quation
1. C
ombin
e like
term
s.
2. U
nd
o ad
dition
and
subtra
ction.
3
. Und
o multiplica
tion a
nd
d
ivision.
Solu
tion:
P
= S
um
of side le
ngth
s
6
0 =
(x + 5
) + 3x +
(x + 5
) + 5x
6
0 =
10x + 10
— 10
—
10
5
0 =
10x
50
= 10x
10
10
5
= x
The va
lue of x is 5
.
Gra
ph th
e lin
e th
at pa
sses th
rough th
e tw
o points
(-2, 2) and
(1, 2). Then fin
d th
e slope
of the lin
e.
3min
Your next card will look like this.
Rem
ind
er
5
Key Id
eas
ord
ere
d pa
ir (x, y) is a pa
ir of
num
bers th
at is u
sed
to locate
a
poin
t in a
coordin
ate
plane.
Slo
pe is th
e ra
te of ch
ange
be
tween a
ny tw
o points on
a lin
e.
To find
the slope
of a lin
e, fin
d
th
e ra
tio of the ve
rtical ch
ange
to th
e h
orizonta
l change.
Solu
tion:
What is th
e d
iffere
nce
of 1— a
nd
3—
?
2min
Your next card will look like this.
Rem
ind
er
0
Key Id
eas
ad
d its o
pposite
.
LC
D
.
45310
—
0yx
03
y
x2
4
2 4 6
-2-4
Fin
d th
e su
rface
are
a of th
e cylin
der in
square
inch
es. R
ound
your a
nsw
er to th
e n
eare
st tenth
.
5min
Your next card will look like this.
Rem
ind
er
1 2-1
12.7 cm
1 in. ≈ 2.54 cm
9 in.
Solu
tion:
1— —
3—
= 1—
+ ( - 3
—) = —
+ ( -—
) = —
+ ( -—
) = -—
= -1—
The d
iffere
nce
is -1—.
45
310
4595
310
1810151012
12
3310
3310
Key Id
ea
The su
rface
are
a of a
cylind
er is th
e
sum
of the a
reas of th
e ba
ses a
nd
the
late
ral su
rface
.
Surfa
ce A
rea: S
= 2
r2 +
2rh
r
h
Base
Lateral surface
rr
h
Base
r2
Solu
tion:
First, con
vert 12
.7 centim
ete
rs to inch
es.
12.7 cm
x — ≈ 5
in.
Then, fin
d th
e su
rface
are
a.
S =
2r
2 + 2
rh
= 2
(5)
2 + 2
(5)(9
)
= 5
0 +
90
= 14
0
≈
43
9.6
in. 2
The su
rface
are
a is a
bout 4
39
.6 sq
uare
inch
es.
In a
coordin
ate
plane, d
raw
the fig
ure
s with
the g
iven
vertice
s. W
hich
figure
s are
simila
r? Expla
in you
r reason
ing
.
5min
Congratulations!Once you have checked
the solution with your teacher,
your group is all done!
439.6 in.2
1 in.
2.54 cm
Rem
ind
er
Key Id
eas
sh
ape
but n
ot nece
ssarily th
e
sa
me size
are
calle
d s
imila
r
fig
ure
s.
sim
ilar if
corre
spond
ing sid
e le
ngth
s are
proportion
al, a
nd
correspon
din
g
angle
s have
the sa
me m
easu
re.
Triangle A: (0, 0), (9, 0), (0, 9)
Triangle B: (0, 0), (6, 0), (0, 9)
Triangle C: (0, 0), (6, 0), (0, 6)
Solu
tion:
A h
exa
gon
al pyra
mid
is a solid
that h
as on
e
hexa
gon
al ba
se a
nd
six triangula
r late
ral fa
ces.
So, th
e solid
show
n is a
hexa
gon
al pyra
mid
.
Make
a ste
m-a
nd
-leaf plot of th
e n
um
ber
of songs d
ownloa
ded
.
4min
Your next card will look like this.
Each
card
for your
grou
p shou
ld h
ave
this
solid. If you
do n
ot see
a h
exa
gon
al pyra
mid
, go ba
ck and
try again
.
Key Id
ea
A s
tem
-and
-leaf plot
use
s the d
igits of d
ata
valu
es to org
anize
a d
ata
set. E
ach
data
valu
e is
broken in
to a ste
m (d
igit
or dig
its on th
e le
ft) and
a le
af (d
igit or d
igits on
the rig
ht).
Songs Downloaded
364534
142716
52034
34419
Rem
ind
er
Solu
tion:
To make
a ste
m-a
nd
-leaf plot:
1.) O
rder th
e d
ata
.
2.) C
hoose
the ste
ms a
nd
the le
ave
s. B
eca
use
the
data
valu
es ra
nge from
5 to 4
5, u
se th
e tens d
igits
for the ste
ms a
nd
the ones d
igits for th
e le
ave
s.
3
.) Write
the ste
ms to th
e left of th
e ve
rtical lin
e.
4.) W
rite th
e le
ave
s for each
stem
to the right
of the ve
rtical lin
e.
5.) C
reate
a title
and
a ke
y.
It costs $3
7.50
for 5 ticke
ts to the m
ovies.
Write
and
solve a
proportion to d
ete
rmin
e
how
much
6 ticke
ts cost.
3min
Your next card will look like this.
Key Id
eas
propo
rtion is a
n e
quation
sta
ting th
at tw
o ratios a
re
equiva
lent.
th
e M
ultiplica
tion P
rope
rty
of E
quality or th
e C
ross
P
roducts
Pro
perty.
Rem
ind
er
Key:
1 | 4
= 1
4 s
ongs
Songs Downloaded
Stem
Leaf
0 1 2 3 4
5 9
4 6
0 7
4 4 4 6
1 5
Solu
tion:
Write
and
solve a
proportion.
—
= —
dollars
tickets
3
6 =
5 Cross Products Property
225
=Multiply.
45
=Divide.
It costs $45
for 6 ticke
ts to the m
ovies.
when x =
-2 and
y = 1.
3min
Your next card will look like this.
Rem
ind
er
$45.00
Key Id
ea
Use
the o
rder o
f
ope
ration
s w
hen
eva
luatin
g a
n
x2 —
| y — 2 | +
— 12x
37.5
0
5
x6
Solu
tion:
Substitu
te -2 for x and
1 for y. Then sim
plify.
x2 —
| y — 2 | +
—
= (-2)
2 — | 1 —
2 | + —
= 4
— | -1 | +
(-6)
= 4
— 1 +
(-6)
= 4
+ (-1) +
(-6)
= - 3
The pe
rimete
r of the tra
pezoid
is 100
.
What is th
e va
lue of x?
4min
Your next card will look like this.
x 5 x 3
x + 5x + 5
Rem
ind
er
-3
12x12-2
Key Id
eas
perim
ete
r of a fig
ure
is th
e su
m of th
e sid
e le
ngth
s.
Solvin
g a
n e
quation
1. C
ombin
e like
term
s.
2. U
nd
o ad
dition
and
subtra
ction.
3
. Und
o multiplica
tion a
nd
d
ivision.
Solu
tion:
P
= S
um
of side le
ngth
s
10
0 =
(x + 5
) + 3x +
(x + 5
) + 5x
10
0 =
10x + 10
—
10
— 10
9
0 =
10x
90
= 10x
10
10
9
= x
The va
lue of x is 9
.
Gra
ph th
e lin
e th
at pa
sses th
rough th
e tw
o points
(-2, 2) and
( 3, 0
). Then fin
d th
e slope
of the lin
e.
3min
Your next card will look like this.
Rem
ind
er
9
Key Id
eas
ord
ere
d pa
ir (x, y) is a pa
ir of
num
bers th
at is u
sed
to locate
a
poin
t in a
coordin
ate
plane.
Slo
pe is th
e ra
te of ch
ange
be
tween a
ny tw
o points on
a lin
e.
To find
the slope
of a lin
e, fin
d
th
e ra
tio of the ve
rtical ch
ange
to th
e h
orizonta
l change.
Solu
tion:
What is th
e d
iffere
nce
of -1— a
nd
2—?
2min
Your next card will look like this.
Rem
ind
er
Key Id
eas
ad
d its o
pposite
.
LC
D
.
45310
—
-—.
yx-25
25
y
x2
4
2 4 6
-2-4
( 3
2 5–
Solu
tion:
-1— —
2—
= -1—
+ ( -2—)
= -—
+ ( -—
) = -—
+ ( -—
) = -—
= -4
—
The d
iffere
nce
is -4—
.
Fin
d th
e su
rface
are
a of th
e cylin
der in
square
inch
es. R
ound
your a
nsw
er to th
e n
eare
st tenth
.
5min
Your next card will look like this.
Rem
ind
er
1 10-4
45
310
45
310
1 31041
10
110
110
145
1 310
2810
20.32 cm
1 in. ≈ 2.54 cm
9 in.
Key Id
ea
The su
rface
are
a of a
cylind
er is th
e
sum
of the a
reas of th
e ba
ses a
nd
the
late
ral su
rface
.
Surfa
ce A
rea: S
= 2
r2 +
2rh
r
h
Base
Lateral surface
rr
h
Base
r2
Solu
tion:
First, con
vert 20
. 32 ce
ntim
ete
rs to inch
es.
20. 3
2 cm x —
≈ 8 in
.
Then, fin
d th
e su
rface
are
a.
S =
2r
2 + 2
rh
= 2
(8)
2 + 2
(8)(9
)
= 128
+ 14
4
= 272
≈
85
4.1 in
. 2
The su
rface
are
a is a
bout 8
54.1 sq
uare
inch
es.
In a
coordin
ate
plane, d
raw
the fig
ure
s with
the g
iven
vertice
s. W
hich
figure
s are
simila
r? Expla
in you
r reason
ing
.
5min
Congratulations!Once you have checked
the solution with your teacher,
your group is all done!
854.1 in.2
1 in.
2.54 cm
Rem
ind
er
Key Id
eas
sh
ape
but n
ot nece
ssarily th
e
sa
me size
are
calle
d s
imila
r
fig
ure
s.
sim
ilar if
corre
spond
ing sid
e le
ngth
s are
proportion
al, a
nd
correspon
din
g
angle
s have
the sa
me m
easu
re.
Triangle A: (0, 0), (9, 0), (0, 9)
Triangle B: (0, 0), (6, 0), (0, 9)
Triangle C: (0, 0), (6, 0), (0, 6)
Solu
tion:
A tria
ngula
r pyram
id is a
solid th
at h
as on
e
triangula
r base
and
thre
e tria
ngula
r late
ral fa
ces.
So, th
e solid
show
n is a
triangula
r pyram
id.
Make
a ste
m-a
nd
-leaf plot of th
e n
um
ber
of songs d
ownloa
ded
.
4min
Your next card will look like this.
Each
card
for your
grou
p shou
ld h
ave
this
solid. If you
do n
ot see
a tria
ngula
r pyram
id,
go ba
ck and
try again
.
Key Id
ea
A s
tem
-and
-leaf plot
use
s the d
igits of d
ata
valu
es to org
anize
a d
ata
set. E
ach
data
valu
e is
broken in
to a ste
m (d
igit
or dig
its on th
e le
ft) and
a le
af (d
igit or d
igits on
the rig
ht).
Songs Downloaded
94560
144924
52031
63179
Rem
ind
er
Solu
tion:
To make
a ste
m-a
nd
-leaf plot:
1.) O
rder th
e d
ata
.
2.) C
hoose
the ste
ms a
nd
the le
ave
s. B
eca
use
the
data
valu
es ra
nge from
5 to 6
3, u
se th
e tens d
igits
for the ste
ms a
nd
the ones d
igits for th
e le
ave
s.
3
.) Write
the ste
ms to th
e left of th
e ve
rtical lin
e.
4.) W
rite th
e le
ave
s for each
stem
to the right
of the ve
rtical lin
e.
5.) C
reate
a title
and
a ke
y.
It costs $41.25
for 5 ticke
ts to the m
ovies.
Write
and
solve a
proportion to d
ete
rmin
e
how
much
8 ticke
ts cost.
3min
Your next card will look like this.
Key Id
eas
propo
rtion is a
n e
quation
sta
ting th
at tw
o ratios a
re
equiva
lent.
th
e M
ultiplica
tion P
rope
rty
of E
quality or th
e C
ross
P
roducts
Pro
perty.
Rem
ind
er
Key:
1 | 4
= 1
4 s
ongs
Songs Downloaded
Stem
Leaf
0 1 2 3 4 5 6
5 9 9
4 7
0 4
1 5 9
0 3
Solu
tion:
Write
and
solve a
proportion.
—
= —
dollars
tickets
41.25
8 =
5 Cross Products Property
3
30
=Multiply.
6
6 =
Divide.
It costs $6
6 for 8
tickets to th
e m
ovies.
when x =
1 and
y = - 3
.
3min
Your next card will look like this.
Rem
ind
er
$66.00
Key Id
ea
Use
the o
rder o
f
ope
ration
s w
hen
eva
luatin
g a
n
x2 —
| y — 2 | +
— 12x
41.25
5
x8
Solu
tion:
Substitu
te 1 for x and
- 3 for y. Th
en sim
plify.
x2 —
| y — 2 | +
—
= 1
2 — | (- 3
) — 2 | +
—
= 1 —
| -5 | +
12
= 1 —
5 +
12
= 1 +
(-5) +
12
= 8
The pe
rimete
r of the tra
pezoid
is 42.
What is th
e va
lue of x?
4min
Your next card will look like this.
x 5 x 2
x + 3x + 3
Rem
ind
er
8
12x121
Key Id
eas
perim
ete
r of a fig
ure
is th
e su
m of th
e sid
e le
ngth
s.
Solvin
g a
n e
quation
1. C
ombin
e like
term
s.
2. U
nd
o ad
dition
and
subtra
ction.
3
. Und
o multiplica
tion a
nd
d
ivision.
Solu
tion:
P
= S
um
of side le
ngth
s
42 =
(x + 3
) + 2x +
(x + 3
) + 5x
42 =
9x + 6
— 6
—
6
3
6 =
9x
36
= 9x
9
9
4 =
xTh
e va
lue of x is 4
.
Gra
ph th
e lin
e th
at pa
sses th
rough th
e tw
o points
(-2, 2) and
(1, -1). Then fin
d th
e slope
of the lin
e.
3min
Your next card will look like this.
Rem
ind
er
4
Key Id
eas
ord
ere
d pa
ir (x, y) is a pa
ir of
num
bers th
at is u
sed
to locate
a
poin
t in a
coordin
ate
plane.
Slo
pe is th
e ra
te of ch
ange
be
tween a
ny tw
o points on
a lin
e.
To find
the slope
of a lin
e, fin
d
th
e ra
tio of the ve
rtical ch
ange
to th
e h
orizonta
l change.
Solu
tion:
2min
Your next card will look like this.
Rem
ind
er
Key Id
eas
oppos
ite
LC
D
.
.
yx33
y
x4
2 4 6
-1
—3—
453
Fin
d th
e su
rface
are
a of th
e cylin
der in
square
inch
es. R
ound
your a
nsw
er to th
e n
eare
st tenth
.
5min
Your next card will look like this.
Rem
ind
er
1 2115.24 cm
1 in. ≈ 2.54 cm
8 in.
Solu
tion:
-1— —
( - 3—)
= -1—
+ 3
—
= -—
+ —
= -—
+ —
= —
= 1—
The d
iffere
nce
is 1—.
45
310
4595
310
1810
151012
12
3310
3310
Key Id
ea
The su
rface
are
a of a
cylind
er is th
e
sum
of the a
reas of th
e ba
ses a
nd
the
late
ral su
rface
.
Surfa
ce A
rea: S
= 2
r2 +
2rh
r
h
Base
Lateral surface
rr
h
Base
r2
Solu
tion:
First, con
vert 15
.24 ce
ntim
ete
rs to inch
es.
15.24
cm x —
≈ 6 in
.
Then, fin
d th
e su
rface
are
a.
S =
2r
2 + 2
rh
= 2
(6)
2 + 2
(6)(8
)
= 72
+ 9
6
= 16
8
≈
527.5
in. 2
The su
rface
are
a is a
bout 5
27.5 sq
uare
inch
es.
In a
coordin
ate
plane, d
raw
the fig
ure
s with
the g
iven
vertice
s. W
hich
figure
s are
simila
r? Expla
in you
r reason
ing
.
5min
Congratulations!Once you have checked
the solution with your teacher,
your group is all done!
527.5 in.2
1 in.
2.54 cm
Rem
ind
er
Key Id
eas
sh
ape
but n
ot nece
ssarily th
e
sa
me size
are
calle
d s
imila
r
fig
ure
s.
sim
ilar if
corre
spond
ing sid
e le
ngth
s are
proportion
al, a
nd
correspon
din
g
angle
s have
the sa
me m
easu
re.
Triangle A: (0, 0), (9, 0), (0, 9)
Triangle B: (0, 0), (6, 0), (0, 9)
Triangle C: (0, 0), (6, 0), (0, 6)
Solu
tion:
A pe
nta
gon
al pris
m is a
solid th
at h
as tw
o para
llel,
congru
ent pe
nta
gon
al ba
ses. Th
e oth
er fa
ces a
re
para
llelog
ram
s. S
o, the solid
show
n is a
penta
gon
al prism
.
Make
a ste
m-a
nd
-leaf plot of th
e n
um
ber
of songs d
ownloa
ded
.
4min
Your next card will look like this.
Each
card
for your
grou
p shou
ld h
ave
this
solid. If you
do n
ot see
a pe
nta
gon
al prism
, go
back a
nd
try again
.
Key Id
ea
A s
tem
-and
-leaf plot
use
s the d
igits of d
ata
valu
es to org
anize
a d
ata
set. E
ach
data
valu
e is
broken in
to a ste
m (d
igit
or dig
its on th
e le
ft) and
a le
af (d
igit or d
igits on
the rig
ht).
Songs Downloaded
84535
143117
52031
63489
Rem
ind
er
Solu
tion:
To make
a ste
m-a
nd
-leaf plot:
1.) O
rder th
e d
ata
.
2.) C
hoose
the ste
ms a
nd
the le
ave
s. B
eca
use
the
data
valu
es ra
nge from
5 to 6
3, u
se th
e tens d
igits
for the ste
ms a
nd
the ones d
igits for th
e le
ave
s.
3
.) Write
the ste
ms to th
e left of th
e ve
rtical lin
e.
4.) W
rite th
e le
ave
s for each
stem
to the right
of the ve
rtical lin
e.
5.) C
reate
a title
and
a ke
y.
It costs $41.25
for 5 ticke
ts to the m
ovies.
Write
and
solve a
proportion to d
ete
rmin
e
how
much
3 ticke
ts cost.
3min
Your next card will look like this.
Key Id
eas
propo
rtion is a
n e
quation
sta
ting th
at tw
o ratios a
re
equiva
lent.
th
e M
ultiplica
tion P
rope
rty
of E
quality or th
e C
ross
P
roducts
Pro
perty.
Rem
ind
er
Key:
1 | 4
= 1
4 s
ongs
Songs Downloaded
Stem
Leaf
0 1 2 3 4 5 6
5 8 9
4 7
0 1 1 5
5 8
3
Solu
tion:
Write
and
solve a
proportion.
—
= —
dollars
tickets
41.25
3 =
5 Cross Products Property
12
3.75
=Multiply.
24
.75 =
Divide.
It costs $24
.75 for 3
tickets to th
e m
ovies.
when x =
-1 and
y = 2
.
3min
Your next card will look like this.
Rem
ind
er
$24.75
Key Id
ea
Use
the o
rder o
f
ope
ration
s w
hen
eva
luatin
g a
n
x2 —
| y — 2 | +
— 12x
41.25
5
x3
Solu
tion:
Substitu
te -1 for x and
2 for y. Then sim
plify.
x2 —
| y — 2 | +
—
= (-1)
2 — | 2 —
2 | + —
= 1 —
| 0 | +
(-12)
= 1 —
0 +
(-12)
= 1 +
(-12)
= -11
The pe
rimete
r of the tra
pezoid
is 78.
What is th
e va
lue of x?
4min
Your next card will look like this.
x 5 x 2
x + 3x + 3
Rem
ind
er
-11
12x12-1
Key Id
eas
perim
ete
r of a fig
ure
is th
e su
m of th
e sid
e le
ngth
s.
Solvin
g a
n e
quation
1. C
ombin
e like
term
s.
2. U
nd
o ad
dition
and
subtra
ction.
3
. Und
o multiplica
tion a
nd
d
ivision.
Solu
tion:
P
= S
um
of side le
ngth
s
78
= (x +
3) +
2x + (x +
3) +
5x
78 =
9x + 6
— 6
—
6
72 =
9x
72 = 9x
9
9
8
= x
The va
lue of x is 8
.
Gra
ph th
e lin
e th
at pa
sses th
rough th
e tw
o points
(-2, 2) and
(0, -2). Th
en fin
d th
e slope
of the lin
e.
3min
Your next card will look like this.
Rem
ind
er
8
Key Id
eas
ord
ere
d pa
ir (x, y) is a pa
ir of
num
bers th
at is u
sed
to locate
a
poin
t in a
coordin
ate
plane.
Slo
pe is th
e ra
te of ch
ange
be
tween a
ny tw
o points on
a lin
e.
To find
the slope
of a lin
e, fin
d
th
e ra
tio of the ve
rtical ch
ange
to th
e h
orizonta
l change.
Solu
tion:
2min
Your next card will look like this.
Rem
ind
er
Key Id
eas
oppos
ite
LC
D
.
.
yx4
y
x4
4
-2
—— 45
7
Fin
d th
e su
rface
are
a of th
e cylin
der in
square
inch
es. R
ound
your a
nsw
er to th
e n
eare
st tenth
.
5min
Your next card will look like this.
Rem
ind
er
1 2-4
17.78 cm
1 in. ≈ 2.54 cm
8 in.
Solu
tion:
-1— —
2—
= -1—
+ ( -2—)
= -—
+ ( -—
) = -—
+ ( -—
) = -—
= -4
—
The d
iffere
nce
is -4—
.
45710
45710
17104510
12
12
145
1710
2810
Key Id
ea
The su
rface
are
a of a
cylind
er is th
e
sum
of the a
reas of th
e ba
ses a
nd
the
late
ral su
rface
.
Surfa
ce A
rea: S
= 2
r2 +
2rh
r
h
Base
Lateral surface
rr
h
Base
r2
Solu
tion:
First, con
vert 17.78
centim
ete
rs to inch
es.
17.78 cm
x — ≈ 7 in
.
Then, fin
d th
e su
rface
are
a.
S =
2r
2 + 2
rh
= 2
(7)
2 + 2
(7)(8
)
= 9
8 +
112
= 210
≈
65
9.4
in. 2
The su
rface
are
a is a
bout 6
59
.4 sq
uare
inch
es.
In a
coordin
ate
plane, d
raw
the fig
ure
s with
the g
iven
vertice
s. W
hich
figure
s are
simila
r? Expla
in you
r reason
ing
.
5min
Congratulations!Once you have checked
the solution with your teacher,
your group is all done!
659.4 in.2
1 in.
2.54 cm
Rem
ind
er
Key Id
eas
sh
ape
but n
ot nece
ssarily th
e
sa
me size
are
calle
d s
imila
r
fig
ure
s.
sim
ilar if
corre
spond
ing sid
e le
ngth
s are
proportion
al, a
nd
correspon
din
g
angle
s have
the sa
me m
easu
re.
Triangle A: (0, 0), (9, 0), (0, 9)
Triangle B: (0, 0), (6, 0), (0, 9)
Triangle C: (0, 0), (6, 0), (0, 6)
Solu
tion:
A tria
ngula
r prism
is a solid
that h
as tw
o para
llel,
congru
ent tria
ngula
r base
s. Th
e oth
er fa
ces a
re
para
llelog
ram
s. S
o, the solid
show
n is a
an tria
ngula
r prism.
Make
a ste
m-a
nd
-leaf plot of th
e n
um
ber
of songs d
ownloa
ded
.
4min
Your next card will look like this.
Each
card
for your
grou
p shou
ld h
ave
this
solid. If you
do n
ot see
a tria
ngula
r prism, g
o ba
ck and
try again
.
Key Id
ea
A s
tem
-and
-leaf plot
use
s the d
igits of d
ata
valu
es to org
anize
a d
ata
set. E
ach
data
valu
e is
broken in
to a ste
m (d
igit
or dig
its on th
e le
ft) and
a le
af (d
igit or d
igits on
the rig
ht).
Songs Downloaded
334560
144315
52031
6359
Rem
ind
er
Solu
tion:
To make
a ste
m-a
nd
-leaf plot:
1.) O
rder th
e d
ata
.
2.) C
hoose
the ste
ms a
nd
the le
ave
s. B
eca
use
the
data
valu
es ra
nge from
5 to 6
3, u
se th
e tens d
igits
for the ste
ms a
nd
the ones d
igits for th
e le
ave
s.
3
.) Write
the ste
ms to th
e left of th
e ve
rtical lin
e.
4.) W
rite th
e le
ave
s for each
stem
to the right
of the ve
rtical lin
e.
5.) C
reate
a title
and
a ke
y.
It costs $41.25
for 5 ticke
ts to the m
ovies.
Write
and
solve a
proportion to d
ete
rmin
e
how
much
4 ticke
ts cost.
3min
Your next card will look like this.
Key Id
eas
propo
rtion is a
n e
quation
sta
ting th
at tw
o ratios a
re
equiva
lent.
th
e M
ultiplica
tion P
rope
rty
of E
quality or th
e C
ross
P
roducts
Pro
perty.
Rem
ind
er
Key:
1 | 4
= 1
4 s
ongs
Songs Downloaded
Stem
Leaf
0 1 2 3 4 5 6
5 5 9
4 5
0 1 3
3 5
0 3
Solu
tion:
Write
and
solve a
proportion.
—
= —
dollars
tickets
41.25
4 =
5 Cross Products Property
16
5 =
Multiply.
3
3 =
Divide.
It costs $3
3 for 4
tickets to th
e m
ovies.
when x =
-1 and
y = 3
.
3min
Your next card will look like this.
Rem
ind
er
$33.00
Key Id
ea
Use
the o
rder o
f
ope
ration
s w
hen
eva
luatin
g a
n
x2 —
| y — 2 | +
— 12x
41.25
5
x4
Solu
tion:
Substitu
te -1 for x and
3 for y. Th
en sim
plify.
x2 —
| y — 2 | +
—
= (-1)
2 — | 3
— 2 | +
—
= 1 —
| 1 | + (-12)
= 1 —
1 + (-12)
= 1 +
(-1) + (-12)
= -12
The pe
rimete
r of the tra
pezoid
is 60
.
What is th
e va
lue of x?
4min
Your next card will look like this.
x 5 x 2
x + 3x + 3
Rem
ind
er
-12
12x12-1
Key Id
eas
perim
ete
r of a fig
ure
is th
e su
m of th
e sid
e le
ngth
s.
Solvin
g a
n e
quation
1. C
ombin
e like
term
s.
2. U
nd
o ad
dition
and
subtra
ction.
3
. Und
o multiplica
tion a
nd
d
ivision.
Solu
tion:
P
= S
um
of side le
ngth
s
6
0 =
(x + 3
) + 2x +
(x + 3
) + 5x
6
0 =
9x + 6
— 6
—
6
5
4 =
9x
54 =
9x
9
9
6
= x
The va
lue of x is 6
.
Gra
ph th
e lin
e th
at pa
sses th
rough th
e tw
o points
(-2, 2) and
(1, 1). Then fin
d th
e slope
of the lin
e.
3min
Your next card will look like this.
Rem
ind
er
6
Key Id
eas
ord
ere
d pa
ir (x, y) is a pa
ir of
num
bers th
at is u
sed
to locate
a
poin
t in a
coordin
ate
plane.
Slo
pe is th
e ra
te of ch
ange
be
tween a
ny tw
o points on
a lin
e.
To find
the slope
of a lin
e, fin
d
th
e ra
tio of the ve
rtical ch
ange
to th
e h
orizonta
l change.
Solu
tion:
2min
Your next card will look like this.
Rem
ind
er
Key Id
eas
oppos
ite
LC
D
.
—
-—.
yx-13
13
y
x4
2
2-2 4
-2-4
1 3
—3—
45310
-
Fin
d th
e su
rface
are
a of th
e cylin
der in
square
inch
es. R
ound
your a
nsw
er to th
e n
eare
st tenth
.
5min
Your next card will look like this.
Rem
ind
er
1 10-5
22.86 cm
1 in. ≈ 2.54 cm
6 in.
Solu
tion:
-1— —
3—
= -1—
+ ( - 3
—)
= -—
+ ( -—
) = -—
+ ( -—
) = -—
= -5
—
The d
iffere
nce
is -5—
.
45
310
45
310
9551
10
110
110
3310
1810
3310
Key Id
ea
The su
rface
are
a of a
cylind
er is th
e
sum
of the a
reas of th
e ba
ses a
nd
the
late
ral su
rface
.
Surfa
ce A
rea: S
= 2
r2 +
2rh
r
h
Base
Lateral surface
rr
h
Base
r2
Solu
tion:
First, con
vert 22
.86
centim
ete
rs to inch
es.
22.8
6 cm
x — ≈ 9
in.
Then, fin
d th
e su
rface
are
a.
S =
2r
2 + 2
rh
= 2
(9)
2 + 2
(9)(6
)
= 16
2 +
108
= 270
≈
847.8
in. 2
The su
rface
are
a is a
bout 8
47.8
square
inch
es.
In a
coordin
ate
plane, d
raw
the fig
ure
s with
the g
iven
vertice
s. W
hich
figure
s are
simila
r? Expla
in you
r reason
ing
.
5min
Congratulations!Once you have checked
the solution with your teacher,
your group is all done!
847.8 in.2
1 in.
2.54 cm
Rem
ind
er
Key Id
eas
sh
ape
but n
ot nece
ssarily th
e
sa
me size
are
calle
d s
imila
r
fig
ure
s.
sim
ilar if
corre
spond
ing sid
e le
ngth
s are
proportion
al, a
nd
correspon
din
g
angle
s have
the sa
me m
easu
re.
Triangle A: (0, 0), (9, 0), (0, 9)
Triangle B: (0, 0), (6, 0), (0, 9)
Triangle C: (0, 0), (6, 0), (0, 6)
Solu
tion:
A con
e is a
solid th
at h
as on
e circu
lar ba
se
and
one ve
rtex. S
o, the solid
show
n is a
cone.
Make
a ste
m-a
nd
-leaf plot of th
e n
um
ber
of songs d
ownloa
ded
.
4min
Your next card will look like this.
Each
card
for your
grou
p shou
ld h
ave
this
solid. If you
do n
ot see
a con
e, g
o back a
nd
try a
gain
.
Key Id
ea
A s
tem
-and
-leaf plot
use
s the d
igits of d
ata
valu
es to org
anize
a d
ata
set. E
ach
data
valu
e is
broken in
to a ste
m (d
igit
or dig
its on th
e le
ft) and
a le
af (d
igit or d
igits on
the rig
ht).
Songs Downloaded
414527
14615
52031
63159
Rem
ind
er
Solu
tion:
To make
a ste
m-a
nd
-leaf plot:
1.) O
rder th
e d
ata
.
2.) C
hoose
the ste
ms a
nd
the le
ave
s. B
eca
use
the
data
valu
es ra
nge from
5 to 6
3, u
se th
e tens d
igits
for the ste
ms a
nd
the ones d
igits for th
e le
ave
s.
3
.) Write
the ste
ms to th
e left of th
e ve
rtical lin
e.
4.) W
rite th
e le
ave
s for each
stem
to the right
of the ve
rtical lin
e.
5.) C
reate
a title
and
a ke
y.
It costs $41.25
for 5 ticke
ts to the m
ovies.
Write
and
solve a
proportion to d
ete
rmin
e
how
much
9 ticke
ts cost.
3min
Your next card will look like this.
Key Id
eas
propo
rtion is a
n e
quation
sta
ting th
at tw
o ratios a
re
equiva
lent.
th
e M
ultiplica
tion P
rope
rty
of E
quality or th
e C
ross
P
roducts
Pro
perty.
Rem
ind
er
Key:
1 | 4
= 1
4 s
ongs
Songs Downloaded
Stem
Leaf
0 1 2 3 4 5 6
5 5 9
4 5
0 7
1 1 5
1 3
Solu
tion:
Write
and
solve a
proportion.
—
= —
dollars
tickets
41.25
9 =
5 Cross Products Property
3
71.25 =
Multiply.
74
.25 =
Divide.
It costs $74
.25 for 9
tickets to th
e m
ovies.
when x =
1 and
y = -2
.
3min
Your next card will look like this.
Rem
ind
er
$74.25
Key Id
ea
Use
the o
rder o
f
ope
ration
s w
hen
eva
luatin
g a
n
x2 —
| y — 2 | +
— 12x
41.25
5
x9
Solu
tion:
Substitu
te 1 for x and
-2 for y. Then sim
plify.
x2 —
| y — 2 | +
—
= 1
2 — | -2 —
2 | + —
= 1 —
| -4| +
12
= 1 —
4 +
12
= 1 +
(-4) +
12
= 9
The pe
rimete
r of the tra
pezoid
is 96
.
What is th
e va
lue of x?
4min
Your next card will look like this.
x 5 x 2
x + 3x + 3
Rem
ind
er
9
12x121
Key Id
eas
perim
ete
r of a fig
ure
is th
e su
m of th
e sid
e le
ngth
s.
Solvin
g a
n e
quation
1. C
ombin
e like
term
s.
2. U
nd
o ad
dition
and
subtra
ction.
3
. Und
o multiplica
tion a
nd
d
ivision.
Solu
tion:
P
= S
um
of side le
ngth
s
9
6 =
(x + 3
) + 2x +
(x + 3
) + 5x
9
6 =
9x + 6
— 6
—
6
9
0 =
9x
90
= 9x
9
9
10
= x
The va
lue of x is 10
.
Gra
ph th
e lin
e th
at pa
sses th
rough th
e tw
o points
(-2, 2) and
( 3, 4
). Then fin
d th
e slope
of the lin
e.
3min
Your next card will look like this.
Rem
ind
er
10Key Id
eas
ord
ere
d pa
ir (x, y) is a pa
ir of
num
bers th
at is u
sed
to locate
a
poin
t in a
coordin
ate
plane.
Slo
pe is th
e ra
te of ch
ange
be
tween a
ny tw
o points on
a lin
e.
To find
the slope
of a lin
e, fin
d
th
e ra
tio of the ve
rtical ch
ange
to th
e h
orizonta
l change.
Solu
tion:
2min
Your next card will look like this.
Rem
ind
er
Key Id
eas
oppos
ite
LC
D
.
—
—.
yx25
25
y
x4
2
2-2 4
-2-4
3
2 5
—— 45
7
Fin
d th
e su
rface
are
a of th
e cylin
der in
square
inch
es. R
ound
your a
nsw
er to th
e n
eare
st tenth
.
5min
Your next card will look like this.
Rem
ind
er
1 24
12.7 cm
1 in. ≈ 2.54 cm
6 in.
Solu
tion:
1— —
( -2—) = 1—
+ 2—
= —
+ —
= —
+ —
= —
= 4
—
The d
iffere
nce
is 4—
.
45710
45710
17104510
12
12
145
1710
2810
Key Id
ea
The su
rface
are
a of a
cylind
er is th
e
sum
of the a
reas of th
e ba
ses a
nd
the
late
ral su
rface
.
Surfa
ce A
rea: S
= 2
r2 +
2rh
r
h
Base
Lateral surface
rr
h
Base
r2
Solu
tion:
First, con
vert 12
.7 centim
ete
rs to inch
es.
12.7 cm
x — ≈ 5
in.
Then, fin
d th
e su
rface
are
a.
S =
2r
2 + 2
rh
= 2
(5)
2 + 2
(5)(6
)
= 5
0 +
60
= 110
≈
345.4
in. 2
The su
rface
are
a is a
bout 3
45.4
square
inch
es.
In a
coordin
ate
plane, d
raw
the fig
ure
s with
the g
iven
vertice
s. W
hich
figure
s are
simila
r? Expla
in you
r reason
ing
.
5min
Congratulations!Once you have checked
the solution with your teacher,
your group is all done!
345.4 in.2
1 in.
2.54 cm
Rem
ind
er
Key Id
eas
sh
ape
but n
ot nece
ssarily th
e
sa
me size
are
calle
d s
imila
r
fig
ure
s.
sim
ilar if
corre
spond
ing sid
e le
ngth
s are
proportion
al, a
nd
correspon
din
g
angle
s have
the sa
me m
easu
re.
Triangle A: (0, 0), (9, 0), (0, 9)
Triangle B: (0, 0), (6, 0), (0, 9)
Triangle C: (0, 0), (6, 0), (0, 6)
Solu
tion:
Triangle
s A a
nd
C a
re sim
ilar be
cause
correspon
din
g sid
e le
ngth
s are
proportional a
nd
correspon
din
g a
ngle
s have
the sa
me m
easu
re
Triangle
A
— =
— =
199
Leg 1 of A
Leg 2 of A
y
x2
46
8
2 4 6 8
(0, 0
)
(0, 9
)
(9, 0
)
Triangle
B
— =
— =
—69
23
Leg 1 of B
Leg 2 of B
y
x2
46
8
2 4 6 8
(0, 0
)
(0, 9
)
(6, 0
)
Triangle
C
— =
— =
166
Leg 1 of C
Leg 2 of C
y
x2
46
8
2 4 6 8
(0, 0
)
(0, 6
)
(6, 0
)
Key Id
ea
A s
tem
-and
-leaf plot
use
s the d
igits of d
ata
valu
es to org
anize
a d
ata
set. E
ach
data
valu
e is
broken in
to a ste
m (d
igit
or dig
its on th
e le
ft) and
a le
af (d
igit or d
igits on
the rig
ht).
Rem
ind
er
Rem
ind
er
Key:
1 | 4
= 1
4 s
ongs
Songs Downloaded
Stem
Leaf
0 1 2 3 4
5 8 8 9
2 4 5 8
0 1 4
5
Key Id
eas
propo
rtion
Multiplica
tion P
rope
rty
of E
quality
Cros
s
P
roducts
Pro
perty
Rem
ind
er
$7.50
Key Id
ea
Use
the o
rder o
f
ope
ration
s w
hen
eva
luatin
g a
n
expre
ssion.
Rem
ind
er
12
Key Id
eas
perim
ete
r
3
Rem
ind
er
1
Key Id
eas
ord
ere
d pa
irx
y
Slo
pe
Rem
ind
er
5 2-Key Id
eas
oppos
ite
LC
D
.
Rem
ind
er
1 101Key Id
ea
The su
rface
are
a of a
cylind
er is th
e
sum
of the a
reas of th
e ba
ses a
nd
the
late
ral su
rface
.
Surfa
ce A
rea: S
= 2
r2 +
2rh
r
h
Base
Lateral surface
rr
h
Base
r2
1492.2 in.
2
Rem
ind
er
Key Id
eas
sim
ilar
fig
ure
s.
sim
ilar
Key Id
ea
A s
tem
-and
-leaf plot
use
s the d
igits of d
ata
valu
es to org
anize
a d
ata
set. E
ach
data
valu
e is
broken in
to a ste
m (d
igit
or dig
its on th
e le
ft) and
a le
af (d
igit or d
igits on
the rig
ht).
Rem
ind
er
Rem
ind
er
Key:
1 | 4
= 1
4 s
ongs
Songs Downloaded
Stem
Leaf
0 1 2 3 4
5 9 9
2 2 3 4
0 5
1 4
5
Key Id
eas
propo
rtion
Multiplica
tion P
rope
rty
of E
quality
Cros
s
P
roducts
Pro
perty
Rem
ind
er
$8.25
Key Id
ea
Use
the o
rder o
f
ope
ration
s w
hen
eva
luatin
g a
n
expre
ssion.
Rem
ind
er
-5
Key Id
eas
perim
ete
r
3
Rem
ind
er
7
Key Id
eas
ord
ere
d pa
irx
y
Slo
pe
Rem
ind
er
3 2
Key Id
eas
oppos
ite
LC
D
.
Rem
ind
er
1 2-3K
ey Id
ea
The su
rface
are
a of a
cylind
er is th
e
sum
of the a
reas of th
e ba
ses a
nd
the
late
ral su
rface
.
Surfa
ce A
rea: S
= 2
r2 +
2rh
r
h
Base
Lateral surface
rr
h
Base
r2
571.8 in.2
Rem
ind
er
Key Id
eas
sim
ilar
fig
ure
s.
sim
ilar
Top Related