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Teaching 2-Step Word Problems
SMARTTraining NOW
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Presented by: Peggy Golden / Linda West July 2015 [email protected] Scottsdale, Arizona
1
2-Step Word Problems Grades 2 – 5
All problems are found in Engage NY’s Math Modules. G2, M2 1. Mr. Peterson decorated with 15 meters of ribbon in the morning. He decorated
with 8 more meters in the afternoon than in the morning. How many meters of ribbon did Mr. Peterson use to decorate in the morning and afternoon in all?
2. The red colored pencil is 17 centimeters long. The green colored pencil is 9 centimeters shorter than the red colored pencil. What is the total length of both pencils?
3. Maura's ribbon is 26 cm long. Colleen's ribbon is 14 cm shorter than Maura's ribbon. What is the total length of both the ribbons?
4. Jesse’s doll is 30 cm tall. Sarah’s doll is 9 cm shorter than Jessie’s doll. What is the total length of both dolls?
2
5. Steven has a black leather strip that is 13 centimeters long. He cut off 5 centimeters. His teacher gave him a brown leather strip that is 16 centimeters long. What is the total length of both strips?
G2, M4
6. There are 31 students on the red bus. There are 29 more students on the yellow bus than on the red bus. How many students are on the yellow bus? How many students are on both buses combined?
7. Ms. Lopez cut 46 cm of yarn. Ms. Hamilton cut 22 cm less than Ms. Lopez. How
many centimeters of yarn did Ms. Hamilton cut? How many centimeters of yarn did they have altogether?
3
8. Kiera has 62 blocks and Pete has 37 blocks. They give away 75 blocks. How many blocks do they have left?
9. Ian bought a pack of 47 water balloons. 19 were red, 16 were yellow, and the
rest were blue. How many water balloons were blue?
10. Kevin had 53 balloons. His cat popped 17 of them. His father gives him 18 more balloons. How many balloons does Kevin have now?
11. Lee’s fish tank has 24 goldfish and some silver fish. In all, there are 59 fish in the aquarium. Lee puts in some more silver fish. Now, there are 51 silver fish.How many silver fish did Lee put in the tank?
4
12. There were 35 apples on the table. 17 of the apples were rotten and were thrown out. 9 apples were eaten. How many apples are still on the table?
13. There are 32 brown dogs and 19 white dogs at the park. 16 more brown dogs come to the park. How many dogs are there now at the park?
14. Antonio gave 27 tomatoes to his neighbor and 15 to his brother. He had 72
tomatoes before giving some away. How many tomatoes does Antonio have left?
15. The bakery made 92 muffins. Seventeen were blueberry, 23 were cranberry, and
the rest were chocolate chip. How many chocolate chip muffins did the bakery make?
5
G3, M1
16. Red, orange, and blue scarves are on sale for $4 each. Nina buys 2 scarves of each color. She also buys a hat that costs $4. How much does she spend altogether?
17. Mr. Lim buys 7 plants for his garden. Each plant costs $5. The next day, he buys a rose bush that also costs $5. How much more do the 7 plants cost than the rose bush?
18. Ten children equally share 40 almonds. How many almonds will 3 children get?
19. There are 25 blue balloons and 15 red balloons at a party. Five children are given an equal number of each color balloon. How many blue and red balloons does each child get?
6
G3, M3
20. Rose has 6 pieces of yarn that are each 9 centimeters long. Sasha gives Rose a piece of yarn. Now, Rose has a total of 81 centimeters of yarn. What is the length of the yarn that Sasha gives Rose?
21. Julio spends 29 minutes doing his spelling homework. He then completes each math problem in 4 minutes. There are 7 math problems. How many minutes does Julio spend on his homework in all?
22. Tanner’s beaker had 45 milliliters of water in it at first. After each of his friends poured in 8 milliliters, the beaker contained 93 milliliters. How many friends poured water into Tanner’s beaker?
23. On Saturday, Warren swims laps in the pool for 45 minutes. On Sunday, he runs 8 miles. It takes him 9 minutes to run each mile. How long does Warren spend exercising over the weekend?
7
G4, M1
24. Last year, Big Bill’s Department Store sold many pairs of footwear. 118,214 pairs of boots were sold, 37,092 more pairs of sandals than pairs of boots were sold, and 124,417 more pairs of sneakers than pairs of boots were sold. How many pairs of footwear were sold last year?
25. On Saturday, 32,736 more bus tickets were sold than on Sunday. On Sunday, only 17,295 tickets were sold. How many people bought bus tickets over the weekend?
26. In January, Scott earned $8,999. In February, he earned $2,387 more than in January. In March, Scott earned the same amount as in February. How much did Scott earn altogether during those three months?
27. A company has 3 locations with 70,010 employees altogether. The first location has 34,857 employees. The second location has 17,595 employees. How many employees work in the third location?
8
28. There were 12,345 people at a concert on Saturday night. On Sunday night, there were 1,795 fewer people at the concert than on Saturday night. How many people attended the concert on both nights?
29. Martin’s car had 86,456 miles on it. Of that distance, Martin’s wife drove 24,901 miles, and his son drove 7,997 miles. Martin drove the rest.
30. A pair of hippos weighed 5,201 kilograms together. The female weighed 2,038 kilograms. How much more did the male weigh than the female?
31. At a parade, 97,853 people sat in bleachers and 388,547 people stood along the street. How many fewer people were in the bleachers than standing on the street?
9
32. The shop sold 12,789 chocolate and 9,324 cookie dough cones. It sold 1,078 more peanut butter cones than cookie dough cones and 999 more vanilla cones than chocolate cones. What was the total number of ice cream cones sold?
G4, M2
33. The gas tank in Zachary’s car has a capacity of 60 liters. He adds 23 liters 825 milliliters gas to the tank, which already has 2,050 milliliters of gas. How much more gas can Zachary add to the gas tank?
34. Jeff places a pineapple with a mass of 890 grams on a balance scale. He balances the scale by placing two oranges, an apple, and a lemon on the other side. Each orange weighs 280 grams. The lemon weighs 195 grams less than each orange. What is the mass of the apple?
10
G4, M3
35. The rectangular projection screen in the school auditorium is 5 times as long and 5 times as wide as the rectangular screen in the library. The screen in the library is 4 feet long with a perimeter of 14 feet. What is the perimeter of the screen in the auditorium?
36. The width of David’s rectangular tent is 5 feet. The length is twice the width. David’s rectangular air mattress measures 3 feet by 6 feet. If David puts the air mattress in the tent, how many square feet of floor space will be available for the rest of his things?
37. The Turner family uses 548 liters of water per day. The Hill family uses 3 times as much water per day. How much water does the Hill family use per week?
G4, M5
38. A seamstress needs 15
8 yards of fabric to make a child’s dress. She needs 3 times
as much fabric to make a woman’s dress. How many yards of fabric does she need for both dresses?
11
39. A piece of blue yarn is 52
3 yards long. A piece of pink yarn is 5 times as long as
the blue yarn. Bailey tied them together with a knot that used 1
3 yard from each
piece of yarn. What is the total length of the yarn tied together?
40. A truck driver drove 352
10 miles before he stopped for breakfast. He then drove 5
times as far before he stopped for lunch. How far did he drive that day before his lunch break?
41. Jeff has ten packages that he wants to mail. Nine identical packages weigh 27
8
pounds each. A tenth package weighs two times as much as one of the other packages. How many pounds do all ten packages weigh?
G4, M6
42. Barrel A contains 2.7 liters of water. Barrel B contains 3.09 liters of water. Together, how much water do the two barrels contain?
12
43. A team of three ran a relay race. The final runner’s time was the fastest, measuring 2 .2 seconds. The middle runner’s time was 1.8 seconds slower than the final runner’s. The starting runner’s time was 0.9 seconds slower than the middle runner’s. What was the team’s total time for the race?
44. Vanessa has 6 dimes and 2 pennies. Joachim has 1 dollar, 3 dimes, and 5 pennies. Jimmy has 5 dollars and 7 pennies. They want to put their money together to buy a game that costs $8.00. Do they have enough money to buy the game? If not, how much more money do they need?
G4, M7
45. A girl’s height is feet. A giraffe’s height is times that of the girl. How many inches taller is the giraffe than the girl?
46. Twenty servings of pancakes require 15 ounces of pancake mix. a. How much pancake mix is needed for 120 servings? The mix is bought in pound bags. How many bags will be needed to make 120 servings?
13
G5, M4
47. Kim and Courtney share a 16-ounce box of cereal. By the end of the week, Kim
has eaten 3
8 of the box, and Courtney has eaten
1
4 of the box of cereal. What
fraction of the box is left?
48. Mathilde has 20 pints of green paint. She uses 2
5 of it to paint a landscape and
3
10
of it while painting a clover. She decides that for her next painting she will need 14 pints of green paint. How much more paint will she need to buy?
49. Mrs. Diaz makes 5 dozen cookies for her class. One-ninth of her 27 students are absent the day she brings the cookies. If she shares the cookies equally among the students who are present, how many cookies will each student get?
50. A baseball team played 32 games and lost 8. Katy was the catcher in 5
8 of the
winning games and 1
4 of the losing games. What fraction of the games did the
team win? In how many games did Katy play catcher?
51. Three-fifths of the students in a room are girls. One-third of the girls have blond hair. One-half of the boys have brown hair. What fraction of all the students are girls with blond hair? What fraction of all the students are boys without brown hair?
52. Cody and Sam mowed the yard on Saturday. Dad told Cody to mow 1
4 of the yard.
He told Sam to mow 1
3 of the remainder of the yard. Dad paid each of the boys an
equal amount. Sam said, “Dad, that’s not fair! I had to mow one-third and Cody only mowed one-fourth!” Explain to Sam the error in his thinking.Draw a picture to support your reasoning.
53. Joakim is icing 30 cupcakes. He spreads mint icing on 1
5 of the cupcakes and
chocolate on 1
2 of the remaining cupcakes. The rest will get vanilla icing. How
many cupcakes have vanilla icing?
54. Three-quarters of the boats in the marina are white, 4
7 of the remaining boats are
blue, and the rest are red. If there are 9 red boats, how many boats are in the marina?
Mat
hem
atic
s G
loss
ary
» T
able
1
PR
INT
TH
IS P
AG
E
Co
mm
on
ad
dit
ion
an
d s
ub
trac
tio
n.
RE
SULT
UN
KN
OW
NC
HA
NG
E U
NK
NO
WN
STA
RT
UN
KN
OW
N
AD
D T
O
Tw
o b
un
nie
s sa
t o
n t
he
gras
s. T
hre
e
mo
re b
un
nie
s h
opp
ed t
her
e. H
ow
man
y
bu
nn
ies
are
on
th
e gr
ass
no
w?
2 +
3 =
?
Tw
o b
un
nie
s w
ere
sitt
ing
on
th
e gr
ass.
Som
e m
ore
bu
nn
ies
ho
pped
th
ere.
Th
en t
her
e w
ere
five
bu
nn
ies.
Ho
w
man
y b
un
nie
s h
opp
ed o
ver
to t
he
firs
t
two
? 2
+ ?
= 5
Som
e b
un
nie
s w
ere
sitt
ing
on
th
e gr
ass.
Th
ree
mo
re b
un
nie
s h
opp
ed t
her
e.
Th
en t
her
e w
ere
five
bu
nn
ies.
Ho
w
man
y b
un
nie
s w
ere
on
th
e gr
ass
bef
ore
? ?
+ 3
=5
TA
KE
FR
OM
Fiv
e ap
ples
wer
e o
n t
he
tab
le. I
ate
tw
o
appl
es. H
ow
man
y ap
ples
are
on
th
e
tab
le n
ow
?5-2
= ?
Fiv
e ap
ples
wer
e o
n t
he
tab
le. I
ate
som
e ap
ples
. Th
en t
her
e w
ere
thre
e
appl
es. H
ow
man
y ap
ples
did
I ea
t?5
– ?
= 3
Som
e ap
ples
wer
e o
n t
he
tab
le. I
ate
two
app
les.
Th
en t
her
e w
ere
thre
e
appl
es. H
ow
man
y ap
ples
wer
e o
n t
he
tab
le b
efo
re??
-2 =
3
TO
TA
L U
NK
NO
WN
AD
DE
ND
UN
KN
OW
NB
OT
H A
DD
EN
DS
UN
KN
OW
N
PU
T T
OG
ET
HE
R /
TA
KE
AP
AR
T
Th
ree
red
app
les
and
tw
o g
reen
app
les
are
on
th
e ta
ble
. Ho
w m
any
appl
es a
re
on
th
e ta
ble
? 3
+ 2
= ?
Fiv
e ap
ples
are
on
th
e ta
ble
. Th
ree
are
red
an
d t
he
rest
are
gre
en. H
ow
man
y
appl
es a
re g
reen
? 3
+ ?
= 5
, 5-3
= ?
Gra
nd
ma
has
five
flo
wer
s. H
ow
man
y
can
sh
e pu
t in
th
e re
d v
ase
and
ho
w
man
y in
her
blu
e va
se?
5 =
0 +
5, 5
+ 0
5
= 1
+4
, 5 =
4 +
1 5
= 2
+ 3
, 5 =
3 +
2
CO
MP
AR
ED
IFF
ER
EN
CE
UK
NO
WN
BIG
GE
R U
NK
NO
WN
SMA
LLE
R U
NK
NO
WN
(“H
ow
man
y m
ore
?” v
ersi
on
):Lu
cy h
as
two
app
les.
Ju
lie h
as fi
ve a
pple
s. H
ow
man
y m
ore
app
les
do
es J
ulie
hav
e th
an
Lucy
?(“H
ow
man
y fe
wer
?”
vers
ion
): Lu
cy h
as t
wo
app
les.
Ju
lie h
as
five
app
les.
Ho
w m
any
few
er a
pple
s
do
es L
ucy
hav
e th
en J
ulie
? 2
+ ?
= 5
, 5 –
2 =
?
(Ver
sio
n w
ith
“mo
re”)
: Ju
lie h
as t
hre
e
mo
re a
pple
s th
an L
ucy
. Lu
cy h
as t
wo
appl
es. H
ow
man
y ap
ples
do
es J
ulie
hav
e?
(Ver
sio
n w
ith
“few
er”)
: Lu
cy h
as
3 fe
wer
app
les
than
Ju
lie. L
ucy
has
tw
o
appl
es. H
ow
man
y ap
ples
do
es
Julie
hav
e? 2
+ 3
= ?
, 3 +
2 =
?
(Ver
sio
n w
ith
“mo
re”)
:Ju
lie h
as t
hre
e
mo
re a
pple
s th
an L
ucy
. Ju
lie h
as fi
ve
appl
es. H
ow
man
y ap
ples
do
es L
ucy
hav
e?(V
ersi
on
wit
h “f
ewer
”): L
ucy
has
3
few
er a
pple
s th
an J
ulie
. Ju
lie h
as fi
ve
appl
es. H
ow
man
y ap
ples
do
es
Lucy
hav
e? 5
– 3
= ?
, ? +
3 =
5
1
2
3
1
Ad
apte
d fr
om
Bo
x 2
-4 o
f Mat
hem
atic
s Le
arn
ing
in E
arly
Ch
ildh
oo
d, N
atio
nal
Res
earc
h C
ou
nci
l (2
00
9, p
p. 3
2, 3
3).
Th
ese
take
apa
rt s
itu
atio
ns
can
be
use
d t
o s
ho
w a
ll th
e d
eco
mpo
siti
on
s o
f a g
iven
nu
mb
er. T
he
asso
ciat
ed e
qu
atio
ns,
wh
ich
hav
e th
e to
tal o
n t
he
left
of t
he
equ
al s
ign
, hel
p ch
ildre
n
un
der
stan
d t
hat
th
e =
sig
n d
oes
no
t al
way
s m
ean
, mak
es o
r re
sult
s in
bu
t al
way
s d
oes
mea
n is
th
e sa
me
nu
mb
er a
s.
Eit
her
ad
den
d c
an b
e u
nkn
ow
n, s
o t
her
e ar
e th
ree
vari
atio
ns
of t
hes
e pr
ob
lem
sit
uat
ion
s. B
oth
ad
den
ds
Un
kno
wn
is a
pro
du
ctiv
e ex
ten
sio
n o
f th
e b
asic
sit
uat
ion
, esp
ecia
lly fo
r sm
all
nu
mb
ers
less
th
an o
r eq
ual
to
10
.
Fo
r th
e B
igge
r U
nkn
ow
n o
r Sm
alle
r U
nkn
ow
n s
itu
atio
ns,
on
e ve
rsio
n d
irec
ts t
he
corr
ect
ope
rati
on
(th
e ve
rsio
n u
sin
g m
ore
for
the
big
ger
un
kno
wn
an
d u
sin
g le
ss fo
r th
e sm
alle
r
un
kno
wn
). T
he
oth
er v
ersi
on
s ar
e m
ore
dif
ficu
lt.
1
2
3
4
Mat
hem
atic
s G
loss
ary
» T
able
2
PR
INT
TH
IS P
AG
E
Co
mm
on
mu
ltip
licat
ion
an
d d
ivis
ion
sit
uat
ion
s.
UN
KN
OW
N P
RO
DU
CT
GR
OU
P S
IZE
UN
KN
OW
N (“
HO
W
MA
NY
IN E
AC
H G
RO
UP
?” D
IVIS
ION
)
NU
MB
ER
OF
GR
OU
PS
UN
KN
OW
N
(“H
OW
MA
NY
GR
OU
PS?
” D
IVIS
ION
)
3 x
6 =
?3
x ?
= 1
8, a
nd
18
+3
= ?
? x
6 =
18
, an
d 1
8 +
6 =
?
EQ
UA
L G
RO
UP
S
Th
ere
are
3 b
ags
wit
h 6
plu
ms
in e
ach
bag
. Ho
w m
any
plu
ms
are
ther
e in
all?
Mea
sure
men
t exa
mpl
e. Y
ou
nee
d 3
len
gth
s o
f str
ing,
eac
h 6
inch
es lo
ng.
Ho
w m
uch
str
ing
will
yo
u n
eed
alto
geth
er?
If 1
8 p
lum
s ar
e sh
ared
eq
ual
ly in
to 3
bag
s, t
hen
ho
w m
any
plu
ms
will
be
in
each
bag
? M
easu
rem
ent e
xam
ple.
Yo
u
hav
e 1
8 in
ches
of s
trin
g, w
hic
h y
ou
will
cut
into
3 e
qu
al p
iece
s. H
ow
lon
g w
ill
each
pie
ce o
f str
ing
be?
If 1
8 p
lum
s ar
e to
be
pack
ed 6
to
a b
ag,
then
ho
w m
any
bag
s ar
e n
eed
ed?
Mea
sure
men
t exa
mpl
e. Y
ou
hav
e 1
8
inch
es o
f str
ing,
wh
ich
yo
u w
ill c
ut
into
piec
es t
hat
are
6 in
ches
lon
g. H
ow
man
y pi
eces
of s
trin
g w
ill y
ou
hav
e?
AR
RA
YS
, AR
EA
Th
ere
are
3 r
ow
s o
f app
les
wit
h 6
appl
es in
eac
h r
ow
. Ho
w m
any
appl
es
are
ther
e? A
rea
exam
ple.
Wh
at is
th
e
area
of a
3 c
m b
y 6
cm
rec
tan
gle?
If 1
8 a
pple
s ar
e ar
ran
ged
into
3 e
qu
al
row
s, h
ow
man
y ap
ples
will
be
in e
ach
row
? A
rea
exam
ple.
A r
ecta
ngl
e h
as
area
18
sq
uar
e ce
nti
met
ers.
If o
ne
sid
e
is 3
cm
lon
g, h
ow
lon
g is
a s
ide
nex
t to
it?
If 1
8 a
pple
s ar
e ar
ran
ged
into
eq
ual
row
s o
f 6 a
pple
s, h
ow
man
y ro
ws
will
ther
e b
e? A
rea
exam
ple.
A r
ecta
ngl
e
has
are
a 1
8 s
qu
are
cen
tim
eter
s. If
on
e
sid
e is
6 c
m lo
ng,
ho
w lo
ng
is a
sid
e n
ext
to it
?
CO
MP
AR
E
A b
lue
hat
co
sts
$6
. A r
ed h
at c
ost
s 3
tim
es a
s m
uch
as
the
blu
e h
at. H
ow
mu
ch d
oes
th
e re
d h
at c
ost
?
Mea
sure
men
t exa
mpl
e. A
ru
bb
er b
and
is 6
cm
lon
g. H
ow
lon
g w
ill t
he
rub
ber
ban
d b
e w
hen
it is
str
etch
ed t
o b
e 3
tim
es a
s lo
ng?
A r
ed h
at c
ost
s $
18
an
d t
hat
is 3
tim
es
as m
uch
as
a b
lue
hat
co
sts.
Ho
w m
uch
do
es a
blu
e h
at c
ost
? M
easu
rem
ent
exam
ple.
A r
ub
ber
ban
d is
str
etch
ed t
o
be
18
cm
lon
g an
d t
hat
is 3
tim
es a
s
lon
g as
it w
as a
t fi
rst.
Ho
w lo
ng
was
th
e
rub
ber
ban
d a
t fi
rst?
A r
ed h
at c
ost
s $
18
an
d a
blu
e h
at c
ost
s
$6
. Ho
w m
any
tim
es a
s m
uch
do
es t
he
red
hat
co
st a
s th
e b
lue
hat
?
Mea
sure
men
t exa
mpl
e. A
ru
bb
er b
and
was
6 c
m lo
ng
at fi
rst.
No
w it
is
stre
tch
ed t
o b
e 1
8 c
m lo
ng.
Ho
w m
any
tim
es a
s lo
ng
is t
he
rub
ber
ban
d n
ow
as
it w
as a
t fi
rst?
GE
NE
RA
La
x b
= ?
a x
? =
p a
nd
p +
a =
??
x b
= p
, an
d p
+ b
= ?
1
23
1
Th
e la
ngu
age
in t
he
arra
y ex
ampl
es s
ho
ws
the
easi
est
form
of a
rray
pro
ble
ms.
A h
ard
er fo
rm is
to
use
th
e te
rms
row
s an
d c
olu
mn
s: T
he
appl
es in
th
e gr
oce
ry w
ind
ow
are
in 3
ro
ws
and
6
colu
mn
s. H
ow
man
y ap
ples
are
in t
her
e? B
oth
form
s ar
e va
luab
le.
Are
a in
volv
es a
rray
s o
f sq
uar
es t
hat
hav
e b
een
pu
shed
to
geth
er s
o t
hat
th
ere
are
no
gap
s o
r o
verl
aps,
so
arr
ay p
rob
lem
s in
clu
de
thes
e es
peci
ally
impo
rtan
t m
easu
rem
ent
situ
atio
ns.
Th
e fi
rst
exam
ples
in e
ach
cel
l are
exa
mpl
es o
f dis
cret
e th
ings
. Th
ese
are
easi
er fo
r st
ud
ents
an
d s
ho
uld
be
give
n b
efo
re t
he
mea
sure
men
t ex
ampl
es.
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