### Grade 4 Unit 7 - Rockwood Staff Websites

```Date Time
Divide each shape into equal parts. Color a
fraction of the parts. Write the name of the
"whole" in the "whole" box.
Whole
hex.agon
Divide the hexagon into 2 equal parts. .
Color ~ of the hexagon.
2. Whole
-,
rhombus i
"!"'~'7~':"';'>_I'_"~~rp"'1'!/~(~f:?JttfIY-
Divide the rhombus into 2 equal parts.
Color ~ of the rhombus.
3. Whole
trapezoid
i
r
I
';'~''''''''Y'''''''''4"W~F';'~)",';_'''~:t'~~-
Divide the trapezoid into 3 equal parts.
Color ~ of the trapezoid.
Divide the hexagon into 3 equal parts.
Color of the hexagon.
t
185
Date
Time
.­
_
5.
Fraction Review
continued
Whole
hexagon
Divide the hexagon into 6 equal parts.
Color ~ of the hexagon.
6.
Whole
hexagon
Divide each hexagon into thirds.
Color 1 hexagons.
i
7.
Whole
rhombus
Divide each rhombus into 2 equal parts.
Color
rhombuses.
2t
Grace was asked to color ~ of a hexagon. is what she did. What is wrong? m Ie answer: She did
not divide the hexagon
into . .~ equal part~_._ _
186 •
Date
Time
• . Fraction Review
continued
~
Fill in the missing fractions and mixed numbers on the number lines.
9. ~4~1----------+----------+1----------+1----------+1~.
0I2 3
4
'f
1
4
10. ~4~1------------~1--------------+1--------------+1~.
o
11.
4
1
2
3
3
1
I
I
I
I
I
I
o
1
2
3
5
1
6
6
6
6
III'
12. ~4~1----~1-----+1----~1-----+1----~1-----+1----~1-----+1~.
1
o
13.
14.
4
4
2
3
4
5
6
7
888
8
888
1
I
I
I
I
o
1
2
2~
3
/~
/
I
I
I
I
I
o
1
2
5
3
5
4
5
5
2
I
/
III'
2
I
I
I
1~ 1~ 1~ 1~
555
I
III'
2
5
Try This
15. Enter the fractions above on your calculator. Record the keystrokes you used to enter
j
and 1 ~.
Sample answer: On my TI-15, I pressed 2 ( n J 4 ( d J for ~.
To enter 1i, I pressed 1wn:ID 1 QJJ 5GLJ. On my Casio fx-55 ,
I pressed 2 (hie] 4 for ~ and 10 1lEJ 5 for 11.
187
Time
Date 1. What fraction of the clock face is shaded?
or ~
12
1
4'
2. LPOL is an
0
tuse
(acute or
obtuse) angle.
o
L
The measure of LPOL is
145
3. Multiply. Use a paper-and-pencil algorithm.
~196
=94*34
°
4. The five largest birds that are able to fly
have the following weights: 16.3, 16.8,
20.9, 15.8, and 15.8 kilograms.
a. What is the median weight?
b. What is the mode?
c. What is the range?
d. What is the mean?
5. a. What city in Region 1 is located near
0
30 N latitude and 31°E longitude?
Egypt
kg
kg
kg
side of the rectangle.
2.
_ _ In.
1.
1 .
_ _ In.
_ _ In.
2·
c. On which continent is the city located?
Africa
15.8
5.1
17.12
6. a. Measure and record the length of each
Cairo
b. In which country is the city located?
16.3 kg
_ _ In.
b. What is the total distance around
the rectangle called? Circle one. ~
~ime~
188
area
.
~
Date 1. Time
"-l
Whole
/6 nickels (
'~':l-',,-' T_""¥J'_'''I1'~~''i'':'':::)'
'"
a. Circle~ of the nickels.
b. How much money is that?
0 . 60
\$
2. Whole
12 dimes
a. Fill in the "whole" box.
b. Circle
~ of the dimes.
How much money is that?
1 . 00
\$
3. Whole
!
10 quarte~s
"'~'>')'-",0' ,:;I;
"~~""
.s,
a. Fill in the "whole" box.
b. Circle~ of the quarters.
;ow 1UCh
mongo
that?
189
8
c. 3" of 12
3
=
9
c.
3
=
27
c. :}of 36
54
=
20
c. iof32
= ~36
t of 24 =
16
c.
3
b. 5" of 15
9
b. 4" of 36
4
b.
i
4
b. 7
10. of 22
=
11
11. What is
t of 25? 121.
%
=
b. 3" of 12
=
2
9. 4" of 14
2
4
of 32
5
i
of 15
3
16
=
20
=
21
of 24
=
52
Explain.
Sample answer: ~ of 25 is the same as dividing
25 by 2, which~_1_2-=-~._ _ _ _ _ _ _ _
12. Michael had 20 baseball cards. He gave
and
i to his brother Dean.
i- of them to his friend Alana,
a. How many baseball cards did he give to Alana? __
~_4_ _ cards
__8__ cards
b. How many did he give to Dean?
8
c. How many did he keep for himself?
Try This
13. Maurice spent
t of his money on lunch. He has \$2.50 left.
\$5.00
14. Erika spent! of. her money on lunch. She has \$2.00 left.
190 \$8. 00
cards
Time
Date 1. What fraction of the clock face is shaded?
2. Draw angle
ABC that measures 6So.
Fill in the circle next to the best answer.
®
t
•
1~
@
t
f
B
LABC is an
C
_a_c_u_t_e_ (acute or obtuse) angle. 3. Mary has 27 pictures. She gives
t of them
4. Divide. Use a paper-and-pencil algorithm.
to her sister Barb and! to her cousin Sara.
962/12
a. How many pictures does Barb get?
=
2
80 R2, or 80 12
__9_ _ pictures
b. How many pictures does Sara get?
_1_8_ pictures
c. How many pictures does Mary keep?
o
____ pictures
~
~
~------------------------------~
5. There are 29 students in Ms. Wright's class.
Each collected SO bottle caps. How many
bottle caps did the students collect in all?
1 450
6. Find the area of the figure.
D=
1 square centimeter
v
bottle caps
Area
'"/1
,
_7_.5__ square cm
191
Time
Date A deck of regular playing cards is placed in a bag. You shake the bag and,
without looking, pick one card.
1. How many possible outcomes are there?
52
(Hint: How many cards are in the bag?) _..
possible outcomes
2. Are the outcomes equally likely?
yes
(Hint: Does each card have an equal chance of being chosen?)
3. Find the probability of each event. Probability of an event =
!
I
Favorable
Outcomes
Event
i
26
Pick a red card Pick a club
Pick a non-face card
I
i
num~er Off favor~~le o~tcomes
num er 0 POSS! e ou comes
Possible
Outcomes
Probability
em
52
52
I
13
52
40
52
[3]
52
40
52
I
3
Pick a diamond face card
52
52
I
Pick a card that is not a
diamond face card
49 52
I
i
i
Pick the ace of clubs
1
52
1
52
52
52
52
52
I
Pick a red
or a black card I
1
I
I
Pick the 23 of hearts
I
I
49
52
0
0
52
52
i
e the word or phrase that best describes the probability of picking a 5
a bag of 52 regular playing cards without looking.
impossible
@
unli~
even chance
likely
choosing a 5 card is only 4 out of 52.
192
i
I
.
Time
Date 1. What fraction of the clock face is shaded?
1
3,
4
acu e
2. LMRS is an
(acute or
obtuse) angle.
or 12
S
The measure of LMRS is
35
3. Multiply. Use a paper-and-pencil algorithm.
8,987
= 19
* 473
°
4. Cleo's friends ran the 50-yard dash in the
following times:
7.9,12.1,8.5,11.7,8.3,11.7,
and 9.8 seconds.
What is the mean time? Fill in the circle
(IS) 11.7 seconds
®
9.8 seconds
•
10 seconds
@ 12.1 seconds
5. a. What city in Region 2 is located near
0
0
60 N latitude and 10 E longitude?
Oslo
6. Measure the length and width of your
journal to the nearest half-inch. Find its
perimeter.
a. Length
11
=
b. In which country is the city located?
Norway
b. Width
8
=
c. Perimeter
=
inches
inches
39
inches
c. On wl"lich continent is the city located?
Europe
193
Time
Date Use Math Masters, page 212. For Problems 1-6, Shape A is the whole.
1. Cover Shape A with trapezoid
blocks. What fraction of the
shape is covered by 1 trapezoid?
2. Cover Shape A with rhombuses.
1
3. Cover Shape A with triangles.
What fraction of the shape
is covered by
What fraction of the shape
is covered by
1 rhombus?
1 triangle?
1
3
2 rhombuses? 2
3
1
3
6,
3 triangles?
6
1
or "2
5
6
5 triangles?
4. Cover Shape A with 1 trapezoid and
3 triangles. With a straightedge, draw
how your shapes look on the hexagon
at the right. Label each part with a
fraction.
5. Cover Shape A with 2 rhombuses
and 2 triangles. Draw the result on
the hexagon below. Label each part
with a fraction.
6. Cover Shape A with 1 trapezoid,
1 rhombus, and 1 triangle. Draw the
result on the hexagon below. Label
each part with a fraction.
1
1
3
1
3
194
2
1
3
Time
Date Use Math Masters, page 212. For Problems 7-12, Shape B is the whole.
Whole
I:
Shape B:
.•
.#~9YE>le,~.~~a,QP~)
7. Cover Shape B with trapezoids.
What fraction of the shape is covered by
1
1 trapezoid? _--,-4__
or 21
2 trapezoids? -=.4_,_ _
2
=
3 trapezoids?
3
_----:..4__
8. Cover Shape B with rhombuses. What fraction of the shape is covered by
1
1 rhombus?
6
3 rhombuses?
orl
3
6,
2
5
5 rhombuses?
6"
9. Cover Shape B with triangles. What fraction of the shape is covered by
1 triangle?
_1 12
2 triangles?
.£. or 1
12 ,
6
3 triangles?
1
3
or
4
_1__2_'__
10. Cover Shape B with hexagons. What fraction of the shape is covered by
1 hexagon?
1
__
2__
1_ _
2 hexagons? __
11. Cover Shape B completely
with 1 hexagon, 1 rhombus,
1 triangle, and 1 trapezoid.
Draw the result on the figure
at the right. Label each part
with a fraction.
12. Cover Shape B completely
with 1 trapezoid, 2 rhombuses,
and 5 triangles. Draw the
result on the 'figure at the right.
Label each part with a fraction.
1
4
195
Time
Date Use Math Masters, page 212. For Problems 13-16, Shape C is the whole.
t Try This 1
Whole
~~,:;-'?'y~;,:'!!,:..t':,,~-""'1
13. Cover Shape C with trapezoids.
What fraction of the shape is covered by
1
1 trapezoid?
2
_---"'S=---_
2 trapezoids?
1
8', 0 r 4'
6
6 trapezoids?
3
8' ,or 4'
14. Cover Shape C with rhombuses. What fraction of the shape is covered by
1 rhombus?
1
12
3 rhombuses?
3
12
or
1
4'
6 rhombuses?
6 or 21
-,-1..; ; ; ;.2_'_---.;-'­
15. Cover Shape C with triangles. What fraction of the shape is covered by
_1 1 triangle?
24
3 triangles?
~
24,
or 1
S
12 triangles?
12
1
24, 0 r '2
16. Cover Shape C completely, using one or more trapezoids, rhombuses, triangles, and
hexagons. Draw the result on the big hexagon below. Label each part with a fraction.
1
8
1
8
•
1
12
196
1
4
Date
Time
1. What fraction of the clock face is shaded?
2
3",
or
LMN that measures 120°.
2. Draw angle
8
12
M
N
obtuse
LLMN is an
(acute or obtuse) angle.
3. a. In December,
*
of a foot of snow fell
on Wintersville. How many inches of
snow fell?
4. Divide. Use a paper-and-pencil algorithm.
· 3
809/13
_62 R3, or 62"13
__9__ inches
b. Tina's daughter will be
~ of a year old
next week. How many months old will
she be?
_1_0_ months
5. Each student eats an average of
17 servings of junk food per week. About
how many servings of junk food would a
class of 32 students eat in a week?
6. Find the area of the figure.
D=
1 square centimeter
I
_5_4_4_ servings
i
L
VI
Area
.'"
I
i
= __7_"_5__ square cm
197
Date Time
Use pattern blocks to find fractions that add up to 1 whole.
lines to show the blocks you used. Write a number
to show that the sum of your fractions is 1.
Whole
hexagon
3 + 1
6
2
--
1.2 + 1.2 = 1 2. Use pattern blocks to find fractions that add up to ~. Draw lines to show the blocks
you used. Write a number model to show that the sum of your fractions is ~.
Solve. You may use pattern blocks or any other method. 1
3
2
3. 6-6
5. ~ - t:
198 - -6
i, or ~
4.
i
5
6. 6
~
=
1
-"2
1
_---..::2=--_
~, or i
1
Date
Time
.[F!,~~!~!,Cllld Mixed-Number Sums &
7. Use pattern blocks to find three different pairs of mixed numbers
2l
mixed numbers. Write a number model to show that the sum of each pair of mixed numbers is
2l
Differences
Whole
hexagon
a.
1
1
24
13
+_13
6
Number model: _ _
--=-_
---=_ _ _--=-_
b.
1
16 + 13 =
\ 7
246
6 _ _-=--_
l\lumber model: _ _--=­_ _--'=_
c.
0 0
Number model:
7
r------7,\
1
24
- _----'''---_
221
6
6
_ _---"'-'---_-"'-_
+
Solve. You may use pattern blocks or any other method.
9.
10.
1i - t =
5
6=--_
_--.e
11.
1~ -1t =
1
_--,3=-_
~ ~ = _~=-'--,_o_r--=~::.-
1 _
198A Time
Date 1. Rithik ate
~ of a cheese pizza. He then ate ~ of a veggie pizza.
4 f'
a. What fraction of a pizza
~d he eai in all?
.
loa pizza, ors3 0f a.Plzza
+ · = 6
2
amp le num ber
models are given.
6
Number model: _ _----==~_---=-.
6 _ _= _ __ _
b. Did he eat more or less than a whole pizza? _
less
How do you know?
Sample answer: ~ would be 1 whole pizza, and
2. Karina walked
t < ~.
t of a mile to school. After school, she walked
t of a mile to the store, and then t of a mile back3to her home.
mile
4 _ _ _ _ __
a. How far did she walk after school? _ _~--=-
213
Number model:
'4
b. How far did she walk in all?
Number model:
+ '4 = '4 ~ mile, or 1 mile
121
4
_ _4L--+~--,4--,+,---4-,----__4,---_
3. Stephana is making pancakes and waffles for his guests.
a. He needs ~ cup of milk for the pancakes and ~ cup of
4,
3
milk for the waffles. How much milk does he need in all? _ __
0r
1-31 CU pS
224
'3
Number model:
+ '3 =..
""'3_ __
b. Stephana has 1 ~ cups of milk. Will he have
any left over? If so, how much milk will be left?
Number model:
132
-
Yes.
i cup
113 ---=3=--_
1
Try This
4. Kumba has one dollar. He spent
t of the dollar on a pencil and 1~ of the dollar on an eraser.
7
a. What fraction of the dollar did he spend?
1
Number model: _ _.. . . 2
2
+ TO =
10__ b. What fraction of the dollar does he have left?
Number model:
1988
1- ~
=
TO
7
3
______
1_0_____
3
1.0_
.. _
Time
Date 1. Circle
~ of all the triangles. Mark Xs on ~
2. Insert parentheses to make these
number sentences true.
of all the triangles.
a. 8.2 -(5.2 + 2.5) = 0.5
b.
13.6-~+8)=0.6
c. 9.1 =(28.4 - 1.1) -:- 3
d. 9
*(2.5 + 3.5)= 54
4. Draw and label a
3. Plot and label each point on the
45° angle.
coordinate grid.
A (5,0)
5 1--+--+--+=-+----+-
8
C
E
3 t-=-+--+--+--+--+---
B (3,5)
4
c
(1,4)
2 I--+---t--+--+--+---
o (1,1)
1 I----t>-=O:+-+-+-A-=--l0
0
1
2
3
4
5
5. A bag contains
red blocks, blue blocks, green blocks, and orange blocks. You put your hand in the bag and, without
looking, pull out a block. About what fraction of the time would you expect to get a blue block?
4
2(5,
R
This angle is an
acute
Y
(acute or obtuse) angle.
E (2,4)
6
4
7
3
T
Sample
1
or 5"
6. If 1 centimeter on a map represents
10 kilometers, then
b.
6_0__ km.
19.5 cm represent _1_9_5
__ km.
c.
__3__ cm represent 30 km.
d.
__5_"_5__ cm represent 55 km.
a. 6 cm represent __
e. 0.5
cm represent 5 km.~
~
199
Date Time
1. Which fraction is another name for
~?
Fill in the circle next to the best answer.
t
• !
®
2. A bag contains
2 blue blocks,
3 red blocks,
5 green blocks, and
10 black blocks .
You put your hand in the bag and, without
looking, pull out a block. About what
fraction of the time would you expect to
get a black block?
@ ~
~
10
20, or
1
2
~
~------------~~--------------~
these problems.
a. LTAPis an
0
use
(acute or
obtuse) angle.
4 or 23
t + ~ = _6=----,_
_-=­
5
b. t + 1= _----.;6=---_ 1
1
§-
i = ~, 0 r !
c. "3 - "3 =
d. 3
-----==--­
2
~
~
5. Next month 486 students, teachers, and
parents are going on a field trip to the
zoo. Each bus holds 35 people. How
many buses are needed for the trip?
14
buses
p
A
The measure of LTAP is
135
0
6. Tell if each of these is closest to 1 inch,
1 foot, or 1 yard.
a. the length of your smile
b. the length
1f
c. the distance from
1 inch
t
00 1
d
YCJ._r_ _
1 inch
d. the width of your wrist --~--
~
200
Date Time
1.
i +i
=
7.
9.
4.
1t+t= 1t or 2 11
2TO
1
1
10
1
TO,
or
11"0 + 1"0 =
6.
1
~ ~ = _--,9~,=---o_r------,,3,"---_
4
6
2
11. "8 - "8 =
13. 1 ~
10.
1
8, or 2
--=------=---
12.
1~ 4
t + - __----"5=---_ _
5
2
3
3
12
112 + 212 = ----=-==--­
61
4~,
or
+ 1"21 = - =----=­
1
2 1
3
"3 - "3 = - - - ' ' ' " - - - ­
t -t =
1
_ _ _-=-7_ __
1- 41 = - - - - -11
=---­
16. 4~ - 2% = ___1~
~ = _ _ _--=--_ _
is. 10% -
---=-----­
4
8. 3"2
--'---=-----"-=-
3
~, or 1
4 2
2. "6 + "6 =
~, or 1~ 3• ~
2 +.1
2
5.
2
_ _---"3""--_ _
14. 5
4
6~ = _ _ _ _ __
--=-_ __
17. Ryan and Reggie baked an apple pie that was cut into 12 equal pieces, Ryan had
5
?2 of the pie, and Reggie ate 12'
Who ate more?
Reggie
8
What fraction of the pie did the boys eat all together?
-12, or
_--::...;;;;;:=---_--=-_
18. Alice and Cherice run at the same park. On Saturday, Alice ran
ran
t of a mile.
~ of a mile, and Cherice
A_Ii_c_e_-------.
Who ran the shorter distance? _ _
How far did Alice and Cherice run all together?
_O_,_o_r_1_1_ miles
_18
200A Time
2
5
3 2
4
8
2. a-8+a=---­
4
2
5
3
4
7 6 , or 73
4. 76 + 16 - 16 = ---:8-'---­
1
1• 14 + ~4 _14 = 4' or 2
3.
5.
1~ -
122 -
1~
=
1
12 2
1
4~-~ + 11 = 54' or 52
4
4
~ ~_
7. 2+2
4
9. (29
6.
1
2' or 12
43
1 _
2-----
2
+ 9)
-
1
(9
+ 193 ) =
8.
2
19 ----
3
s 1
428
11. (a-a)
(a-a)
=- - -
10.
± + ~ + 3~ = 38 , 0 r 4
8 8 8
4
1
2
4
1
(a3 a)
+ (a-a)
=-8'-or
-­2 10
5
11 _1 _ ~ _ 1 _ 5 12 , or 56
(1012 + 12) (5 12 12 - - - - ­
5
3
12. (5
1
2
1
-,
or 1
+ 5) + (5 - 5) = ~. .- --­
13. Paulo, Regina, and Ted picked a bucket of apples on the
ls
of the apples,
field trip to the apple orchard. Paulo took
Regina took 1~ of the apples, and Ted took 1~ of the apples.
They decided to give the rest of the apples to the teacher.
Who took the most apples?
Regina
What fraction of the apples did their teacher get?
How do you know?
Sample answer: I added fs + ~ + ~ and I got i¥. Since I
know that the total number of apples was
I subtracted i¥
from that and I got fs. That's how many the teacher gets.
..
14. Julie was making a quilt. She had
.
....
~ yard of fabric.
She bought another ~ yard of fabric. She gave: yard
of the fabric to her friend.
How many yards of fabric does she have left?
2008
*,
8
8 ' or 1 yard
_=--____
..
Time
Date
Color the squares and write the missing numerators.
1of each large square.
1. Color
IJl
_L2.J_ is colored. 1
square
1
2
1
is colored. 4
2
2. Color
Whole
t of each large square.
1
1 is
colored. 4
f21.
~ colored.
_ _ IS
8
f4l.
L::!J
__ IS colored.
16 3. Color! of each large square.
~
is colored.
4
[ [ ] is colored.
8
1121 is colored.
16 201
Time
Date 1. Circle
-i of all the squares. Mark Xs on i
of all the squares ..
2. Insert parentheses to make these
number sentences true.
DDDDD~
~DODD~
DDDDD~
a. 2 *(3
+ 10)= 26
b. 12 =
6*(6 - 4)
c. (24 - 5)* 2
d. 12
+ 24 = 3*(6 + 6)
4. Draw and label a
3. Plot and label each point on the
38
1250 angle.
coordinate grid.
A (0,2)
B (4,0)
5
D (5,5)
T
4 1--1---1---f----1f-:=E=+-
3
C (1,5)
~--=C=-'I---'f----1r=D4-
A
2.---1----'---I---+--t-
1
0
o
f--+--+-+---l--=B::+0 1
E (5,3)
2
3
4
p
5
~
This angle is an
obtuse !:Ftl
~________________________~~_-~l«~-~Ir-~(a~c~u~te~or~o~b~tu=s~e~)~an~g~le~.______~~14~J~
5. A bag contains
5
6
1
3
green blocks,
red blocks,
blue block, and yellow blocks. You put your hand in the bag and, without looking, pull out a block. About what
fraction of the time would you expect to get a blue block? 1
15
202
6. If 1 inch on a map represents 40 miles,
then how many inches represent
10 miles? Fill in the circle next to the
®
2in. •
l'
'4
tin.
@ 4in.
Date
Time
,
Whole
f
large square)
~~~",,~Yt~~r::,~t?'~
,
,,
,,
,,
,,
,
,
,,,
,
,,
,,
,,
,,,
,,,
,,
,,,
,,
,,
,,,
,,
,,,
,,
:,
:,
,,
,,
,,
:,
,
,,,
,
,
,,
,,
,, ,, ,, , ,,
,, , , , ,,
,,
,, ,, ,,
,
:, ,, ,,, ,,,
,, ,, ,, ,,, ,,
, , :
,,, ,,, ,,, , ,,,
:
,,, ,, , : ,,,
:
,,
:, ,,
,, : :,, ,,, ,,
:, , ,
, , , :
,,
,,
:,
,,
,,,
lo of the square is shaded.
2
How many tenths?
,,
,,
,,,
,,,
2
10
1
10' or 0.1
2
o.--=-­
~oT5nJ tenths? 5
2-
3
5. "5
10
10
8
[[]
"5
10
1
100' or
10
How many tenths?
1
0.--­
[]]=0._6_
6. 4
"5
5
2
2
0.--""'-'---­
0.01
How many tenths?
2
"5
@]
4
4
o.---=-­
10
1
"4
[25]
100
25
0.---­
3
"4
[Z§J
75
0.--­
100
203
Time
Date 1. Complete the name-collection box.
2. A bag contains
4
"'---_ _ _5_ _____:
8 blue blocks,
2 red blocks,
1 green block, and
4 orange blocks.
Sample
3 + .1
55,
0.8
You put your hand in the bag and, without
looking, pull out a block. About what
fraction of the time would you expect to
get a red block?
8
10
9
1
1(5-1(5 2
15
these problems.
2
b.
c.
%-
d. 1
6
64 - 2"
= -----'''---­
i=
LARTis an
6,
4
6,
acute
(acute or
obtuse) angle.
6
3
t t=
~ +i =
a. 4.
A
i, or 1 or~
R
1
~
T
-
The measure of LART is 40° ~
r-------------------------------~
5. There are 252 pages in the book Ming is
reading for his book report. He has two
_.18
204
pages
6. Tell if each of these is closest to 1 inch,
1 foot, or 1 yard. 1 yard
b. the width of your journal
1 foot
c. the length of
l' h
Inc
d. the length of your shoe
1 foot
a. the height of the door
Time
Date Math Message: Eating Fractions
Quinn, Nancy, Diego, Paula, and Kiana were given 4 chocolate bars to share.
All 4 bars were the same size.
1. Quinn and Nancy shared a chocolate bar. Quinn ate
Nancy
Who ate more?
t of the bar, and Nancy ate f.
1
How much of the bar was left? _ _ _4-=--_ _
2. Diego, Paula, and Kiana each ate part of the other chocolate bars. Diego ate ~ of
a bar, Paula ate
t of a bar, and Kiana ate i of a bar.
Diego
How do you know? Sample answer: Diego ate ~, which is
more than ~. Paula ate ~ which is less than 1.
Who ate more, Diego or Paula?
Comparing Fractions with ~
Turn your Fraction Cards fraction-side up. Sort them into three piles:
t
fractions equal to t
• fractions less than
•
• fractions greater than
You can turn the cards over to check your work. When you are finished,
write the fractions in each pile in the correct box below.
Less than ~
Equal to
1
1
0
1 2
2
2
3
0
3, 4, 5, 5, 5,
4
3
234
2, 4, 6, 8,
5 6
10,12
6, 8, 9, 10,
2
1
4
10,10,12,12
!
Greater than
!
2 3 345
3, 4, 5, 5, 5,
4 6 6 6
6, 8, 9, 10,
8 10 8
9
10,10,12,12
205
Date
Time
Write the fractions in order from smallest to largest.
1.
4
7
8
2
1
TO, TO, TO, TO, TO
1
10
4
2
10
10
7
10
1
.1
2'
1
1
100
9' 5'
1
100
1
9
1
5
1
4"
2
2
2
2
100
2' 9' 5'
2
2
100
9
2
5
2
4
smallest
4
4. 25'
1
25'
1
25
1
2
largest
smallest
2
3. 4'
10 largest
smallest
1
2. 4'
8
2
2
largest
7
6
7
8' 12' 15
4
25
7
15
6
12
7
8
largest
smallest
5. Choose 5 fractions or mixed numbers. Write them in order from smallest to largest.
smallest
largest
Which fraction is larger: ~ or ~?
2
5"
Explain how you know.
ample answer: ~ has a smaller denominator
than ~, so each fifth is bigger than each
seventh.
--------------~~------------------------------
206
Date
Time
t of the day at school. Lunch,
recess, music, gym, and art make up t of
1. Sari spends
2. Multiply. Use a paper-and-pencil algorithm.
5,152
her total time at school. How many hours
are spent at these activities? 2
= 92 * 56 hours Show how you solved this problem. Sample answer:
8 hr;
1
4
of 8 hr
1of 24 hr =
= 2 hr
3. Adena drew a line segment
t
t inch long.
Then she erased inch. How long is the
line segment now? Fill in the circle next to the best answer.
®
®
•
~
l!l
4. Write an equivalent fraction, decimal, or
whole number. Decimal
4'In.
'6
a. 0.40
2'
2 m. b.
1 .
4 m.
c.
~
55-5:
.
@ 1141n.
5. Complete the table and write the rule.
Rule:
+ 5.73
in
out
6.19
11.92
12.03
17.76
3.26
0.01
8.99
4.41
10.14
40
JOO
0.3
1.0
d.0.6
100
100
~
6. Complete.
=
b. 43 in.
c. 6 ft
=
d. 11 ft =
e. 73yd
a
...a.
10 6
jQ
a. 17 in.
5.74
Fraction
=
1 ft 5
3 ft 7
2 yd
3 yd 2
219 ft
in.
in.
ft
~
129'
207
Date
•
Time
What Is the ONE?
Math Message
1. If the triangle below is
.
~, then what is the whole-the ONE? Draw it on the grid .
.
.
2. If
~ of Mrs. Chin's class is 8 students, then
how many students does she have altogether?
32
"
students
3. If
6. If
<> iS~,
D.:J iS~,
then what is the ONE?
then what is the ONE?
I
208
4. If a s
~,
then what is the ONE?
is 2 then what is the ONE?
Date Time
1111
What is the ONE?
continued
Solve. If you wish, draw pictures at the bottom of the page to help you
solve the problems.
00
0 0 0
00
15
counters
16
counters
~, then what is the ONE?
25
counters
10. If 12 counters are ;, then what is the ONE?
16
counters
7. If
8. If 0 0
iS~, then what is the ONE?
iS~, then what is the ONE?
9. If 10 counters are
11. If ~ of the cookies that Mrs. Jackson baked is 12,
then how many cookies did she bake in all?
12. In Mr. Mendez's class,
60
! of the students take music
lessons. That is, 15 students take music lessons.
How many students are in Mr. Mendez's class?
20
students
13. Explain how you solved Problem 12.
Sample answer: I divided 15 by 3, which told me
that each fractional pa.rt is equal to 5 students.
So, the whole is 4 * 5, which is 20 students.
is an equivalent fraction to ~.
19
209
Time
Date
f
,J
~_"
":..,..r~/{
Veronica collected 15 insects for a science project. She measured the length of each
insect to the nearest ~ inch. Her measurements are shown in the table below.
Length
(to the nearest
inch)
Insect
I
Insed
t
,
1.12
Darner dragonfly
Red
3
Length
(to
nearest
inch)
t
.I.
"<;;J<;;J
Boreal fi refly
8"
Yellow bumblebee
"4
Damselfly
1.1
4
Paper wasp
1~
American cockroach
3
i
7
8"
i
Ground beetle
8"
7
Field cricket
8"
7
Green lacewing
1
Indian meal moth
8"
8"
5
Katydid
1~
4
3
1~
4
Carolina mantid
" ~4J:lj£"'i}t+1':WWMi,iiYi'"",
Plot the insect lengths on the line plot below. Then use the completed plot to answer
the questions on the next page.
Insect Lengths
I
I
en
.....
I
I
0
i
Q)
en
c:
I
0
'­
Q)
I
X
Xi XI
X XIX X X X
..0
E
X
.. XI
::::l
z
I
3
I
1
8
2
I
5
8
I
3
4
I
7
8
1
1
I
18 1"4
Length (inches)
209A 1
X
X
.X
X
:
I
1~
8
I
13
4
...
Date Time
Use the line plot on journal page 209A to answer the questions. Write a number model
Sample number models are
to summarize each problem.
1. a. What is the maximum insect length?
13
4"
b. What is the range of the data set?
7
2. a. What is the median of the data set?
in.
'8
4 -
Number model:
in.
4
3
"8 - '8
Number model:
1
7
_--=8__
7
4" - '8
1
or '2 in.
in.
b. How much longer is the maximum length than the mode length?
13
­
138
= '2 3. a. What is the mode of the data set?
Number model:
"8,
given.
in.
13 3 _
b. How much longer is the median length than the minimum length?
7
'8
in. The minimum? 3
18
3
.
7
_--"",8__
in.
= "87
1
4. Two insects have the maximum length. What is the difference
in length between these insects and the next-longest insects? _---"-__ in.
Number model:
143 -1 12 ­- 14
5. There are three insects in Veronica's collection that are from
t inch to ~ inch long.
If these three insects were placed end to end, how long would the line of insects be?
1§.
8 , 0
r2 in.
Number model:
5
8
+ 85 + 3-2
4
6
insects less than t inch long were placed end to end? 8,
333 6. How long would the line of insects be if all the
Number model:
"8
3
or 4" in. + "8 = 4"
7. Make up and solve your own problem about the insect data.
Number model:
209B
Date Time
1. Name the shaded area as a 'fraction and
a decimal.
2. Which number sentence is true? Fill in the
circle next to the best answer.
a. fraction:
27 100 b. decimal:
0.27
@ ..£.=~
12
6
~
~
3. Write 6 fractions equivalent to
7
28 "8
32 21
70 24
80 35
168 40
~:.
4. Divide. Use a paper-and-pencil algorithm.
_ 51 R9, or 51
~2: 9
~
:
2223 179
5. Multiply. Use a paper-and-pencil algorithm.
8,432
= 68 * 124 6. Compare.
12 times as long as 2 hours. b. 6 years is 18 times as long as a. 1 day is
4 months. 6
c. 3 gallons is
8 cups.
d. 8 cm is
40
e. 1 meter is
210
times as long as 2 mm.
50
long as 2 cm. times as much as
times as Date Time
• • MakingSpinners
1. Make a spinner. Color the circle in 6 different
12
colors. Design the spinner so that the paper
clip has the same chance of landing on each
of the colors.
3
12
2. Make another spinner. Color the circle red,
blue, and green so that the paper clip has
• a
i chance of landing on red and • a
~ chance of landing on blue.
9
a. What fraction of the circle did you color
3
1
2
1
red?
6
blue? 6,
'3 green?
0r
3
0r
b. Suppose you plan to spin the paper clip 24 times.
About how many times would you expect it to land on
red?
4
blue?
8
green?
12
c. Suppose you plan to spin the paper clip 90 times.
About how many times would you expect it to land on
red?
15
blue?
30
green?
45
211
Time
Date Math Boxes' 1. According to a survey of 800 students at
-i
Martin Elementary, about of them chose
pizza as their favorite food. Of those who
chose pizza, ~ liked pepperoni topping the
best. How many students liked pepperoni
topping the best?
300
2. Multiply. Use a paper-and-pencil algorithm.
71
2,698
* 38 =
students
~
~
3. a. Hannah drew a line segment 1 ~ inches
long. Then she erased ~ inch.
How long is the line segment now? 1~
inches
-i
~
-2.96
70
100
9
9
2
10
d. 0.2 ~
6. Complete.
a. 5 ft
=
b. 40 in.
=
100.54
97.58
c. 80 in.
=
55.91
52.95
72.03
69.07
70.4
67.44
59.21
56.25
d. 108 in.
a
25
100
b. 0.25
c. 1.0
out
in
Fraction
a. 0.70
5. Complete the table and write the rule.
212
whole number. inches
i
Rule:
4. Write an equivalent fraction, decimal, or
Decimal
b. Joshua drew a line segment inch
long. Then he added another inch. How long is the line segment now? 1~
181:
1
e. 3yd
=
=
1
3
2
9
12
yd
ft
yd
2
4
8
ft
in.
in.
ft
in.
~
Date Time
1. If this spinner is spun 24 times, how many times do you
expect it to land on each color?
a. Fill in the table.
I
!
Color
Expected Number
in 24 Spins
8
8
red
blue
i
4
4
yellow
green
i
Total
24
b. Explain how you determined the expected number of times the
spinner would land on each color.
Sample answer: Red and blue each cover ~ or
of the circle.
of 24
yellow each cover
4 spins.
!
ins is 8 s ins. Green and
i of the circle. i of 24 spins is
,":.­
2. If a six-sided die is rolled 12 times, how many times would you expect to roll
a. an odd number?
6
b. a number less than 4?
c. a6?
_6__
_2__
_4__
a triangular number? _6
__
a prime number? _6
__
d. a square number?
e.
f.
213
Time
1. Follow the directions for coloring the grid on Math Masters, page 238. You may
color the squares in any way. The colors can even form a pattern or a picture.
2. For this experiment, you are going to place your grid on the 'floor and hold a
centimeter cube about 2 feet above the grid. Without aiming, you will let it drop
onto the grid. You will then record the color of the square on which the cube
finally lands .
• If the cube does not land on the grid, the drop does not count.
• If the cube lands on more than one color, record the color that is covered
by most of the cube. If you cannot tell, the toss does not count.
Making a Prediction
white
3. On which color is the cube most like/yto land?
~llow
4. On which color is it least like/yto land?
5. Suppose you were to drop the cube 100 times. How many times would you
expect it to land on each color? Record your predictions below.
Predicted Results of 100 Cube Drops
Color
I Number of
Squares
yellow
red
4
green
10
blue
214
1
I
I
35
white
50
Total
100
I
i
I
Predicted Results
Fraction
Percent
1
100
4
100
i
!
10
100
35
100
50
100
1
I
i
1
%
4
%
10
0/0
35
0/0
50
%
100%
..
Date IIDlY
Time
A Cube-Drop -Experiment
continued
Doing the Experiment You and your partner will each drop a centimeter cube onto your own colored grid. 6. One partner drops the cube. The other partner records the color in the grid below
by writing a letter in one of the squares. Drop the cube a total of 50 times.
Write
y for yellow,
r for red,
9 for green,
b for blue, and
w for white.
Sa.mple a.nswer:
w w w
b
IW
r
Y
W
b
W
W
b
W·
9
W
W
b
W
W
b
W
b
W· W
I
:Pw
9 b b b
r
W
b
W
b
b
b
W
W
b
b
W
W1W
W
W
W
b
I
I
7. Tl1en trade roles. Do another 50 drops, and record the results in the other
partner's journal.
My Results for 50 Cube Drops
Sample a.nswers:
8. Count the number for each color.
Number of
Drops
Percent
white
1
2
3
16
28
20/0
4%
60/0
32%
56%
Total
50
100%
Color
yellow
red
Write it in the "Number of
Drops" column.
Check that the total is 50.
9. When you
green
blue
I
:
,
have finished, fill in the percent column in the table.
Example: If your cube landed on blue 15 times out of 50 drops, tl1is is the same as
30 times out of 100 drops, or 30% of the time.
215
Time
Date
1. Write these numbers in order from least
to greatest.
964
9,460
96,400
400,960
94,600
964
9,460
94,600
96,400
400 960
0
7
hundreds place,
ten-thousands place,
ones place,
thousands place, and
tens place.
7
with the following digits:
5
5 in the
7 in the
o in the
9 in the
8 in the
Write the number.
3. Write the greatest number you can make
3
2. A number has
9
9
5
8
o
4. What is the value of the digit 8 in the
numerals below?
2
_.975,320
a. 807,941 __
80
b. 583
8,00_0_
c. 8,714
80,000
d. 86,490
5. Write each number using digits.
a. four hundred eighty-seven thousand,
sixty-three
800,00_0_
6. I am a 5-digit number.
• The digit in the thousands place is the
result of dividing 64 by 8.
487,063
• The digit in the ones place is the result
of dividing 63 by 9.
b. fifteen thousand, two hundred
• The digit in the ten-thousands place is
the result of dividing 54 by 6.
ninety-seven
15,297
• The digit in the tens place is the result
of dividing 40 by 5.
• The digit in the hundreds place is the
result of dividing 33 by 11.
What number am I?
9
216
8
3
8
7
Date
Time
1. Name the shaded area as a fraction and
2. Write <, >, or = to make each number
a decimal.
sentence true.
a. fraction:
63
a. 8 - - 8
< 7
5 < 5
12 - - 6
1
1 >
4 - - 15
3
b.
b. decimal:
c.
0.63
500
8
d. 1000 - - 16
.§.
<
~
e. 7 - - 20
3. Write 6 fractions equivalent to
2
12
3
4
5
i.
4. Divide. Use a paper-and-pencil algorithm.
769
15 -
51 R4, or 51 ~
-----------=-=-­
24
6
36
~
5. Multiply. Use a paper-and-pencil algorithm.
9,476
= 46
* 206
r-------------------------------~
6. Compare.
a. 1 day is
_4_ times as long as 6 hours.
b. 6 years is
36
times as long as
2 months.
c. 3 gallons is
4 cups.
12
times as much as
16 times as long as 5 mm.
e. 1 meter is 10 times
d. 8 cm is
PJ\
~
as long as 10 cm.
217
Time
Date For Problems 1-3, fill in the blanks to complete an equation describing the number line.
1....
~~~~~
I
0
Equation: 5
I
I
I
I
I
1
8
2
8
3
8
4
8
5
8
1
8
*
I ..
1
7
8
6
8
5
8
-
~~~
2. •
I
I
I
I
o
1
6
2
6
3
6
3
6,
3__ *6 ­
1_
Equation: _ _
I
4
6
5
6
1
5
3
6
3
orl2
~~~~
3. •
..
I
I
I
o
1
3
2 3 4
I
I
I
3 3 3
4
1
4
_ _ * _--=3__ = 3", or
Equation: _ _
11
...
3
For Problems 4-6, use the number line to help you multiply the fraction by the whole number.
4. ...
~~
I
I
I
0
1
4
2
4
2
4,
Equation: 2 * l =
5.
•
...
3
4
1
or 1
~~~~~.~
I
I
I
I
I
I
I
3
4
1
2
5
6
0
10
10
10
10
10
10
I
...
10
7
8
9
10
10
10
10
8
5
9
5
10
10, or~
6
Equation: 6
* 1ri
=
~~~~~~~
6. •
I
I
I
I
I
I
o
1
2
5
3
5
4
5
5
Equation: 7
217A
5
*i = t, or 1~
5
6
5
I
I
7
5
5
..
Time
Date Example 1: Equation: 6
-1
5
*~
-1
5
=
~
-1 5
5
5
5
~~~~~~
...
I
I
I
I
I
I
o
Example 2: Equation: 3
* %=
2
5
...
I
I
5
5
...
10
5
~
2
5
2
5
-
I
I
5
5
o
...
10
5
Write an equation to describe each number line.
1
1
1.
a."
1
_-----==6=----_
1
6
* __4-=--_ - _ _4-=--_
4
I
4
4
3
4
4
*
1
4
I
4
4
6
4
3
-
111
4
1
1
333
1
3
~,...----.,...,...----.,...,...----.,...~~~~
I
I
o
8
I
I
~
1
*
3
-
2
3
I
I
I
I
I
~
8
I
o
4
I
2
3
I
~
2
*
3
-
...
3
2
3
I
I
9
3
2
3
~~~~
b. III
...
8
1
3
...
8
4
3
333
a....
1
4
I
I
O
2
2. 1
444
I
o
b ....
1
.......---...........---...........---...........---...........---...........---....
I
I
I
I
I
4
I
8
I
I
I
I
~
I
III
9
3
3
3. Study the pairs of number lines above. Use the patterns you see to describe a way
to multiply a fraction by a whole number.
Sample answer: If I take the whole number, multiply it by
the numerator of the fraction and then write the product over the denominator, that is my answer.
2178
Time
1.5*
5
~
"6
=
11111
6
6
6
6
6
~~~~~
..
I
I
I
1
3
..
I
1
I
1
I
"8
3. 8
3,
4
4.2*"3=_-
I
4
8
4
3
1
1
1
1
o
3
3
6
9
¥, 0 r31~, 0 r 13 ~ =
4
*~
8
-
8
8
3"
3
8
6
3
3
-
8
4
8
12
8" 8
8
10, 0 r '5
6. = 3
* 120
222
10 10
10
..
~~~
I
o
217C I
I
I
I
...
3"
~~~~
I
1
I
I
1
I
1
I
i
I
I
I
i
o
...
8
8
3
..
3"
~
223"
or
4
-
...
9
~~~
I
I
I
I
o
5. .1
3"
=3*
1
1
1
888
..
1
6
3" 3
...
1
3
3
o
..
1
3
~~~~~~
I
1
6
111
3
3
3
-
I
6
* 1= ----'=--~-----
6
I
Q,or2 o
2.
I
I
5
10
I
...
16
8
I
I
10
10
..
Time
Date
Suma and her sister Puja are making 12 blueberry-wheat muffins for breakfast. The
recipe lists the following ingredients:
1 cup flou r
1 egg
t cup whole-wheat flour
t cup skim milk
2 teaspoons baking powder
~ cup honey
~ cup blueberries
~ cup cooking oil
t teaspoon salt
~ teaspoon cinnamon
Use the list of recipe ingredients to help you solve the number stories below. For each
problem, write an equation to show what you did.
1. The sisters decided to double the recipe.
a. How many cups of whole-wheat flour do they need now?
2
2,
or 1 cup(s)
Equation:
2
* 12 == 22
b. How many cups of blueberries do they need now?
or 12
2 * 34
14 , cup(s) Equation:
or 12
c. How many cups of honey do they need now?
6
4,
4
3,
or 113 cup(s)
Equation:
2
6
4"
* 32
4
3
2. Suma and Puja decide to make 48 muffins instead of 12.
a. How many teaspoons of salt do they need now?
4
4,
or 1 teaspoon(s)
4
Equation:
* 14
4
4"
b. How many teaspoons of cinnamon do they need now?
.1£ or
14
1 8, teaspoon(s)
or1­
8 ,
c. How
4
2,
4
Equation:·
* 38
12
If
ma~ cups of skim milk do they need now?
or 2
cup(s)
Equation:
4
*1
'24
2170
Time
Date The Hillside Elementary School walking club meets every Monday after school.
The table below shows how far some students walked at their last meeting.
(
.
I Student
Katie
Mahpara
1
Miles
Cole
Jack
4
2"
"4
10
Maria
5
5
9
3"
Nikhil
5
3"
6"
Use the information in the table to solve the number stories.
2
3. a. If Katie walks the same distance atevery
meeting, how far will she walk after 2 meetings? _.....
b. After 7 meetings?
~, 0 r 2~
miles
'3
miles
.
c. After 7 meetings, Katie will have walked between _ _ _ __
1 and 2 miles
~nd 3 m~
4. a. If Jack walks the same distance at every
3 and 4 miles
~5, 0 r 2 ~, 0 r 21
meeting, how far will he walk after 3 meetings? _____ miles
b. After 3 meetings, Jack will have walked between _ _ _ _ __
1 and 2 miles
~d 3 m~
8. a. If Mahpara walks the same distance at every
3 and 4 miles
~g, 0 r 3 160 , 0 r 3 ~
meeting, how far will she walk after 4 meetings? _____ miles
b. After 4 meetings, Mahpara will have walked between _ _ _ _ __
1 and 2 miles
l
Try This
2 and 3 miles
~nd4m~
-'
"b:~r""'>'4l:Jt'i't,*",y?,"j;<!IJr:ry:*-'l'~'4\~r~;*:;o;!f'
6. If Cole walks the same distance at every meeting and wants to
walk a total of
~
7. Make up your own multiplication number story about Nikhil or Maria.
'217E 3=-__ meetings
miles, how many meetings will he need to attend? _ _
Date Time
1. Karen used 60 square feet of her back
i
yard for a garden. Vegetables fill of
her garden space. Tomato plants fill of
the space taken up by vegetables. How
many square feet are used for tomatoes?
i
2. Multiply. Use a paper-and-pencil algorithm.
3,74 1
= 87 * 43
__6__ square feet
:,
..
a
1819
Lukasz drew a line segment that was
inches long. Then he extended it
another 2-i inches. How long is the line
segment now?
2i
5
4
8 inches
_---""'--
4. Write an equivalent fraction, decimal, or
whole number.
Decimal
Fraction a. 0.60
3i inches
long. Then she extended it another 2t
inches. How long is the line segment now?
57
P\
_---"8'"--- inches b. Sybil drew a line segment
0.65
c. 1.0
b. d. 0.9
-60-
100 65
100 50
50
-
9
~
10
~
5. Complete the table and write the rule.
Rule:
-3.49
in
out
104.16
100.67
87.35
83.86
45.72
42.23
51.92
55.41
77.69
I
74.20
6. Complete.
3
192
b. 16 ft
5
c. 67 in. =
7
d. 22 ft =
1
4
e. 12 yd =
a. 42 in.=
a
162-1~
ft
6
in.
in.
ft
yd
ft
7
1
6
in.
ft in.
~
129'
217F Date Time
1. Measure the length and width of your desk
to the nearest half-inch. Find its perimeter.
a. Length
b. Width
=
inches
=
2. Find the area of the figure.
D
= 1 .square centimeter
c. Perimeter
=
v
v
inches
Area
3. If 1 centimeter on a map represents
20 kilometers, then
160 km.
b. 3.5 cm represent 70 km.
c. 1.5 cm represent 30 km.
d. 2.5 cm represent 50 km.
e. 0.5 cm represents 10 km.
2
4
b. 57 in. =
=
e. 8 yd =
1 ~ard
the width of your ankle 1 inch
c. the length of
1 inch
~
3
5
24
ft
2
in.
ft
9
in.
d. the length of
1 foot
~
130
~ times as long as 12 hours.
b. 3 years is ~ times as long as a. 1 day is
6 months. yd
yd
1
c. 12 cm is
ft
d. 1 m is
60
times as long as 2 mm.
~ times as long as 20 cm.
ft
~
218
square cm
6. Compare.
a. 26 in. =
d. 16 ft
10
4. Tell if each of these is closest to 1 inch,
1 foot, or 1 yard.
b.
5. Complete.
=
=
IV
a. the width of a door .
a. 8 cm represent
c. 9 ft
'"v
inches
e. 3 gallons is
24 times as much as 2 cups. ~
```