Math  2: Summer Work 6th to 7th	Prime Time (1}

Name: 	_

List all of the factors of each number.

1.  12 	2.  45

Tell whether each number is prime or composite.

.. 3.	95 	4. 	17

Tell whether the second number is a multiple of the first.

5.    2;71 	6. 	1;18 	7. 	3;81

Write the prime factorization.Use exponents where possible.

8. 126

Show your work to solve this problem.

9. 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?

Find the least common multiples and the greatest common factor for each pair of numbers:

lOa.  8 and 12 	b.  7 and 15

LCM:	LCM: GCF:	GCF:

Write each mixed number as an improper fraction.

Write each decimal as a fraction.

3. 	1.25 	4.   0.29

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

Comparing Bits and  Pieces {2}

5.	
8	6.	5	
	3		2	

Write each fraction as a decimal.

7.	8.

9
100

7
9.	" 25

Order from least to greatest.

10. 	11.

Compare each pair of fractions. Use <, >, or=. Fill in the 0

2

'	.

12.   IO.E...
8 	10

13.   45 0. 1.

Write this decima l number in words.

14.   12.873

Use the information  to solve the following problems.

15. In a class of 24 sixth-graders, 25% walk to school, 1/8 ride bicycles to school,1/3 take the bus to school,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 school? 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.

label the unlabeled  marks with decimal numbers. Then tell the step  (interval).

Sample:

E      l 	l -
0.4

16.

0.1
E        I	I ,	The ep is 0.1.
0.1 	0.2 	0.3 ·o.4
··

I

'  I 	I •
I
0:15 	0.17

17. Fill in the missing parts ofthe table.

	Percent	
'i	I		
1  o.88
I		
I	35%	
\	i		
1   0.625
l
!		
I	275%	

Fraction 	IDecimal

Note:DO NOT use a calculator on this unit's work!!	Let's Be RaUonal (4}

1.  Jack and Helen are making cookies. The recipe says to combine one-half cup of butter with three­
fourths cup chocolate chips and three-eighths 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.

2. Find each quotient. Show your strategy!!(Use Khan Academy if you forget!)

..  3

a. 	12 ..;-	b.	3 ..:...

·

c.	d.

8

4
0

Estimate each sum.Use the benchmarks,0,  and 1. {DO NOT actually solve!!)

3.	4.

Show your work to solve this problem.

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

Find each sum or difference.Show your strategy!!

10 	-.1

7.	11 -
16   . :) 8

8.	9-32-
5

Show your work to solve this problem.

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

Find each product.Show your strategy!!(Cross simplify before multiplying??)

10.

-2of1-
3 	4

11.

12. 	13.	lX
3 	4

Find the perimeter and area of each rectangle.Show formula work!!

1.	2.  Length= 18m,Width= 12m

8cm

15 em

Perimeter: 	Perimeter:

Area: 	Area:

Find the area of each triangle. Show formula work!

3.	4.
13 em

21

46cm

9.4mi

15.7 mi

12.6 mi

Find the area of each parallelogram below.Show formula  work!

5.	6.

· /:1cm  /
/h	.
2cm

4cm

Show your work to solve the following problem. Include the formula,substitution,and solution steps.

7. The length of a rectangle is 8 centimeters.The width is 6 centimeters. a. What is the area?

b. What is the perimeter?

Variables and Patterns (B)

1. A Student Council wants to throw a party for students. They decide to have a breakfast cat:ered 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 0,20,40,60, 80,100, and 120 students would attend. (See next page)

a. Make tables that show costs for each company in cases where 0,20,40,60,80,100, and 120 students would attend. (See next page)

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 next page)

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

Catering Crew: Urbandale:

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? Defend your reasoning.

60:

100:

1.   a.

												

												

												

												

												

b.

fly :

Ufbt\110-oJ
a:,._+-e."'i,  Compo.

2.In parts (a-b) use symbols to express the rule as the equation.Use single letters to stand for the variables.Identify what each Jetter represents.

a. The perimeter of a rectangle is twice the length plus twice its width.

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

Note: DO NOT use a calculator for this unit!!	Decimal Ops (10}

First estimate.Then find each sum or difference.Show your strategy!!

1.  2.1+ 3.4 	2.   3.4-0.972

Show any work that helps you solve the following problems.

GO

3.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. 	r---------,
en
+'
50 r-------- ­

".'Ca
.Vl
'5	40	
	30	
s..		
]	20	
z5	
10	

0
0 	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  blue?

c. What percent of students 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.

4.  0.2, 0.6, 0.5

I	
l l-   I I I I	I l  : I	
0		1.0	

(

Find each product.Show your strategy!!

4. 	5.
5.342
X 13

0.19
x o_os

Find each quotient.Show your strategy!!

6. 	7.
.
0.4h.08	

8.	9.

. 9}21.6	108+5

For each of the following, decide if the quotient is less than or greater than 1. DO NOT actually solve!!

lOa.   12. 6 + 11.8 	b.   5.6 + 9.9

Decimal Op.s (12}

11. Last year} the Widget Corporation had $6501000 in sales. This year1 sales are down 4%. H<lw much did the Widget Corporation sell this year? Show your strategy!!

12.A store is selling a sweater on sale for $17.90. The regular price is $22.95. What percent of the regular price is the sale price. Show your strategy!!

Write  a number sentence you could use for each situation.

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

Use <, =,>to complete each statement.Fill in the 1:].

14. 	2.8 X 1<:Q26 ·100	15.	38.6 ·10Q2 . 38.6 .·s

Solve.

16. A bicycle goes on sale at 75% of its original price of $160. What is its sale price? Show your strategy·!

Use the number sentence 123 x 4 = 49.2 to help you solve the following:

17a. 12.3 x 4 	b.1.23 X  4 	C.    0.123 X 4

Data Abor.r t: Us (13}

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. Show your strategy!!

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. How many students are in Mr. 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 for the food drive.
3. Which class has a greater mean number 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

h.The means are equal. 	i. There isn't enough information to tell.

Shapes and Designs (14)

Find the measure of each angle labeled x.

1. 	2.	4
L2

Find the  measure of angle 1in this figure.

3.

Use the diagram below to identify all the polygons for each name. List as many letters as t:here are that fit the  name.

4.quadrilateral 	5.parallelogram 	6. rhombus

7. rectangle 	8. square	9. trapezoid

.

•  av.

. . .

•	• 	• 	•

'	. 	....: .	• 	•
. 	•
. . • 	. 	• 	• 	• 	.
L7: •	•	: o

• 	• 	• 	• . 	•  .

• 	•	•	• 	• 	• 	• 	• 	•

• 	•
• 	•	• 	• 	• 	•

.

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.  . •	• · •

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• 	• 	• 	• 	•

I .-:	: I 	•	g.

•	·h.n

• 	•	• 	•	• 	•	• 	•	• 	•	• 	•
f.
•	.· . . . 	. . . 	.
•	•	•	• 	• 	•

Shapes and Designs(15}

10. An isosceles triangle has two 50 degree angles. What is the measure ofthe third angle? Explain how you found your answer.

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

a. 	b.

c.	d.

In the each diagram below,lines l1and L2 are parallel lines cut by a transversal.Find the measure of each numbered angle.

12. 	13.

2 3
4

m<l. 	_	m<l.  	_

m<2 	

m<3 	

m<2 	

m<3 	

m<4 	

m<4