NYS COMMON CORE MATHEM
ATICS CURRICULUM
Lesson 20
Lesson 20: Writing and Evalua
ting Expressions—Multiplic
ation
and Division
Classwork
Exercises
1.
The farmers’ market is selling bag
s of apples. In every bag, ther
e are 3 apples.
a.
Complete the table.
Number of Bags
Total Number of Apples
1
3
2
3
.
4
B
b.
What if the market had 25 bag
s of apples to sell? How man
y apples is that in all?
) )
z....
/
.
c.
If a truck arrived that had some
number, a, more apples on it,
then how many bags would
uptheapp)es?
the clerks use to bag
‘
d.
If a truck arrived that had 600 mo
re apples on it, how many bag
s would the clerks use to bag
up the apples?
e.
How is part (d) different from
part (b)?
/./J
II
.
COMMON
CORE
© 2013 Gxnn,cn Ca,i. r Sxn.
rWf
Lesson 20:
Date:
.
Writing and Evaluating Expr
essions—Multiplication and
Division
12/15/13
.
.,,
engage fly
5.84
NYS COMMON CORE MATHEMATICS CURRICULUM
2.
Lesson 20
cans and bottles. When you return the
New York State, there is a five-cent deposit on all carbonated beverage
empty can or bottle, you get the five cents back.
a. Complete the table.
In
Ii
b.
how much money is returned?
If we let C represent the number of cans, what is the expression that shows
c.
222 cans.
Use the expression to find out how much money Brett would receive if he returned
d.
to collect and return?
If Gavin needs to earn $4.50 for returning cans, how many cans does he need
e.
How is part (d) different from part (c)?
COMMON
CORE
Lesson 20:
Date:
Writing and Evaluating Expressions—Multiplication and Division
12115/13
engage
S.85
NYS COMMON CORE MATHEMATIC
S CURRICULUM
3.
Lesson 20
The fare for a subway or a local bus
ride is $2.50.
a.
Complete the table.
Number of Rides
‘
2
3
Cost of Rides in Dollars
22O
4
7.5
4
S
10
30
R
II
b.
If we let R represent the number
of rides, what is the expression
that shows the cost of the rides
?
c.
Use the expression to find out how
much money 60 rides would
cost.
d.
If a commuter spends $175.00 on
subway or bus rides, how man
y trips did the commuter take
?
e.
How is part (d) different from par
t (c)?
COMMON
CORE
Lesson 20:
Date:
Writing and Evaluating Expressio
ns—Multiplication and Division
12)15/13
enqaqe fly
S.86
Lesson 20
NYS COMMON CORE MATHEMATICS CURRICULUM
4.
Owen made a pendulum that swings 12
A pendulum swings though a certain number of cycles in a given time.
times ever/ iS seconds.
Include data for up to one
Construct a table showing the number of cycles through which a pendulum swings.
a.
for the pendulum to make
minute. Use the last row for C cycles, and write an expression for the time it takes
C cycles.
4:
LI
-i..
1
,
LI
-
,,
1
b.
15,
What was the elapsed
Owen and his pendulum team set their pendulum in motion and counted 16 cycles.
time?
I5i()
c.
Write an expression for the number of cycles a pendulum swings in S seconds.
d.
35 seconds.
n a different experiment. Owen and his pendulum team counted the cycles of the pendulum for
How many cycles did they count?
—
II
COMMON
CORE
Lesson 20:
Date:
Writing and
12/15/13
Evaluating Expressions—Multiplication and Division
engage fly
5.87
NYS COMMON CORE MATHEMATICS CURR
ICULUM
Lesson 21
Lesson 21: Writing and Evaluating Expressi
ons—Multiplication
and Addition
Classwork
Exercise 1
The Italian Villa Restaurant has square
tables that the servers can push toge
ther to accommodate the custo
mers. Only
one chair fits along the side of the squa
re table. Make a model of each situa
tion to determine how many
seats
will fit
around various rectangular tables.
I1It1fIII1IIL1IIIII1
Number of Square Tables
Number of Seats at the Table
1
2
3
4
Ia.,
J
(
50
200
V
/
Are there any other ways to think abou
t solutions to
It
is impractical to
long, how many
this
r
7
—
&.
problem?
I
model of pushing 50 tables together to
chairs would fit on the long sides of
the table?.
make a
How many chairs
fit
on the ends of the long table?
How many chairs
fit
in all? Record
make a long rectangle. If we
did
have a rectangle that
it.
Work with your group to determine how
many chairs would
were pushed together.
fit around
a very long rectangular table
if 200
square tables
T represent the number of square tables that mak
e one long rectangular table, what
is the expression for the
number of chairs that will fit around it?
If we let
II
COMMON
CORE
lesson 21:
Date:
02013 Con,n,.n Corn, I, Son,. rhti rn.n
Writing and Evaluating Expressions—Multip
lication and Addition
12/15/13
engage fly
5.90
lesson 21
CURRICULUM
NYS COMMON CORE MATHEMATICS
Example 2
determine the
ine the cost for various numbers of pizzas, and also
Look at Example 2 with your group. Determ
P pizzas delivered.
expression that describes the cost of having
how
each. They charge $2.00 to deliver, regardless of
Pizza Queen has a special offer on lunch pizzas: $4.00
a.
sion
expres
for various numbers of pizzas, and also determine the
many pizzas are ordered. Determine the cost
ed.
that describes the cost of having P pizzas deliver
Total Cost in Dollars
Number of Pizzas Delivered
‘
2
3
4
10
so
(?L
P
‘
perform to find the total cost?
What mathematical operations did you need to
would cost.
for everyone in our class? Determine how much this
Suppose our principal wanted to buy a pizza
b.
If
what is the greatest number of pizzas they could order?
the booster club had $400 to spend on pizza,
*
c.
the
delivery price was raised to $3.00, create a table that shows
If the pizza price was raised to $5.00 and the
of
cost
new
the
es
describ
that
sion
5 pizzas. Include the expres
total cost (pizza plus delivery) of 1, 2, 3, 4, and
ordering P pizzas.
Total Cost in Dollars
Number of Pizzas Delivered
1
3
4
-
S
p
II
i
COMMO N
CORE
I.eSSOn 21:
Date:
Addition
Writing and Evaluating Expressions—Multiplication and
12/15/13
engage fly
NYS COMMON CORE
MATHEMATICS CU
RRICULUM
Lesson 22
Lesson 22: Writing an
d Evaluating Expressio
ns: Exponents
Classwork
Example 1: Foldi
ng Paper
Exercises
1.
Predict how many
times you can fold
a piece of paper in
half.
My Prediction:
2.
Before any folding
(zero folds), there is
only one layer of
paper. This is rec
Fold your paper in hal
orded in the first row
f. Record the num
of the table.
ber of layers of pa
per that result.
Continue as long as
possible.
Number of Folds
Number of Paper
Layers That
Number of Paper
Layers Written
Result
as a Power of 2
0
1
2°
1
-
..__
___
___
___
2
___
___
___
___
___
__
.
3
.
.
1
,
.,
j
4
.
..
:...
5
-
6
.
7
R
-!
a
Are you able to con
tinue folding the
paper indefinitely
? Why or why no
t?
b.
How could you use
a calculator to
find
the next number in
the series?
.
What is the relationsh
ip between the num
ber of folds and the
number of tayers
?
I
d
How is this relations
hip represented in
the exponential for
m of the numeri
cal expression?
e.
II
i
I
c.
.
If you fold a paper
COMMON
CORE
f times, write an expression to show the
Lesson22:
Date:
number of pape lay
r
ers.
Writing and Evaluating
Expressions—Exponents
12/15/13
enawr
lesson 22
EMATiCS CURRICULUM
NYS COMMON CORE MATH
3.
, and it
would double at each successive stage
ad of folded, the height of the stack
inste
cut
be
to
were
r
pape
If the
.
would be possible to continue
result from 16 cuts.
ribes how many layers of paper
Write an expression that desc
a.
ng it in standard form.
Evaluate this expression by writi
b.
tion
Example 2: Bacterial Infec
in a
celled organisms that reproduce
Bacteria are microscopic oneIn
of which is called binary fission.
couple of different ways, one
gh
enou
large
is
it
until
size
its
ases
binary fission, a bacterium incre
they
until
grow
two
e
are identical. Thes
to split into two parts that
into two individual bacteria. This
split
to
gh
are both large enou
conditions are favorable.
continues as long as growing
a.
n.
that result from each generatio
Record the number of bacteria
Generation
Number of bacteria
Number of bacteria written as
a power of 2
21
2
1
22
4
2
2
8
3
IC
4
I \iJ
S
..J,
6
7
D
8
9
j
10
1 .)
...“
..1
11
,.
12
.,
13
14
II
COMMON
CORE
Lesson22:
Date:
...
.)
.
.
I Q
ents
Writing and Evaluating Expressions—Expon
13
12/15/
engage’
S.96
NYS COMMON CORE MATH
EMATICS CURRICUUJM
b.
c.
d.
Lesson 22
How many generations would
it take until there were ove
r one million bacteria presen
t?
I
4
Under the right growing conditi
ons, many bacteria can rep
roduce everi IS minbtes. Und
how long would it take for one
er these conditions,
bacterium to reproduce itse
lf into more than one million
bacteria?
Write an expression for how man
y bacteria would be presen
t after g generations.
Example 3: Volume of
a Rectangular Solid
h
=
2w
w
=3w
This box has a width, w. The
height of the box, h, is twice
the width. The length of the
That is, the width, height, and
box, 1, is three times the wid
length of a rectangular prism
th.
are in the ratio of 1: 2: 3.
For rectangular solids like this,
the volume is calculated by
multiplying length times wid
th times height.
V=Lwh
V=3w•w2w
V=32www
V = 6w
3
Follow the above example to calc
ulate the volume of these rect
angular solids, given the
width, w.
Width in centimeters (cm>
Volume in cubic centimeter
s (cm
)
3
1
3
4
.:
w
.
II
COMMON
CORE
2013 conman
car..
isonn:
Writing and Evaluating Expr
essions— Exponents
12/15/13
Date:
n So,e rVt res.,v.d.
-—
engage
S.97
NYS COMMON CORE MATHEMATICS CURRICUlUM
Lesson 23
Lesson 23: True and False Number Sentences
Cl asswork
Opening Exercise
Determine what each symbol stands for and provide an example.
What the Symbol Stands For
Symbol
Example
>
<
<
>
Example I
or inequality, then substitute 3 for every x.
For each inequality or equation your teacher displays, write the equation
or a false number sentence.
Determine if the equation or inequality results in a true number sentence
1.
1
3.
4.
5.
6.
II
:
COMMON
CORE
Lesson23:
Date:
True and False Number Sentences
12/16/13
engage
s.100