....... ;cC;n..·.....·.....-.....

"-5....u.!.!s'

'::N.9.'!:...._......................... 	.P...•.:1
s+& cl&nt5	-	Prim rnne

r:..

liSt- all the factors of each number.
1. 12 	2. 45	3.- 41

Tell whether each number iS prime or composite.
4. 53 	5. 86	6.  95	1. 17

. 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 prime fa orization. Use exponents where possible.
12.- 78 	13.  126

14.  At a 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 tb.e·gr. atest corn.mon  for .pair
of numbers:
• \_(1-\:a. 8and12 	:b. 7 and 15 	-  -- c. 11 and 17 	..d.
36· d108...

GCF:

••••.•••••••••••••.•••••••••••••••a•••••t••i•1••••.••b••••u••••+••••e•••••. ••••••••••••••••••••..•·-····.................• ........ (;r I

Wnte each nmed number as an improper fraction.

1.lg7

3

2. 24	3. 7.:>

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

Write each improper fraction as a m:i:s:ed number in simplest fonn.

8.   15 	9. 	10
2 	3 	•  2

11.  ;

Write each fraction as a decimal.
9	7

14.  3

15.

1
125

·

12·  100 	13   25	50

Order from least to greatest.

18·1 2 3

16   1 1 1

1 5 7

17

·

4•5•8

•  4'3'6

2'6·8

· each pair of fra<f!oas, Use <,>,or=.F;II  i f'\ -the.. 0•
19. i D{o	2o. 3D 	21•  1 0	22. ;s D

•

Write each·of the decimal numbers in words.
23. 12.873 	24.  8.0552

.................................f..f?:.\..
Comparing Bits and Pieces

25. In a class of 24 sixth-graders, 25% walk to school,iride 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 the class·ride bicycles to scl:lool? Explain 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? Expl$.your reasoning.

Label the unlabeled marks with decimal numbers. Sample: 	-+1--+--+---I--•l

0.1
' I
0.1	0.2

0.4
I '
0.3 0.4

The step is 0.1.

26. 	 , I 	I   • 	. 27. 	-tl--+--+-+-1-·

0 5 	0.17

-2.1	-1.8

28. Fill in the mis.cring parts of the table.

·Ftaction
.. . .	· Decimil :,· Percent:	
i	I	
	I	0.88 	I
I
I	
		35%	
11
4			
	0.625		
		275%	

..

•

\J\S! it 	De 	c\ L.LS a.. c.o.\ c. u\0-to( 	o(\ -thi	unit\s we( f( 1  pf,,'1
---•-••••L•E••W•••••••••••A••••••••••••••••••••· ··••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••

•

Let's Be Rational

1. Jack and Helen are making cookies.The recipe  ys to combinecup of butter
withcup chocolate chips md  cup 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. Fmdeachquotient. 5hovJ 	ur s+ro.Ae..o'(	(use.\<,hO.f\ J\c.o-demIf  ov 	\
.J; 	2

a•  12 1. 2

b; 12 	.,

c. 3 + .-;,;

d. 	4	f

5  .  1

·6-=-3

Estimate each sum. Use the benchmarks o,f,and L (Do not	l{

3

5	5	

·   +

16 	8 	4•

10 +
12 	5

•

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

·············-···........P r:::,. 5
Let's Be Rational
Find each som or difference. .Sh0W   'fQ'J '( 	S1-'fa.t'/	!

+ 4

7
8. 1110

10.

11  -  7

1.2. 9- 35

1016

38 	2

13.· A kitten eats i_cnp 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?

16. 52 X 21

.	1 	4

17.  4 ofs

19. 	1

3f3o

20.

1 	25	21 	1

3

X	X 	• 	£ X
•

••••••••••••••••••••••••••••••••••••••••••••·•t•••••••.••••••••••••;;"O•••••••·••••••••••••••••••••••••••••••••••••u••••••  P&  lo
Covering and Surrounding	•
Find the perimeter' and area of each figure. ShC\f\1 ..fm-rnuk.l \tJOY' K

1.

Scm

15an

2. 	e = 18m, w = 12m

3.

23 yd

19yd
J

30yd  •

37 yd

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

13cm

21

46cm

6.	•

9.4 mi

12.6 mi

7. 'Ifacy 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?

...............·-....

PG-."T

8. 	Fmd the area of each parallelogram below.

Covering and surn: ;di  ·
Shew ftt<n'"\\l\c. WOf" K..\
•

9. The lenifu 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?

•

..............................................................................................................	t=>l:r.
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
cass where 20, 40, 60, 80,100, and 120 students would  attend.	( Se.e  r.e ·+  pce.)

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. (see nt)(t 	e.)

•

c. Write equations relating total cost and number of students for each catering  company.

d.  Why, if at 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?
•

·························-·················p6.'\
Variables and Patterns

												

												

												

												

												

Ufba.f"lttoJ
Co.. v-i -n  Cow-,pa(ly

•

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.

'Cl\E.,!  Oo  t-\o\ u e.	co-tcui } -cr 	I{ -+h's uti + J
a	.•......•-·..........··•·....................... «••••.••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••

•

I	- ..,

Fll'St estimate. Then find each sum or difference. 	ho"-H 	\'o\J(  S.+'lcct€._C{ l(
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.

Blue	Red	Green
Preferred Color for Logo

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

b. What percent of students surveyed preferred  blu!!?

c. What percent of stud 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 I I I   I I	• I	
l  I I   I    I i I	
I	I I	
0	1.0	0			1.0	

 

Find each product.

7.   5.342
.x...u

8. 	0.19
X   0.05

9.	6.4
X   0.09

...·········-........ Pb.' '
DecimalOps

10. 0.4)1.08 	11. 0.68-;.. 0.2

14:15)123

12.  0.02) 0.06

15.108+5

•

16.  For each of the following, decide if the quotient is less than 1or greater than 1.('tJ\-\hov+, 	\)
a. 9.22 -;.. 2.8	b. 0.9 -;.. 03	c. 12.6 + 11.8	d. 5.6 + 9.9	so\""(\•

P&.

··•·•······••·•·······•
Decimal Ops	\1.
17.  A restauranfoffers' a 13% discoUnt on chicken wings on Mondays. IfTravis  -

•

eats $7.95 worth of chicken wings on Friday, how much would those wings cost on Monday? 	S 'r\ ow	0\J f	St('a.+	'

it..e

18.  Last year, the Widget Corporation had $650,000 in sales.This year,sales are 	\
· down 4%.How much did the Widget ,Corporation sell this year?  S\o\ () W  CIJ t' 	S+rt..	'f •

19.  A store is selling a sweater on sale'for $17.90.The regular price is $22.95.Wh	I
percent of the regular price is the sale price?  hb\1-J	'V\J f	S+'(" 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?

$0.02

21.  A mint costs  -	.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  +he.. 0•
23.  2.8 X 1C(J26 ·100	.	24.  38.6 ·10{]2 ·38.6 ·5

25,- 3.1 X 1{0(0.5 · 0.2)3.1	26.  8.3 ·10 ·lo8.3 X .100

Solve.
21. A bicycle goes on sale at 75% of its original price of $160.What is its sale

•

price? 5ha'N 'lcus't -t-e. '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

..................................................................................................-

u,·P.

b. 	'3

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. Suppose Glenda's rolls were 12, 7,3,10, 9,2,11,7, and 8.
i. What is the median of Glenda rolls?   .

ii. What is the mean of Glenda's rolls?

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

iv. Which 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. Ho

w many students are inMr.Watkins's afternoon math class?

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. Johnson'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. "YVh.ich 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 of food?
F.  Mr. Johnson's class	G. Ms.Smith's class
The means are equal. 	J. There isn't enough information to tell.
H.

2.6

............................................................ . . .T•••••••••••••••••••••••••••••••     h- d. 	-; · 	Pb.\

Find the measure of each angle l eled x.

1.
51"

62"	X

Find the measure of angle 1in each oure.

4.	6.

Use the diagram below to identify an the polygons for each   e. \... \St O..S  rt\O.'t\ 'f \ e.t\e,.'(" 	•
7. quadrilateral	8. parallelogram 	9. rhombus	O..S  +he.'f"E!.  O..f"e,
b	e 	-\'h t  f'+ e..
,	no..me...
10. rectangle	11. square 	12.  trapezoid	@

• a\/.

• 	•	• 	• 	•

. 	. 	. .

• • 	•	" 	" 	..

. . . .

...D

• •	• • 	• 	• 	• 	•

• • 	• 	•

• 	• 	. . . • • 	• 	• 	• 	• 	•

•	• 	•	• 	• 	•	• 	•	• 	•

2:

" 	•
• 	•
• 	• 	•
• • • 	• • • 	•
• • 	• •	• 	•	•
• • • •	• 	• 	• •	•	•

•	• • • 	• 	• •

e.
• 	•	•
• 	• 	•

•

•
•	• 	• 	•	• 	•
•	• •	• 	• • •

f.
I -:   : I : .	·D:

.. .."

. ..	.

......

• 	• 	• 	•

13.  An.isoscelestriangle 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.

b.

••

In each  diagram below,liDes  Lt and are parallel lines cut by a transversaL
Fmd the measure of each numbered  angle.

15.

2  3

16. 	17.

34

\YI L \ ':  ·z·---·..·----·•
rr L.Z:......,.........,.

•

mL3 =---­
MLL.f =.....--

L1	L2.

'VY\'-' =	m L.l  =

'(Y'\   '- 2	 	

rt\i...2=
yv"\ 	3=	'rf) L3=	 -
Y'1"',    Llf=	v-n L Lf::

•

•

•