Unit 1 The Number System Homework 2013 - Wikispaces1+The+Number... · 7 Greatest Common Factor GCF Worksheet 8 Least Common Multiple & Greatest Common Factor LCM & GCF Worksheet ...

Content Standard

Least Common Multiple 6.NS.B.4 Find the greatest common factor of two whole numbers less than or

equal to 100 and the least common multiple of two whole numbers less than or

equal to 12. Use the distributive property to express a sum of two whole numbers

1–100 with a common factor as a multiple of a sum of two whole numbers with

no common factor. For example, express 36 + 8 as 4 (9 + 2)..

Greatest Common Factor 6.NS.B.4 Find the greatest common factor of two whole numbers less than or





Distributive Property 6.NS.B.4 Find the greatest common factor of two whole numbers less than or





Exponents 6.EE.A.1 Write and evaluate numerical expressions involving whole-number ex-

ponents

Prime Numbers and Composite Numbers

6.NS.B.MA.4a Apply number theory concepts, including prime factorization and

relatively prime numbers, to the solution of problems.

Prime Factorization 6.NS.B.MA.4a Apply number theory concepts, including prime factorization and

relatively prime numbers, to the solution of problems.

Name _________________________________ Date ___________________ Class __________

Date Day Content Standard Homework

1 Exponents

6.EE.A.1

Exponents Worksheet #1

2 Exponents IXL 6E1 (95/10)


3 Exponents IXL 6E2 (95/10) Show Work


4 Prime Numbers 6.NS.B.MA.

4a IXL 6N3 (95/10) Prime Worksheet

5 Prime Factorization 6.NS.B.MA.

4a Prime Factorization Worksheet

6 Assessment

Least Common Multiple

6.NS.B.4

LCM Worksheet

7 Greatest Common Factor GCF Worksheet

8 Least Common Multiple & Greatest Common Factor

LCM & GCF Worksheet

9 Distributive Property Distributive Worksheet #1

10 Distributive Property Distributive Worksheet #2

11 Review SEE

ABOVE Study

Review Worksheet

12 Assessment SEE

ABOVE None

6.NS.B.4

UNIT OVERVIEW In this unit students will: • Evaluate expressions with whole number exponents • Identify numbers as prime or composite • Find the prime factorization of numbers within 100 • Find the greatest common factor of two whole numbers less than or equal to 100 • Find the least common multiple of two whole numbers less than or equal to 12 • Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor ENDURING UNDERSTANDINGS

In this unit students will understand that: All natural numbers greater than one are either prime or can be written as a product of prime numbers (composite) The number 1 (one) is always a factor of any number Exponential notation is a way to express repeated products of the same number Least common multiple and greatest common factor are helpful when solving real-world problems. Properties of numbers can be used to simplify and evaluate expressions ESSENTIAL QUESTIONS

How are different numbers related to each other? How can two different expressions be equivalent?

ESSENTIAL VOCABULARY

• Base • Composite Number • Distributive Property • Exponent • Factor • Greatest Common Factor • Least Common Multiple • Multiple • Prime Factorization • Prime Number • Product • Relatively Prime Numbers • Square Number

WORD DEFINITION EXAMPLE

Base The basis of each place value in the

number system 6³

Composite Number

A number with more than two fac-tors

Examples: 4, 6, 8, 9 Non-Examples: 2, 3, 5, 7

Distributive Property

The sum of two addends multiplied by a numbers equals the sum of the product and each addend and that

number

36 + 40 4(9) + 4(10)

4(9 + 10)

Exponent

A small number placed to the upper right of a number that represents

the number of times a base is multi-plied by itself

6³

Factor

A whole number that multiplies with an-other number equals a third number OR a whole number that divides exactly into

another number

40 Examples:

{1, 2, 4, 5, 8, 10, 20, 40}

Greatest Common Factor

The largest numbers that divides evenly into two or more numbers

24 and 30 1, 2, 3, 4, 6, 8, 12, 24 1, 2, 3, 5, 6, 10, 15, 30

Least Common Multiple

The smallest number (other than zero) that two or more numbers have

in common

24 and 30 24, 48, 72, 96, 120

30, 60, 90, 120

Multiple The product of a given whole number

and an integer

40 Examples:

{40, 80, 120, 160 . . . }

Prime Factorization

To write a number as a product of its prime numbers

2 x 3 x 5 = 30

Prime Number A number with exactly two factors,

one and itself Examples: 2, 3, 5, 7

Non-Examples: 4, 6, 8, 9

Product A number that is the result of multi-

plication 4 • 8 = 32

Relatively Prime Numbers

When comparing two numbers, their greatest common factor is 1 (one)

Example: 12 and 25 None-Example: 12 and 20

WORD DEFINITION EXAMPLE

Square Number

A number that results from multiply-ing an integer by itself

Examples: 1, 4, 9, 16 Non-Examples: 3, 5, 10, 20

“Say It” Exponential

Form

Visual

Image

Expanded

Form

Standard Form

12

4 x 4

Seven Squared

32

25

Two Squared

Name _________________________________ Date ___________________ Class __________

DIRECTIONS: Fill in the table below. Be

sure to fill in all parts of the table. Show

any necessary work. 6.EE.A.1

“Say It” Exponential

Form

Expanded

Form

Standard

Form

Two Cubed

32

5 x 5 x 5

23

100

DIRECTIONS: Place each of the numbers below in the correct location on the number

lines. Be sure to be accurate.

12 22 32 42 52

62 72 82 92 102

0 100

Name _________________________________ Date ___________________ Class __________

“Say It” Exponential Form Expanded Form Standard Form

4 x 4 x 4

26

Six Cubed

73

25

35

8 x 8 x 8 x 8

92

Twelve Squared

DIRECTIONS: Fill in the table below. Be

sure to fill in all parts of the table. Show

any necessary work. 6.EE.A.1

113 53 + 32

25 ÷ 4 12 + 43

DIRECTIONS: Evaluate each expression below. Show all work. Be sure to try

them all. They increase in difficulty, so the last few might be a challenge.

DIRECTIONS: Place each of the numbers below in the correct location on the num-

ber lines. Be sure to be accurate.

52 23 32 42 33 62

0 50

92 26 43 72 19 82

0 100

Fill in the table below. The last couple are a challenge, try your best! 6.EE.A.1

What is the trick to writing standard form when the base is 10. Look at the table

above to help find a pattern. Write your answer in the space below.

Exponential

Form

Expanded Form Standard

Form

106

105

104

103

102

101

100

10-1

10-2

Name _________________________________ Date ___________________ Class __________

Jocelyn and Paige both invested $100. Jocelyn tripled her investment while Paige cubed her investment. Who has more money now? Explain.

Which of the following is equal to 108 ? Choose the correct answer below. A. Eighty B. One hundred million C. One billion D. One hundred billion

DIRECTIONS: Evaluate each expression below. Show all work. Be sure to try

them all. They increase in difficulty, so the last few might be a challenge.

3 • 105 3(106)

8(103) 36 • 108

4.25 • 104 4.5 • 10-5

DIRECTIONS: Answer the questions below.

Name _________________________________ Date ___________________ Class __________

Fill in the blank spaces of the paragraph below. 6.NS.B.MA.4a

Prime numbers have only __________ factors, the number __________ and

__________. The only even prime number is the number __________ and some other ex-

amples of prime numbers are _____ , _____ , _____ , _____ , _____, and _____. Com-

posite numbers have __________ __________ two factors. Some examples of composite

numbers are _____ , _____ , _____ , _____ , _____ , _____ , and _____. The number

___________ is neither prime nor composite.

Help the dog find its bone by fol-

lowing the path of prime numbers.

The first few are done for you.

Help the dinosaur find its dinner

by following the path of com-

posite numbers. The first few

are done for you.

There is only one even prime number. What is the only even prime number? Explain why all other even numbers must be composite.

Name _________________________________ Date ___________________ Class __________

Use any strategy to find the prime factorization of each of the numbers below.

6.NS.B.MA.4a

20 30 36

15 24 32

60 94 72

84 42 81

90 54 98

Find the number that is equal to each of the prime factorizations below. Write the

number on the line provided.

3x5x7 = _____ 23 x 5 = _____ 2 x 32 x 11 = _____

52 2 x 3 x 52 23 x 33

CHALLENGE: Mrs. Stanton insisted that 22 • 9 was the prime factorization of 36. Do you

agree or disagree? Explain why or why not.

Name _________________________________ Date ___________________ Class __________

Fill in the table below. For each set of numbers list the multiples, find the common multiples, and then find the least common multiple. 6.NS.B.4

Number Multiples Common Multiples

Least Com-mon Multiple

3 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36

4 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

6

8

10

12

9

6

8

12

For each set of numbers list the multiples, find the common multiples, and then find the least common multiple. Show all work. 1.) 5, 3 LCM = _____ 2.) 12, 4 LCM = _____ 3.) 6, 5 LCM = _____

6.) Mrs. Symonds vacuums her floors every 12th day and does laundry every 5th today. If she completes BOTH chores today, in how many days will she complete BOTH chores again on the same day?

7.) Bob is training for a marathon. He takes a day off from running every 6th day and lifts weights every 10th day. Today he took a day off of running and lifted weights. In how many days will he BOTH take a day off of running and lifts weights on the same day again?

8.) The Starks family goes to Disney World every 9th year and to the beach every 6th year. The year 2008 was the last time the Starks family went to BOTH Disney World and the beach. When is the next year they will BOTH go to Disney World and the beach?

The Walget Store is throwing a HUGE Black Fri-day sale. • Every 6th customer will receive a free gift. • Every 8th customer will receive a $10 gift

card. 1.) Hector was the first person to receive a free gift. What number customer was Hector? 2.) Laura was the first customer to receive a $10 gift card. What number customer was Laura? 3.) Sandra was the first customer to receive BOTH a free gift and a $10 gift card. What number customer was Sandra? 4.) Quinn was the second person to receive BOTH a free gift and a $10 gift card. What number customer was Quinn? 5.) Colin was the last person to enter the store for the day. He was the 30th person to receive a free gift. How many $10 gift cards were given out by Walget that day?

Use your knowledge of least common multiple to answer the questions below.

Walget

20

1 x 20 2 x 10 4 x 5

16

40 60

24 36

48 32

18 42

Name _________________________________ Date ___________________ Class __________

Give the factor pairs for each set of numbers below. Then fill in the table with all fac-tors, common factors, and the greatest common factor. 6.NS.B.4

Number Factors

20 1, 2, 4, 5, 10, 20 Common Factors:

16 GCF:

40

Common Factors:

60

GCF:

24

Common Factors:

36

48

Common Factors:

32

GCF:

18

Common Factors:

42 GCF:

Common Factors

List the factor pairs. GCF = __________

30 24


12 20


72 48

30 24

12 20

72 48

Give the factor pairs for each set of numbers below. Then fill in the Venn Diagram with all factors. Finally write the greatest common factor in the space provided.

Name _________________________________ Date ___________________ Class __________

DIRECTIONS: For each example below, find BOTH the greatest common factor AND

least common multiple. Show all work and use the strategy of your choice. 6.NS.B.4

1.) 12 and 20 GCF (12,20) = _____ LCM (12,20) = _____

2.) 8 and 15 GCF (8,15) = _____ LCM (8,15) = _____

3.) 24 and 20 GCF (24,20) = _____ LCM (24,20) = _____

4.) 12 and 9 GCF (12,9) = _____ LCM (12,9) = _____

5.) 6 and 8 GCF (6,8) = _____ LCM (6,8) = _____

6.) 32 and 24 GCF (32,24) = _____ LCM (32,24) = _____

Give an example of two numbers that are relatively prime. Explain why they are rela-tively prime to each other.

Matthew goes hiking every 12 days and swimming every 6 days. He did both kinds of exercise today. How many days from now will he go both hiking and swimming again?

Joanne is campaigning for class president and plans to distribute some campaign mate-rials: 20 flyers and 16 buttons. She wants each classroom to receive an identical set of campaign materials, without having any materials left over. What is the greatest number of classrooms Joanne can distribute materials to?

Edeena is packing equal numbers of apple slices and grapes for snacks. Edeena bags the apple slices in groups of 18 and the grapes in groups of 9. What is the smallest number of grapes that she can pack?

A word problem is started below. Finish the word problem so that it is a LEAST COM-

MON MULTIPLE WORD PROBLEM. Boxes that are 12 inches tall are being

stacked next to boxes that are 18 inches

tall. ___________________________

_______________________________

_______________________________

_______________________________

A word problem is started below. Finish the word problem so that it is a GREATEST

COMMON FACTOR WORD PROBLEM. A club has 16 girls and 8 boys as members. The president wants to break the club into groups, with each group containing the same combination of girls and boys. The president also wants to make sure that

no one is left out. __________________

________________________________

________________________________

DIRECTIONS: Answer each question below. Show all necessary work.

DIRECTIONS: Answer each question below. Show all work. 6.NS.B.4

12 + 8 20 + 15

Make and label an array. Make and label an array.

Rewrite using distributive property.

12 + 8

4( ____ ) + 4( ____ )

4( ____ + ____ )


20 + 15

____ ( ____ ) + ____ ( ____ )

____ ( ____ + ____ )

6 + 15 24 + 18



6 + 15

____ ( ____ ) + ____ ( ____ )

____ ( ____ + ____ )


24 + 18

____ ( ____ ) + ____ ( ____ )

____ ( ____ + ____ )

3 2

4

+

Name _________________________________ Date ___________________ Class __________

14 + 6 18 + 12



14 + 6

____ ( ____ ) + ____ ( ____ )

____ ( ____ + ____ )


18 + 12

____ ( ____ ) + ____ ( ____ )

____ ( ____ + ____ )

9 + 24 16 + 20



9 + 24

____ ( ____ ) + ____ ( ____ )

____ ( ____ + ____ )


16 + 20

____ ( ____ ) + ____ ( ____ )

____ ( ____ + ____ )

Expression Visual Distributive Property

6 + 10

6 ( 3 + 5 )

30 + 12

48 + 72

Name __________________________ Date _______________ Class __________

Distributive Property Fill in the table below with the missing expression as a sum, visual, or expression rewritten using the distributive property. 6.NS.B.4

Expression Visual Distributive Property

7 ( 2 + 3 )

24 + 32

3 ( 6 + 5 )

14 + 16

Factor each expression below using your knowledge of the distributive property and

greatest common factor.

1.) 32 + 40

8(4) + 8(5) 8(___ + ___)

2.) 90 + 60 3.) 18 + 24

4.) 48 + 36 5.) 20 + 28 6.) 80 + 64

SECRET NUMBER: Juanita has a secret number. Read her clues and then answer the

questions that follow: Juanita says, “Clue 1” My secret number is a factor of 60.” 1. What are all the possible secret numbers? 2. Daren said that Juanita’s number must also be a factor of 120. Do you agree or disagree with Daren? Explain your reasoning. 3. Malcolm says that Juanita’s number must also be a factor of 15. Do you agree or disagree with Malcolm? Explain your reasoning. 4. What is the smallest Juanita’s number could be? Explain. 5. What is the largest Juanita’s number could be. Explain. Suppose for Juanita’s third clue she says, “Clue 3: 15 is a multiple of my secret num-

ber.” 6. Now can you tell what her number is? Explain your reasoning. Suppose for Juanita’s fourth clue she says, “Clue 4: My secret number is a factor of

20.” 7. What is Juanita’s secret number?

Name _________________________________ Date ___________________ Class __________

8. Your secret number is 36. Write a series of interesting clues using factors, multiples, and other number properties needed for somebody else to identify your number.

LET’S DISTRIBUTE!!!!

42 + 12 = 6(7+2) Is it true or false? Explain your thinking. 6(7+2) = (6 x 7) + (6 x 2) Is it true or false? Explain your thinking. 6(7 + 2) = (6 x 7) + (6 x 2) = 42 + 12 Is it true or false? Explain your thinking. How is 6 related to 42 and 12? Look at the array model that illustrates the expression 42 + 12 and shows the common factor is 6. Draw array models for each expression below. Then write equivalent expressions

for each expression.

24 + 32 18 + 15 12 + 8

Unit 1 The Number System Homework 2013 - Wikispaces1+The+Number... · 7 Greatest Common Factor GCF Worksheet 8 Least Common Multiple & Greatest Common Factor LCM & GCF Worksheet ...

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