My hair is the main factor for my dashing good looks! Mike s Math Mall

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1 My hair is the main factor for my dashing good looks!

2 This bundled lesson completely covers CCSS 4.OA.B.4 for Gaining Familiarity with Factors and Multiples. Gain familiarity with factors and multiples. CCSS.Math.Content.4.OA.B.4 Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one-digit number. Determine whether a given whole number in the range is prime or composite.

3 Factors, Multiples, Prime, and Composite from 1 to 100 Table of Contents Note: Colored pencils, crayons, or markers needed for Practice C and Practice D. 11 x 17 white poster paper works best for Practice C. Practice and Activities Practice A Skip Counting 2 Practice B Factors and Multiples Decoder Puzzle 3 Practice C Factor Rainbow Activity Preface 4 Practice C Factor Rainbow Poster Activity 5 Practice D Discovering Prime and Composite Numbers Activity 6 Practice D Hundreds Chart (for Practice D Activity) 7 Practice E Exploring Prime and Composite Numbers 8 Practice F Sorting Prime and Composite Numbers 9 Practice G Word Problems; Factors, Multiples, Prime and Composite 10 Note: Flash cards are ready to print back-toback with cut lines. Laminating is optional. Assessment Factors and Multiples 11 Prime and Composite Numbers 12 Practice and Activity Answers Practice A Answers 13 Practice B Answers 14 Practice D Answers 15 Practice D Answer Diagram 16 Practice E Answers 17 Practice F Answers 18 Practice G Answer 19 Assessment Answers Factors and Multiples - Answers 20 Prime and Composite Numbers - Answers 21 Factors/Multiples/Prime/ Composite Flash Card Set See Flash Cards PDF PowerPoint See PowerPoint File 27 pages 17 slides 1

4 Skip Counting! I can skip Practice A count, chew gum, Gymnastics for your Brain and breath all at the same time! Mentally skip count by the following numbers to each given place. Every level completed advances you to the next difficulty level. Good luck, my number skipping friends! 1) Skip count by 5s to 65: Difficulty Level: Beginning Number Cruncher 2) Skip count by 3s to 39: Difficulty Level: Number Skipping Cadet 3) Skip count by 4s to 52: Difficulty Level: Number Ninja 4) Skip count by 6s to 72: Difficulty Level: Basic Human Calculator 5) Skip count by 7s to 84: Difficulty Level: Elementary Math Expert 6) Skip count by 8s to 96: Difficulty Level: Future Math Professor 7) Skip count by 9s to 99: Difficulty Level: You Scare Numbers Everywhere 8) Skip count by 12s to 96: Difficulty Level: World Number Dominator 9) Skip count by 13s to 91: Difficulty Level: Master of the Numbered Universe 2

5 Exploring Factors and Multiples Practice B Find the factor pair in the answer bank that goes along with each multiple to help you solve the puzzle below. Number 1 has been completed for you! 1) ) 16 3) 24 4) 31 5) 45 6) 32 7) 47 8) 54 9) 66 10) 48 11) 75 12) 82 13) 87 14) 72 15) 69 16) 52 17) 86 18) 98 19) 91 Answer Bank 11 6 I 15 5 S 3 23 H 2 43 N 6 9 U 2 11 V M 2 41 O 8 4 A 6 12 B 47 1 G 8 3 K 7 13 L C 4 13 Y 14 7 E 3 15 W 1 31 R 1 87 F How can you tell when Sparky s had too many burritos to eat? ! V

6 Practice C Factor Rainbow Activity Preface (for teacher) This is a fun activity that illustrates factor pairs graphically. It s also a great way to brighten up your room or bulletin board any time of year. The completed posters are a great visual aid for those tough multiplication facts. This activity is automatically differentiated as you might assign less-rigorous multiples to your lower achievers and tougher multiples to your high fliers. Because the posters may be displayed and used by some students as visual aids, continue to emphasize to your students to use the entire paper and to make their numbers large and bold. Obviously, the larger and whiter the paper, the better. Colored pencils, crayons, or markers all work great, and if you re brave enough, paint can be used to create rainbow arches! Good luck and have fun with the activity. I hope your room becomes a colorful and useful explosion of factor rainbows! 4

7 Factor Rainbows! Notice! You ll need plain white paper (11 x 17 is best) and colored pencils, crayons, or markers to complete this activity. 1. Your teacher will assign you a composite number that has several factors. Practice C 2. Write the words Factor Rainbow for (insert number here) near the top of your paper. Be creative when designing your composite number! Don t be afraid to draw BIG and bold! Factor Rainbow for 3. List the factors for your number from least to greatest, and line them up near the bottom of the paper (put a little bit of space between each number, and make the numbers big enough to be seen from a distance) Connect factor pairs with different color rainbow arches. If you have a single, middle factor, just put a colorful square around it, showing that it gets multiplied by itself. 5. Design the rest of the poster any way you want. You might add clouds, birds, butterflies, trees, kites, airplanes, hotair balloons, flowers, or whatever you want. Be sure to be creative and colorful, and have fun! 5

8 The Prime Time Number Chart! Notice! You ll need a hundreds chart and colored pencils or crayons to complete this activity. Practice D 1. Using your hundreds chart, color box number 1 red since it s our starting number. 2. Using yellow, completely color in the number 2 box. Next, use purple to draw a diagonal line through every multiple of 2 on the entire chart. Try skip counting to do this! 3. Using yellow again, completely color in the number 3 square. Next, use orange to draw a diagonal line through every multiple of 3 on the chart. Try skip counting again! What does a purple and orange X tell you about a number? 4. Using yellow again, completely color in the number 5 square. Then use green to draw a horizontal line through every multiple of 5 on the chart. What s the first number with all three colored lines drawn through it? What does that tell you about this number? Examples Find the next open number box and completely color it in with yellow. Then use blue to draw a vertical line through every multiple of 7. Keep skip counting you can do it! Continue coloring the next open box yellow. Then use a new color to draw lines through all the multiples of that yellow-boxed number. Skip count at your own risk! Color all remaining open boxes yellow. 7. What do we call all of the yellow-boxed numbers? How many of these yellow-boxed numbers are there on this chart? What do we call the numbers that are crossed by colored lines? 6

9 Hundreds Chart For Practice D Divisibility Rules A number is divisible by 2 if its last digit is even. A number is divisible by 3 if the sum of its digits is also divisible by 3. All numbers that can be halved twice (into whole numbers) are divisible by 4. A number is divisible by 5 if its last digit is 0 or 5. A number is divisible by 6 if that number is also divisible by 2 and 3. You re on your own with 7! Sorry! The rule for 8 is not helpful here either! Bummer! A number is divisible by 9 if the sum of its digits is also divisible by A number is divisible by 10 if its last digit is 0. 7

10 Practice E Exploring Prime and Composite Numbers List all of the prime numbers up to 100 (a hundreds chart might come in handy ). I d rather explore the lunch line! 1.,,,,,,,,,,,,,,,,,,,,,,,,. List all of the factors for each number. Then write P for prime or C for composite. Answer the following questions. 2. Why is 1 considered the loneliest number? 3. 2 is the only even prime number. Why is 2 considered prime? 4. What are all of the factors of 20? What are the multiples of 20 up to 100? Number All factors from least to greatest P or C?

11 Practice F Prime or Composite? Place each Prime number on the Pineapple and each Composite number on the Can. The first one has been completed for you. Cross each number off as you go! 9 9

12 Problem Solving! Practice G Answer the following questions. Be sure to read each question carefully. 1) Sparky says that all prime numbers are odd. Explain why Sparky s statement is incorrect. 2) List three different multiples that each have 3, 4, and 6 as factors. 3) List three different multiples that each have 2, 5, and 10 as factors. 4) Which number has more factors, 36 or 40? List the factors for each number to find out. 36: 40: and the winner is? ) Which number is not a factor of 84? 2, 3, 4, 6, 7, 8 6) What are all of the prime numbers between 30 and 60? 6) A number is divisible by 3 if the sum of its digits is also divisible by 3. Use this rule to see which of the following numbers are divisible by 3 (circle all answers). 18, 32, 39, 41, 42, 48, 51, 54, 60, 62, 69, 72, 76, 81, 85, 87, 93, 97 10

13 Assessment page 1 of 2 Read each question and circle the correct the answer. Factors and Multiples Time to show your stuff! 1) Which number is a factor of 27? 2, 4, 9, 13 2) Which number is a multiple of 7? 12, 24, 33, 49 3) Which number is not a factor of 35? 3, 5, 7, 35 4) Which number is not a multiple of 9? 18, 27, 39, 45 Complete the following problems. 5) List all of the factors of 24 from least to greatest: 6) List all of the factors of 31 from least to greatest: 7) List all of the factors of 100 from least to greatest: 8) List five different multiples that each have 2 and 10 as factors: 9) List three different multiples that each have 2, 3, and 4 as factors: 10) Which number has more factors, 12 or 27? 11) Which number has more factors, 20 or 36? 12) List all of the factor pairs for 48: (2 x 10 is a an example factor pair) 11

14 Assessment page 2 of 2 Prime and Composite Numbers You can do it! Place the following numbers into the correct box. 13) 2, 7, 10, 13, 18, 19, 25, 27, 31, 39, 40, 47, 52, 63, 67, 77, 79, 81, 90, 95 Prime Composite Complete the following problems. 14) List all of the composite numbers, in order, from 2 to 20: 15) List all of the prime numbers, in order, from 20 to 40: 16) Explain the difference between a prime number and a composites number. Bonus) What is the greatest prime number between 1 and 100? 12

15 Practice A Answer Key I can skip count, chew gum, and breath all at the same time! 1) Skip count by 5s to 65: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65 2) Skip count by 3s to 39: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39 3) Skip count by 4s to 52: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52 Difficulty Level: Number Ninja 4) Skip count by 6s to 72: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72 5) Skip count by 7s to 84: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84 Difficulty Level: Elementary Math Expert 6) Skip count by 8s to 96: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96 Difficulty Level: Future Math Professor 7) Skip count by 9s to 99: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99 Difficulty Level: You Scare Numbers Everywhere 8) Skip count by 12s to 96: 12, 24, 36, 48, 60, 72, 84, 96 Difficulty Level: World Number Dominator Skip Counting! Mentally skip count by the following numbers to each given place. Every level completed advances you to the next difficulty level. Good luck, my number crunching friends! Difficulty Level: Beginning Number Cruncher Difficulty Level: Number Skipping Cadet Difficulty Level: Basic Human Calculator Gymnastics for your Brain 9) Skip count by 13s to 91: 13, 26, 39, 52, 65, 78, 91 Difficulty Level: Master of the Numbered Universe 13

16 Practice B Exploring Factors and Multiples Answer Key Find the factor pair in the answer bank that goes along with each multiple to help you solve the puzzle below. Number 1 has been completed for you! 1) ) 16 3) 24 4) 31 5) 45 6) 32 7) 47 8) 54 9) 66 10) 48 11) 75 12) 82 13) 87 14) 72 15) 69 16) 52 17) 86 18) 98 19) 91 Answer Bank 11 6 I 15 5 S 3 23 H 2 43 N 6 9 U 2 11 V M 2 41 O 8 4 A 6 12 B 47 1 G 8 3 K 7 13 L 4 12 C 4 13 Y 14 7 E 3 15 W 1 31 R 1 87 F How can you tell when Sparky s had too many burritos to eat? H E S S O F U L L H E C A N N O L O N G E R M A K E ! H I S B E L L Y W A V E

17 Notice! The Prime Time Number Chart! Practice D Answer Key You ll need a hundreds chart and colored pencils or crayons to complete this activity. 1. Using your hundreds chart, color box number 1 red since it s our starting number. 2. Using yellow, completely color in the number 2 box. Next, use purple to draw a diagonal line through every multiple of 2 on the entire chart. Try skip counting to do this! 3. Using yellow again, completely color in the number 3 square. Next, use orange to draw a diagonal line through every multiple of 3 on the chart. Try skip counting again! What does a purple and orange X tell you about a number? Any number with a purple and orange X is a multiple of 2 and 3 (or they have factors of both 2 and 3). 4. Using yellow again, completely color in the number 5 square. Then use green to draw a horizontal line through every multiple of 5 on the chart. What s the first number with all three colored lines drawn through it? What does that tell you about this number? 30 is the first number. 30 is a multiple of 2, 3, and 5 (or 30 has factors of 2, 3, and 5). Examples Find the next open number box and completely color it in with yellow. Then use blue to draw a vertical line through every multiple of 7. Keep skip counting you can do it! Continue coloring the next open box yellow. Then use a new color to draw lines through all the multiples of that yellow-boxed number. Skip count at your own risk! Color all remaining open boxes yellow. 7. What do we call all of the yellow-boxed numbers? Yellow boxes are all prime numbers. How many of these yellow-boxed numbers are there on this chart? There are 25 prime numbers on the chart. What do we call the numbers that are crossed by colored lines? They are composite numbers. 15

18 Practice D Answer Diagram Hundreds Chart Some colors may vary! Divisibility Rules A number is divisible by 2 if its last digit is even. A number is divisible by 3 if the sum of its digits is also divisible by 3. A number is divisible by 4 if its last two digits form a number divisible by 4 (not very helpful here). A number is divisible by 5 if its last digit is 0 or 5. A number is divisible by 6 if that number is also divisible by 2 and 3. You re on your own with 7! Sorry! The rule for 8 is not helpful here either! Bummer! A number is divisible by 9 if the sum of its digits is also divisible by A number is divisible by 10 if its last digit is 0. 16

19 Practice E Answer Key List all of the prime numbers up to ,,,,,,,,,,,,,,,,,,,,,,,,. Exploring Prime and Composite Numbers I d rather explore the lunch line! List all of the factors for each number. Then write P for prime or C for composite. Answer the following questions. 2. Why is 1 considered the loneliest 1 is considered the loneliest number? number because 1 is neither prime nor composite is the only even prime number. Why is 2 considered prime? 2 is considered a prime number because 2 only has two factors, 1 and itself. 4. What are all of the factors of 20? 1, 2, 4, 5, 10, and 20 What are the multiples of 20 up to 100? 20, 40, 60, 80, and Number All factors from least to greatest P or C? 7 1, 7 P 9 1, 3, 9 C 12 1, 2, 3, 4, 6, 12 C 15 1, 3, 5, 15 C 23 1, 23 P 24 1, 2, 3, 4, 6, 8, 12, 24 C 36 1, 2, 3, 4, 6, 9, 12, 18, 36 C 45 1, 3, 5, 9, 15, 45 C 47 1, 47 P 60 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 C 17

20 Practice F Prime or Composite? Place each Prime number on the Pineapple and each Composite number on the Can. The first one has been completed for you. Cross each number off as you go! Answer Key (out of 24)

21 Answer Key Problem Solving! Practice G Answer the following questions. Be sure to read each question carefully. 1) Sparky says that all prime numbers are odd. Explain why Sparky s statement is incorrect. Sparky is incorrect because 2 is an even number and it is prime. 2) List three different multiples that each have 3, 4, and 6 as factors. 12, 24, and 36 (or 48, 60, etc.) 3) List three different multiples that each have 2, 5, and 10 as factors. 10, 20, and 30 (or 40, 50, etc.) 4) Which number has more factors, 36 or 40? List the factors for each number to find out. 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 40: 1, 2, 4, 5, 8, 10, 20, 40 and the winner is? ) Which number is not a factor of 84? 8 2, 3, 4, 6, 7, 8 6) What are all of the prime numbers between 30 and 60? 31, 37, 41, 43, 47, 53, and 59 6) A number is divisible by 3 if the sum of its digits is also divisible by 3. Use this rule to see which of the following numbers are divisible by 3 (circle all answers). 18, 32, 39, 41, 42, 48, 51, 54, 60, 62, 69, 72, 76, 81, 85, 87, 93, 97 19

22 Assessment Answers page 1 of 2 Read each question and circle the correct the answer. Factors and Multiples Time to show your stuff! 1) Which number is a factor of 27? 2, 4, 9, 13 2) Which number is a multiple of 7? 12, 24, 33, 49 3) Which number is not a factor of 35? 3, 5, 7, 35 4) Which number is not a multiple of 9? 18, 27, 39, 45 Complete the following problems. 5) List all of the factors of 24 from least to greatest: 1, 2, 3, 4, 6, 8, 12, and 24 6) List all of the factors of 31 from least to greatest: 1 and 31 7) List all of the factors of 100 from least to greatest: 1, 2, 4, 5, 10, 20, 25, 50, and 100 8) List five different multiples that each have 2 and 10 as factors: Possible answers: 10, 20, 30, 40, 50, etc. 9) List three different multiples that each have 2, 3, and 4 as factors: Possible answers: 12, 24, 36, 48, 60, etc. 10) Which number has more factors, 12 or 27? 12 11) Which number has more factors, 20 or 36? 36 12) List all of the factor pairs for 48: 1 x 48, 2 x 24, 3 x 16, 4 x 12, and 6 x 8 (2 x 10 is a an example factor pair) 20

23 Assessment Answers page 2 of 2 Prime and Composite Numbers You can do it! Place the following numbers into the correct box. 13) 2, 7, 10, 13, 18, 19, 25, 27, 31, 39, 40, 47, 52, 63, 67, 77, 79, 81, 90, 95 Prime Composite 2, 7, 13, 19, 31, 47, 67, 79 10, 18, 25, 27, 39, 40, 52, 63, 77, 81, 90, 95 Complete the following problems. 14) List all of the composite numbers, in order, from 2 to 20: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, and 15) List all of the prime numbers, in order, from 20 to 50: 23, 29, 31, 37, 41, 43, and 47 16) Explain the difference between a prime number and a composites number. A prime number is a whole number that can only be divided evenly by one and itself. A composite number is a whole number that can be divided evenly by numbers other than 1 and itself. Bonus) What is the greatest prime number between 1 and 100? 97 21