.............(..o....,····-

···+···)·/·:·-..· - .\d!nr!).er:.'Y:!J!."\!e:..'w6:.n........................._....P. .. .:.:1

Primere

List- an the factors of each number.
1. 12 	2. 45	3.- 41 	tion

R AO
ALl

TeD whether each number is prime or composite.
4. 53	5. 86	6.  95

DtrtE'TtOMS\
•

TeD whether the second number is a multiple of the first.
8. 2;71 	9. 1;18 	10. 3;81 	11.  4;74

Write the 'rime factorization. Use exponents where possible.
12.• 78 	*	13. 126	I

·

*	14.  Aa store,hot dogs come in packages of eight and hot dog buns come in packages of twelve.What is the least number of packages_of each type that you can buy and have no hot dogs or buns left over?

15.  Find the least common multiple and the greatest commoa for each pair
of numb.ers:
II( a. 8· and 12 	b. 7 and 15 	-   ·:C.  11 and 17 	.d.. ,.36 and 108
LCV\:

············· ············.·.......................................................

............•......• •.·........P.

& , Z

Write each mixed number as an improper fraction.

Comparing Bits and Pieces

1• 178	2. 243

3. 731

Write each decimal as a fraction.
4. 0.6	5. 1.25 	6. 0.74	7. 0.29

Write eadJ. improper fraction as a mixed number in simplest form.

8.	15	_._ 9.	10	11	
	2	"'	3	•  2	•	

7
3

25

Write each fraction as a decimal

14.  3

1
15.

12.

9
100

13.  7

50	125

Order from least to greatest.

16

1 1 1
· 4'3•6

'l;; e>ldlpairof oDS, Use <,>,or=. FiI\  i1'\ -\he_ 0•

0

19.   0{

20. 	0	21• 	0	22.  is D

Write each of the dedmal nmubers in words.

...................................\-:'...\..?.
Comparing Bits and  Pieces

.23. 12.873	24.  8.0552

25. In a class of 24 sixth-graders, 25% walk to school,ride bicycles to sChool, . take the bus to sc}lool, and the remainder of the class are driven to school by their parents or guardians.
a. How many Students in the class walk to·school? Explain your reasoning.
b. How many students in thclass·ride bicycles to school? E:xl>lain your reasoning.

c.  How many students in the class take the bus to school?
d.  What fraction of the class are driven to school by their ·parent or guardian?
Explain your reasoning.
e•. What percentage of the students in the class walk, ride bicycles or the bus, or are driven  to at school by a parent or guardian? Exp}$your reasoning.

Label the unlabeled marks with decimal numbers.

Sample:	•   I	I
0.1 	0.4

•   I			I	•	The step is 0.1.	
0.1	0.2	0.3	0.4		

....
26.	 . I 	I I	. 27. 	.......  -;1--+---+-+-1-

0':15	0.17

'"28. Fillin the missing parts of the table.

I

\   ..

·.F.i:a.ctio.n.·. Decimai·.
3
8

-2.1	-1.8

..
Percf!!nt

'

I	0.88 	I

I

I	35%
11
4
0.625

j	275%

\)\S: 	'if Do	c\ u.se..	c.c. U\o.. ( 	ot'"'\ -thi	IJ\"\\tlWC(	f(. l Pb, Lt
···.···&·M··································;············································································ -.
let's Be Rational

1. Jack and Helen are making cookies.The recipe s ys to combinecup of butter withcup chocolate chips andcup chopped nuts.
a. When _these three ingredients are mixed together,how many cups of the mixture will Jake and Helen have? Show your work.

b. Jack and Helen decide to triple the recipe.
i. How many cups of butter will be needed?

ii. How many cups of chocolate chips will be needed?

iii. How many cups of chopped nuts will be needed?

c. When the ingredients for the tripled recipe are combined, how many cups of the mixture will Jack and Helen have'?

2. Flnd each quotient  sh:>v.J 	b'Jr  5+rcd -'!l	 (use.\( ho.(\ 	e""If	cV 	(11 J
a. 12 -:- !	b. 12 +	c. 3 +

·6"'""3

d. + 4 	e. 1 + 6 	f  5  . 1

•

Estimate each som. Use the benclunarks 0, 'and L  (Do Y' C>T	uaJ!y

5

+ 8 	'.A.. 	+ .51

5

12

3· 1   6 	10

6.  How many bows can you make from 5 meters of ribbon if making a bow takes
1
4 of a meter of nbbon?

...................-.... ........Q/t: r . cJ..
Let's Be Rational
Find each sum or difference.  5h0"/J  'f 0u'(	S1-'fa.t	'I !

7.  7+ 5

8. 11 	+ 4 	..::..-	2	3

7

10	'7' 9. 2j + 44

10. 1016- 3-g7

11. 813- 2-3g

12.  9-32-
5

13. . A kitten eats.cup of cat food.Another cat in the same household eats .
6 times as much.How much food does the cat eat?

14.  Ken used all of a piece of lumber to build a bookshelf If he made three
Shelves that are each 2feet long, how long was the piece of lumber?

19.    1 	3 3

X- -=	x

X 10

20.

1	2
:;,

21•    l3

Covering and Surrounding 	•

······ ·······················································"···················································p& lo
Find the perimeter' and area of each figure.  shef'«mu	\o 'tJOY K \

1.

Scm

15an

2. 	f = 18m, w = 12m

3.

23yd

19yd
I

30yd

37yd

Solve.
4.  The area of a triangle is 6 square units.Both the height and the length of the base are whole numbers.What are the possible lengths and heights?

•

Find the area of each triangle.  5hQ'fJ +-:;, m u\a. \Nt '('t\ \

5. 	13 em

21

46cm

6.

9.4mi

12.6 mi

7. 'ilacy has 40 feet of material to make the perimeter of a rectangular sandbox for her little brother.
a. What rectangle with whole-number side lengths would give the sandbox
with the greatest area?

.b. What rectangle with whole-number side lengths would give the sandbox
with the least area?

...................... .

Pb-."1

8. 	Find the area of each parallelogram below.

                          4cm

Coveringand  Su	di ·
Shew	W'I\l\c.,WOf:K.\
•

.
-1( 9. The lengfu of a rectangle is 8 centimeters.The width is 6 centimeters.
a.  What is the area?
     b. What is the perimeter?

10. The area of a rectangle is 45 square inches.
One dimension is 5 inches. What is the perimeter?

..............••............••............................•.......••........••........••.....•......•..•..	
Variables and Patterns

(),;, \

1.  a.  A Student Council wants to throw a party for students. They decide to have a breakfast catered and they compare bids of two companies.The Catering Crew charges $8 per student Urbandale Catering Company charges a set fee
of $160 plus $6 per student.Make tables that show costs for each company in
cases where 20, 40, 60, 80,100, and 120 students would attend.    (See n e  +

pc e)

('

b. Plot the (number of students, catering costs) on a graph. Use different
colors or plotting symbols for points to show the two catering companies. (St:e.  noc:.+	e.)

c. Write equations relating total cost and number of students for each catering company.
G+er-\f'<j C("e v...) :
Ufbo.(\ :
d. Why, jJat all, does it make sense to connect the dots on your plots of part (c)?

e. Is there any number of students for which both companies would charge the same rental fee?

f. If 60 students signed up to come to the breakfast, which company should the
Student Council select? What if 100 students signed up for the breakfast?

\DO:

............................._................... 	c

U'(b t'"\
O;._re.....i,n  Company

												

												

												

												

												

Variables and  Patterns

P6.

E.P\Q

«

.......=.,  2. In parts (a)-(e), use symbols to express the rule as the equation. Use single
letters  to std for the variables. Identify  what each letter  represents.
a. The perimeter of a rectangle  is twice its length plus twice its width.

b. The area of.a triangle is one-half  its base multiplied by its height.

c. Three big marshmallows  are needed  to make each s'more.

d. The number of quarters in an amount  of money expressed in dollars is four times the number of dollars.

t)\E.,Oc t'\o\ u e. ,u;  tro r 	x fh':; 	u-  ;+  J
as 2      .•••••••.•••••••••••  ··························•c··················································

FirSt estimate.Then find each sum or difference.    '5 ho" n'  \/OOl   S+'to.:t€..Ct y

i

I	- "'
1. 0.6 + 5.8	2. 2.1 + 3.4	.	3. 3.4 - 0.972	.

4. The student council at Metropolis Middle School conducted  a survey to see whether students would prefer blue,red, or green as the ·new color for the school logo.The results of the survey are shown in the bar graph below.

'

a.  What is the total number of students who were surveyed?

b.  What percent of students surveyed preferred blu '?

c. What percent of stnd  nts surveyed preferred red? 	..

d.  What percent of students surveyed preferred green?

e. If 970 students attend Metropolis Middle School, what percent of the students were surveyed?

Order each set of decimals on a number  line.
s. 02,0.6, 0.5	6.  0.26, 0.3, 0.5, 0.59, 0.7

I   I I I )o 	. I I I I : I i I I I I ...
0 	1.0	0 	1.0
·.

Find each product.

7.   5.342
.2L.ll

show 'fOO !) o..-te9\

8. 	0.19
X   0.05

9. 	6.4
X   0.09

............--......_ ... P6.\'
DecimalOps

I

Fmdeachqnotient.	Shov..J	IJ( S·h···	l

10. o.4h.os	11. 0.68 + 0.2

...

13.. 9)21.6	14.. 15)123 	15.108+5

EPlO
16.  For each of the following, decide if the quotient is less than 1or greater than 1.('tJ\-\ho\J+, 	\)
a. 9.22 + 2.8 	b. 0.9 + 03	c. 12.6 + 11.8 	a. 5.6 + 9.9	"=::>O\   I'('I•

P&.

············•········••
Decimal Ops	t'l..
17.  A restauranfoffers- a 13% d.iscoililt on chicken wings on Mondays. If Travis -
eats $7.95 worth of chicken wings on Friday,how much would those wings cost on Monday? 	Show 'f()\)f 	St<"a.+ 	'

18.  Last year, the Widget Corporation had $650,000 in sales.1bis year,sales are 	\
-    down 4%. How much did the Widget porporaiion sell t1ris year?_ ShcW C\l	'f'  S-k. 'f  •

19.  A store is selling a sweater on sale for $17.90.The regular price is $22.95.What 	I
percent of the regular price is the sale price? 	h w ov	f' 	S+t" 0..+ e.8 'f ,

Write a number sentence you could use for each situation.

20.  A pen costs $0.59. How much would a dozen pens cost?

21.  A mint costs $0:02.How much would a roll of 10 mints cost?

22. An orange costs $0.09. How much would 2 dozen oranges cost?

Use <,=,or> to complete-each statement.  F\\ \n t-he  D.
23. 2.8 X  1C{J26 ·100	_	24. 38.6 ·1002 ·38.6 · 5 -

25.- 3.1 X  1C>f](0.5 · 02)3.1	26. 83 ·10 ·108.3 X .100

Solve.
21. A bicycle goes on sale at 75% of its original price of $160.What is its sale
price? Shn'fCU"<  S't"rO..te. 'j

    28. Use the number sentence 123  X 4 = 492 to help you solve the following:
a. 123 X 4 	b. 1.23 X 4 	C.  0.123 X 4

d. 0.123 X 40 	e. 0.123 X 400 	f. 0.123 X 4000

.....................................................................................................- 	- t, 	- u·P&·. I3

o.\\

1.  Glenda rolled  two six-sided number cubes nine times and computed the sum of the numbers rolled each time.
a. If the mean  sum of Glenda's rolls was 6, what was the total of the nine ·
sums Glenda rolled?
b.  SupposeGlenda'srollswerel2, 7,3,10,9,2,11,7,and8.  Shbv..J	()01' 	stca.J 	l

Af \5	i. What is the median of Glenda rolls?   ;

ii. What is the mean dfGlenda's rolls?

iii. What is the mode of Glenda's rolls?

iv. Wbich do you think is the best indicator of a typical roll Glenda made, the median, mean, or mode? Explain  your reasoning.

2. Mr.Watkins arranged  the quiz scores of his afternoon math class from least to greatest:5,5,6,6,6,7, 7,7,7,7,8,8,8,8,8,8,9,9,9,10,10  .

\\

a.  How many students are in Mr. Watkins's afternoon math class?

po '> b.

How do the quiz scores vary?

c. What is the mode of the scores?

            d. What is the median of the scores?

For Exercises 3 and 4, use this information.
Mr.Jolmson's class of 20 students collects 180 cans of food for the food drive. Ms.Smith's class of 25 students  collects 200 cans of food.
3.  Which class has a greater mean number  of cans of food?
A.  Mr. Johnson's class 	B.  Ms. Smith's  class
C. The means  are equal. 	D. There iSn't enough  information  to tell.

4.   Which class has a greater  median number of cans offood?
F.  Mr. Johnson's class 	G.  Ms.Smith's class

H. The means are equal. 	J.  There isn't enough information to tell.

•.•••••••••••.••••••••••••••••••••••••••••.•-.u •••••••••••••••••••••••.••••••••••••••••••••••••••• h --  ci.-  i  - 	Pb.\4

Find the measure of each angle labeled x.

1.                                      

Find the measure of angle 1in each figure.

4. 	6.

Use the diagram beiow to identify all the polygons for each name. \_ \ St 	ft'\O.'f\ '1 \ e.+\-e..'( c;,
7. quadrilateral 	8. parallelogram 	9. rhombus 	0..5 +he'f'E:.  o.re.
b 	e 	.;na    t  f'-\- -the..
•	·rH>.me....
10. rectangle 	.   11. square 	12.  trapezoid 	@

..

(	.

.

•

• a·•\/• • 	•

.··

.· ..

.... .

•	•

• 	• 	•

•	• 	• 	•

•. •.

•	• 	•. .

. . . .

. .•

.•	•.

•. •. •.

• 	•  • 	•

• • • •  • • • • • • 	•	•

• • • 	• 	• 	•

:c	• 	•
LJ:

·e.	o

•. .•

• •
• •

.

.•  .• 	•. .• 	•.

•	• 	•

• 	• 	•
•
•	• 	•	• 	•

• 	• 	•	•
f.

• 	• • 	• 	• 	•	• 	• . . • 	• 	•

:

I <	: I : : 	-D: : : _:h. _	:
...... ..

13.  An isosceles triangle has two 50° angles.What is the measure of the third angle? Explain how you found your answer.

14.  For each of the shapes below, find the unknown angle measure without using your angle ruler.

············- ............

P{,. \5

Shapes artd·DQigns

b.
0.\

Ineach diagram below,Jines Lr and Lz. are parallel lines cut by a transversaL Fmd  the measure of each numbered angle.

15. 	16. 	17. 	L1	L2
L1	95° 1 	1 2
34

2  3
4

ML \-:	..

L1	L2

Y'r\ '-  '  ::	 	   m L-l =	 	

'{V)L2	rn'-.2=	'('('\ L2::	 	

m 3= 	
ML'-f=  	

'(Y'"\

3=
L9=

3=

-

'f'r\ L
"""'!"

Y"1"\ 	Y""r\  L Lt::

•