Summer
Math
Activity
#1
6th
to
7th
“The
Doable
Dozen”
Athletes,
doctors,
mechanics,
musicians
and
artists
continually
practice
to
sharpen
their
skills
–
mathematicians
need
to
do
the
same.
With
this
in
mind,
we
present
“The
Doable
Dozen”
–
12
skill
review
problems
that
will
keep
you
sharp
all
summer
long.
Please
do
not
use
a
calculator
on
this
section
and
remember
that
you
must
show
all
of
your
work.
1.
61.563 + 7.89 2.
76.00098 " 5.44 4.
16.912 ÷ 5.6 6.
5 3
" 7 7
!
!
3.
9.6 " .14 !
!
5.
1 2
+ 5 5
!
!
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#1
7.
3 1
" 4 4
6th
to
7th
8.
5 1
÷ 7 2
10.
3 1
" 4 2
12.
1 3
÷ 2 4
!
!
9.
2 1
+ 3 4
!
!
11.
2 1
" 3 4
!
!
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#1
6th
to
7th
“Tick­tock:
The
Mouse
Ran
Around
the
Clock”
13.
A
small
piece
of
cheese
is
placed
on
top
of
each
of
the
twelve
numbers
on
the
face
of
a
clock.
A
mouse
starts
eating
the
cheese
that
is
over
the
number
1
and
then
moves
clockwise
around
the
clock
eating
every
other
piece
of
cheese.
He
always
skips
a
piece
of
cheese
before
he
eats
the
next
piece.
What
number
will
be
under
the
last
piece
of
cheese
that
is
left
on
the
clock?
Try
to
sketch
a
clock
and
solve
the
problem
for
yourself
–
the
solution
is
on
the
next
page.
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#1
6th
to
7th
Solution:
The
mouse
eats
the
cheese
at
#1,
and
skips
the
cheese
at
#2.
He
eats
the
cheese
at
#3,
and
skips
#4.
He
eats
the
cheese
at
#5,
and
skips
#6.
He
eats
the
cheese
at
#7,
and
skips
#8.
He
eats
the
cheese
at
#9,
and
skips
#10.
He
eats
the
cheese
at
#11,
and
skips
#12.
Here’s
where
you
must
be
careful,
there
is
no
longer
any
cheese
on
#1.
He
eats
the
cheese
at
#2,
and
skips
#4.
He
eats
the
cheese
at
#6,
and
skips
#8.
He
eats
the
cheese
at
#10,
and
skips
#12.
He
eats
the
cheese
at
#4,
and
skips
#8.
He
then
eats
the
cheese
on
#12,
which
leaves
the
cheese
on
#8
as
the
last
piece!
14.
Now
work
the
problem
above
except
have
the
mouse
start
on
#6
–
where
will
the
last
piece
of
cheese
be?
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#1
6th
to
7th
15.
If
the
mouse
started
moving
in
a
counter­clockwise
direction
but
started
on
#10
–
where
will
the
last
piece
of
cheese
be?
16.
Find
out
where
the
last
piece
of
cheese
would
be
if
the
mouse
started
at
#5,
always
skipped
2
pieces
of
cheese
before
eating
and
moved
in
a
clockwise
direction.
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#2
6th
to
7th
“The
Doable
Dozen”
Practice
will
make
you
a
better
mathematics
student
and
will
lead
to
long‐range
success
in
your
future.
A
little
effort
now
will
pay
large
dividends
next
fall.
Please
do
not
use
a
calculator
on
this
section
and
remember
that
you
must
show
all
of
your
work.
You
must
show
the
steps
used
in
solving
equations.
1.
126.6 + 34.76 2.
.3 " .1095 4.
61.5 ÷12.3 6.
5 3
" 6 4
!
!
3.
3.8 " .6 !
!
5.
2 5
+ 5 6
!
!
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#2
7.
7 27
" 9 28
6th
to
7th
8.
3 1
÷ 8 4
10.
x " 38 = 5 12.
x
= 5
4
!
!
9.
x +13 = 48 !
!
11.
7x = 119 !
!
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#2
6th
to
7th
“Measurement
Madness”
To
complete
this
portion
of
your
assignment,
you
will
need
to
use
the
ruler
that
is
provided
in
the
back
of
this
packet
or
one
of
your
own.
In
this
section,
you
are
encouraged
to
use
a
calculator.
There
is
a
ruler
at
the
end
of
the
packet
that
you
can
use
to
do
this
portion.
Turn
one
of
your
hands
over
so
that
your
palms
are
facing
you.
Measure
the
length
of
your
fingers
and
your
thumb
(see
sketch
#1)
to
the
nearest
1
th
of
16
an
inch
(the
smallest
marks
on
your
ruler).
Record
these
measurements
in
the
chart
below:
!
Finger
Name
Measurement
Thumb
Index
Middle
Ring
Pinky
You
must
do
just
a
few
more
tasks
with
this
chart:
13.
Find
the
sum
of
the
lengths
of
all
of
your
fingers
and
thumb.
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#2
14.
Find
the
difference
between
your
longest
and
shortest
measurements.
6th
to
7th
15.
Find
the
average
length
of
your
fingers
and
thumb.
Now,
make
a
clenched
fist,
place
your
“Pinky”
finger
on
the
ground
and
measure
the
height
of
your
fist
(see
sketch
#2).
This
unit
has
traditionally
been
called
a
“hand”
and
is
still
used
in
measuring
the
height
of
a
horse.
So
that
everyone
was
using
the
same
measure,
the
“hand”
was
standardized
to
be
4
inches
in
length.
With
this
in
mind,
answer
the
following
questions:
16.
How
much
larger
or
smaller
is
your
“hand”
than
the
standard
4
inch
“hand”?
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#2
6th
to
7th
17.
The
average
Arabian
horse
has
a
size
of
15
hands
–
convert
this
measure
into
(a)
inches,
and
then
convert
this
answer
into
(b)
feet
and
inches.
18.
The
tallest
horse
ever
measured
was
7
feet
and
1
inch
tall
–
convert
this
measure
into
hands.
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#2
6th
to
7th
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#3
6th
to
7th
“The
Doable
Dozen”
Once
again
we
are
providing
you
with
12
simple
problems
to
keep
your
mind
as
sharp
as
a
tack.
You
may
use
a
calculator
on
this
section,
just
be
sure
to
show
how
you
came
up
with
each
answer.
Some
non‐Barberton
students
believe
that
4 3 = 12 ,
however,
every
Barberton
math
student
knows
that
4 3 = 4 " 4 " 4 = 64 .
Likewise,
36 = 6 ,
since
6 " 6 = 36 .
With
that
!
in
mind,
solve
the
next
dozen
problems.
1.
3!2 !
2.
5 3 ! !
!
3.
10 5 4.
812 !
!
5.
25 6.
49 !
!
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#3
7.
1 6th
to
7th
8.
121 !
!
9.
532 10.
81 !
!
11.
210 !
12.
400 !
“Really
Big
and
Really
Small
Stuff”
To
complete
this
portion
of
your
assignment,
you
are
encouraged
to
use
a
calculator.
As
you
recall,
scientific
notation
is
used
to
describe
numbers
that
are
very
large
or
very
small
–
it
consists
of
a
number
greater
than
or
equal
to
1
and
less
than
10,
multiplied
by
a
power
of
10.
For
instance,
4.85 " 10 7 = 48,500,000 ,
you
can
find
the
solution
by
moving
the
decimal
point
to
the
right
the
same
number
of
places
as
the
!
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#3
6th
to
7th
exponent
in
the
power
of
10.
If
the
exponent
is
negative,
it
will
describe
a
very
small
number,
for
instance,
8.22 " 10 #3 = .00822 ,
and
the
answer
can
be
found
by
moving
the
decimal
point
to
the
left
the
same
number
of
!
places
as
the
exponent
in
the
power
of
10.
Here
are
a
few
problems
that
you
can
try
on
your
own.
Convert
into
standard
notation:
13.
6.94 " 10 4 14.
2.281 " 10 2 16.
1.908 " 10 #1
!
!
15.
9.41 " 10 #3 !
!
17.
5.904 " 10 7 18.
8.88 " 10 #2 !
!
Convert
into
scientific
notation:
19.
5,280 20.
3,000,000 !
!
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#3
21.
.0007 22.
1,650,000,000 6th
to
7th
!
!
23.
.000208 24.
.4 !
!
You
have
now
completed
your
third
math
activity
–
be
sure
to
get
outside
and
get
some
physical
activity
this
week!
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#4
6th
to
7th
“The
Doable
Dozen”
Keep
your
calculator
tucked
away
as
you
try
these
problems.
You
will
have
to
show
your
work
to
be
successful
on
them.
1.
7.8 + .106 2.
6.3 " 2.854 4.
.0135 ÷ .03 6.
4 2
" 5 3
8.
3 3
÷ 4 8
!
!
3.
.81 " 2.3
!
!
5.
2 3
+ 5 4
!
!
7.
4 1
" 7 2
!
!
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#4
9.
64 6th
to
7th
10.
34 12.
x "13 = 87 !
!
11.
x +17 = 29 !
!
“Hot
Wheels
Mania”
Let’s
see
if
you
can
use
mathematics
to
learn
about
scale
measure.
“Hot
Wheels”
cars
are
made
using
a
scale
of
1:64.
This
means
that
1
foot
on
the
actual
car
equals
1
ft
on
the
model
–
the
car
is
64
times
larger
than
64
the
model.
A
2010
Ford
Mustang
has
an
actual
length
of
188.1
in,
a
width
of
73.9
in
!
and
a
length
of
55.6
in
and
weighs
3400
lb.
Round
all
answers
to
the
nearest
hundredth.
You
will
have
to
show
your
work
in
all
of
these
problems.
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#4
6th
to
7th
13.
Find
the
length
of
the
Hot
Wheels
Mustang.
Solution:
actual 1
x
=
=
toy
64 188.1
188.1 = 64 x !
2.93906 = x which
equals
2.94
in
Now
that
you
know
how
to
do
these,
the
next
few
should
be
easy
!
to
do.
!
14.
Find
the
width
of
the
Hot
Wheels
Mustang.
15.
Find
the
height
of
the
Hot
Wheels
Mustang.
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#4
6th
to
7th
16.
How
big
would
you
be
in
the
world
of
Hot
Wheels?
Hint:
Use
your
actual
height
in
inches
just
as
you
used
the
actual
length
of
the
Mustang.
You
may
have
to
think
a
little
harder
to
do
this
problem,
but
we
are
sure
that
you
will
succeed.
17.
If
a
person
is
.75
inches
in
the
Hot
Wheels
world,
how
tall
is
that
person
in
the
real
world?
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#5
6th
to
7th
“The
Doable
Dozen”
Decimals
are
the
focus
of
these
problems
–
make
sure
that
you
show
your
work
and
do
them
without
a
calculator!
1.
2.14 + 211.9 2.
12.907 " 4.38 4.
321.3 ÷ 5.1
6.
26 " 9.08 8.
.008 ÷ .025 !
!
3.
2.1 " .46 !
!
5.
17 + .085 !
!
7.
1.3 " .073 !
!
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#5
9.
81 10.
6th
to
7th
17 2 !
!
11.
.5 2 12.
.25 !
!
“I
Wish
I
Had
a
Million
Dollars”
The
dimensions
of
a
US
dollar
bill
are
6.14
inches
long,
2.61
inches
wide
and
.0043
inches
thick.
Let’s
use
this
information
to
find
out
a
little
about
a
lot
of
money
–
make
sure
that
you
show
all
of
your
work.
You
can
also
use
your
calculator
if
you
like.
13.
How
tall
(in
inches)
would
a
stack
of
a
million
dollar
bills
be?
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#5
14.
6th
to
7th
Since
every
foot
has
12
inches,
how
tall
would
the
stack
be
in
feet
(rounded
to
the
nearest
hundredth)?
15.
Since
you
know
that
a
dollar
bill
is
6.14
inches
long,
how
long
(in
inches)
would
a
row
of
a
million
dollars
be
if
they
were
placed
from
end
to
end?
16.
Since
every
foot
has
12
inches
and
every
mile
has
5280
feet,
how
many
miles
long
would
the
row
of
bills
be?
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#5
17.
6th
to
7th
How
tall
(in
inches)
would
a
stack
of
a
billion
(1,000,000,000)
dollar
bills
be?
18.
Since
every
foot
has
12
inches,
how
tall
would
the
stack
be
in
feet
(rounded
to
the
nearest
hundredth)?
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#5
19.
6th
to
7th
Warren
Buffett,
one
of
the
world’s
richest
people,
has
a
net
worth
of
62
billion
dollars.
If
he
chooses
to
spend
$1,000,000
every
day,
how
long
(in
years
rounded
to
the
nearest
hundredth)
would
it
be
until
he
ran
out
of
money?
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#6
“The
Doable
Dozen”
6th
to
7th
No
calculator
is
needed
on
these
problems
–
just
get
your
math
mind
in
gear
and
be
sure
to
show
all
of
your
work.
1.
.45 + 6.79 2.
85 " 6.22 4.
1.40168 ÷ 5.006 6.
53
!
!
3.
1.01 " .55 !
!
5.
49 !
!
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#6
7.
1
5
2 +4 3
7
6th
to
7th
8.
1
2
3 "1 4
3
10.
5 5
÷ 6 7
12.
7.385 " 10 2 !
!
9.
2
2
1 "2 3
5
!
!
11.
6.5 " 10 5 !
!
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#6
“I
Want
the
Piece
with
All
of
the
Icing”
6th
to
7th
A
birthday
cake
is
baked
in
the
shape
of
a
rectangular
prism
6
inches
long
by
6
inches
wide
by
2
inches
high.
The
cake
is
iced
with
frosting
on
the
top
and
on
four
sides
–
there
is
no
icing
on
the
bottom.
The
cake
is
cut
as
shown
below
into
pieces
that
are
2
in
x
2
in
x
2
in.
Use
the
sketch
and
your
mind
to
compute
how
many
pieces
of
cake
have
icing
on
3
sides,
2
sides
or
1
side
–
and
complete
the
table.
You
then
must
complete
the
table
for
the
larger
birthday
cakes.
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#6
6th
to
7th
Now
work
it
on
your
own
if
the
cake
is
6
inches
by
4
inches
and
cut
into
the
same
2
in
x
2
in
x
2
in
pieces.
The
drawing
for
this
cake
is
below.
You
now
have
three
more
birthday
cakes
to
think
about
–
it
will
help
a
lot
if
you
sketch
out
the
cakes
before
you
work
them.
Developed
exclusively
for
the
Barberton
City
School
District
Summer
Math
Activity
#6
Cake
Size
Number
of
6th
to
7th
3
sides
iced
2
sides
iced
1
side
iced
Pieces
6
in
by
6
in
9
4
4
1
6
in
by
4
in
6
in
by
8
in
12
in
by
12
in
18
in
by
14
in
Developed
exclusively
for
the
Barberton
City
School
District