Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Divisibility Practice to review…I can understand and apply divisibility rules for 2, 3, and 5! A number is divisible by another number if the remainder is zero when the second number divides the first number. I can use rules to test for divisibility! RULE Number Theory HW 9.1A 25 is divisible by 5 because the remainder is zero. 25 ÷ 5 = 𝑅 18 is not divisible by 5 because the remainder is not zero. 18 ÷ 5 = 𝑅 DIVISIBLE NOT DIVISIBLE A number is divisible by 𝟐 if the ones digit is 0, 2, 4, 6, or 8. is divisible by 2. is not divisible by 2. A number is divisible by 𝟑 if the sum of the digits is divisible by 3. is divisible by 3. is not divisible by 3. A number is divisible by 𝟓 if the ones digit is 0 or 5. is divisible by 5. is not divisible by 5. Practice to remember… Complete the table. Use a ✓ to show divisibility. 𝟐𝟒 𝟒𝟓 𝟓𝟒 𝟔𝟓 𝟖𝟏 𝟏𝟎𝟖 𝟏𝟏𝟎 𝟏𝟑𝟕 𝟏𝟓𝟑 𝟐𝟏𝟓 𝟒𝟐𝟕 1. divisible by 2 2. divisible by 3 3. divisible by 5 Answer each question. 4. Write five numbers that are divisible by both 2 and 5. What do you notice? 5. Martha says that every multiple of 4 is divisible by 2. Do you agree? Explain. © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Remembering Practice for fluency… Number Theory RE 9.1A 6. A car gas tank holds 85 liters of gas. A second 7. What is the missing amount? car’s tank holds 860 deciliters of gas. How much 380 mm =
cm
more gas does the second car’s tank hold? a. 1 dl a. 38 b. 10 dl b. 380 c. 10 L c. 3,800 d. 1,000 L d. 38,000 Choose an appropriate graph for the data described. Write pictograph, bar graph, double bar graph, line graph, double line graph, or circle graph. 8. the number of each type of pet owned by students in a fifth grade class _________________________ 9. the length of Spike, a pet snake, recorded every month since his birth 10. the ways a fifth grade student spends a weekly allowance of $7 11. the amount of weight gained by George’s puppy in the first six weeks he owned it _________________________ _________________________ _________________________ Answer each question. Explain your thinking. 12. Mrs. Palmer buys 70 apples for making pies. Each pie uses 11 apples. The rest will be used for applesauce. How many apples will go into the applesauce? Explain. 13. Britney added 1.625 and 0.43 and got 1.668. Explain what mistake B ritney made. Then give the correct sum. © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Prime and Composite Numbers Practice to review…I can identify prime and composite numbers! A factor is one of two or more numbers multiplied to find a product. Number Theory HW 9.1B A multiple is the product of two or more factors. 5 is a factor of 15 because 5 × = 15. 15 is a multiple of 5. A prime number is a number with exactly two factors – 1 and the number itself. A composite number is a number with more than two factors. EXAMPLES OF PRIME NUMBERS EXAMPLES OF COMPOSITE NUMBERS The number 1 has only one factor! 1 is not prime. 1 is not composite. Practice to remember… Write all the factors for each number. 1. 12 2. 15 3. 40 _________________ _________________ _________________ _________________ _________________ _________________ Write the first five multiples for each number. 4. 3 5. 8 6. 12 _________________ _________________ _________________ _________________ _________________ _________________ Write prime or composite for each number. 7. 29 8. 60 9. 99 _________________ _________________ _________________ 10.
83 11.
17 _________________ _________________ © Lincoln Public Schools, 2014 12. 27 _________________ 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Remembering Practice for fluency… Number Theory RE 9.1B 13. The bookcase in class 5A is 64 inches long. The 14. Compare. bookcase in class 5B is 2 feet shorter. How many 2 yd 6 in. 75 in.
inches shorter is the bookcase in class 5B? a. 2 in. b. 12 in. c. 24 in. d. 40 in. a. > b. < ____________________ 16. How many more boys than girls play basketball? ____________________ 17. Suppose that 8 more boys join the tennis team. How would that change the graph? Use the double bar graph to answer the questions. 15. For which sport is there the greatest difference between the number of girls and boys who participate? c. = ____________________ 18. According to the graph, do more boys or girls participate in sports? How ____________________ many more? The line plot shows the number of hours Ben watched television each day. Use the line plot to answer the questions. 19. Find the mean, median, and mode of the data. mean: ______________ median: ____________ mode: ______________ 20. Predict the number of hours Ben will likely spend watching television tonight. Explain your thinking. © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Prime Factorization Practice to review…I can write the prime factorization of a number! Representing a whole number as the product of prime factors is called prime factorization. Every whole number has a unique prime factorization. Number Theory HW 9.2 prime factorization of 45 without exponents: 45 = 3 • 3 • 5 with exponents: 45 = 3! • 5 I can use factor trees to find the prime factorization of whole numbers! 10 24 17 10 = 24 = 17 = Practice to remember… Make a factor tree to find the prime factorization of each number 1. 20 = 2. 28 = 3. 23 = 4. 30 = 5. 65 = 6. 81 = Answer the question. 7. The prime factorization of a number is 2! • 5! . What is the number? Show how you know. © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Remembering Practice for fluency… 8. Number Theory RE 9.2 Tammy works in a bookstore. There are 896 books to be packed into crates. Tammy can pack 128 books into one large crate. The small crates will hold 64 books each. If Tammy only uses small crates, how many will she need? 9. Divide. a. 12 b. 14 a. 4,008 R 4 b. 412 c. 120 d. 140 c. 408 R 4 d. 48 R 4 36 14,692
!
Divide. 10.
94 7,219 !
12. 8,456 ÷ 21 = 11. 47 20,019 !
13. 446,109 ÷ 37
= Use the data from the table to answer the questions. 14. In the United States, Alaska has the highest proportion of people on the Internet. About 348,612 of Alaska’s 627,000 citizens used the Internet in 2000. Round 348,612 to the same place as the figure for the total population. 15. New York had 7,552,448 Internet users in 2000. If these data were a dded to the table, between which two states would its number fall? © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Greatest Common Factor Number Theory HW 9.3A Practice to review…I can find common factors and the greatest common factor of two numbers! Factors that two or more numbers have in common are called common factors of those numbers. The greatest common factor (GCF) of two or more numbers is the common factor that is greater than all other common factors of the numbers. The GCF is also called the greatest common divisor (GCD). Example: The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. The common factors of 18 and 24 are 1, 2, 3, and 6. The greatest common factor (GCF) of 18 and 24 is 6. I can list factors of whole numbers to find common factors and the greatest common factor! The factors of 40 are: The factors of 50 are: The common factors of 40 and 50 are ________________________________________ . The greatest common factor of 40 and 50 is __________ . Practice to remember… List the factors of each number. Tell the common factors and the greatest common factor of the numbers. 1. 4: ______________________________________ 2. 12: ____________________________________ 10: _____________________________________ 14: ____________________________________ common factors of 4 and 10: ________________ common factors of 12 and 14: ______________ GCF (4, 10) = GCF 12, 14 = 3. 6: ______________________________________ 4. 7: _____________________________________ 21: _____________________________________ 9: _____________________________________ common factors of 6 and 21: ________________ common factors of 7 and 9: ________________ GCF 6, 21 = GCF 7, 9 = © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Remembering Practice for fluency… Number Theory RE 9.3A Simplify.
6. 6 + 2 × 6 ÷ 2!
5. 4 + 8 − 2 • 5 a. 2 b. 26 a. 3 b. 6 c. 34 d. 50 c. 9 d. 12 Use the data from the line plot to answer the questions. 7. How many holes were played? __________________ 8. What is the mean of the data? __________________ 9. What is the mode of the data? __________________ 10. What is the median of the data? _________________ Use the data from the table to answer the questions. 11. Give an example showing the use of the Associative Property of Multiplication. Explain. 12. Explain how you could use multiplying by tens to find the product of 82 × 40. © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Greatest Common Factor Number Theory HW 9.3B Practice to review…I can find common factors and the greatest common factor of two numbers! Factors that two or more numbers have in common are called common factors of those numbers. The greatest common factor (GCF) of two or more numbers is the common factor that is greater than any other common factor of the numbers. We can use prime factorization to find the GCF of two numbers. !
18
Example: The prime factorization of 18 is 2 • 3 • 3. !
!!!!!!!!!!!!!!!!
The prime factorization of 24 is 2 • 2 • 2 • 3. The common prime factors of 18 and 24 are 2 and 3. 3
So, the greatest common factor (GCF) of 18 and 24 is 2 • 3 or 6. 24
1, If the GCF is
e no there will b
me common pri
factors! !!!!!!!!!!!!!!!
2
2
3
2
I can use the prime factorization to find the greatest common factor of two numbers! 40 50 Organize the prime factors in the diagram. 40
50
!
!!!!!!!!!!!!!!!!
40 = 50 = !!!!!!!!!!!!!!!
The common prime factors of 40 and 50 are ________________ . The greatest common factor of 40 and 50 is _________________ . Practice to remember… Write the prime factorization of each number. Then find the greatest common factor of the numbers. 1. 40 = _____________________ 2. 16: _______________________ 48 = _____________________ 20: _______________________ GCF (40, 48) = _____________ GCF 16, 20 = _____________ 3. 18: _______________________ 4. 15: _______________________ 25: _______________________ 60: _______________________ GCF 18, 25 = _____________ GCF 15, 60 = _____________ © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Remembering Practice for fluency… Number Theory RE 9.3B 5. Lori gave each of her 2 brothers the same 6. Use mental math to solve for the value of 𝑔. number of crackers. She gave them 8 crackers in 84 ÷ 𝑔 = 7
all. How many did she give each brother? a. 2 crackers b. 4 crackers a. 𝑔 = 588 b. 𝑔 = 91 c. 8 crackers d. 16 crackers c. 𝑔 = 77 d. 𝑔 = 12 List all the factors of each number. Then tell if the number is prime or composite. 7. 18 _____________________________ 8. 19 _____________________________ 9. 20 _____________________________ _____________________________ _____________________________ _____________________________ 10. 21 _____________________________ _____________________________ Use the data from the table to answer the questions. 11. Add parentheses to make the value of the expression 45. Simplify the expression to check. 7 × 4 + 3 − 2! 12. Tameka divided 363 by 58 and got 6. Explain what Tameka’s mistake was. Then tell the correct answer. © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Greatest Common Factor Number Theory HW 9.3C Practice to review…I can find common factors and the greatest common factor of two numbers! Factors that two or more numbers have in common are called common factors of those numbers. The greatest common factor (GCF) of two or more numbers is the common factor that is greater than any other common factor of the numbers. 15
!
!!!!!!!!!!!!!!!!
We can use different strategies to find the GCF of 15 and 20. !!!!!!!!!!!!!!!
WAY 1: Make a list. WAY 2: Use prime factorization. The factors of 15 are 1, 3, 5, and 15. The prime factorization of 15 is 3 • 5. The factors of 20 are 1, 2, 4, 5, 10 and 20. The prime factorization of 20 is 2 • 2 • 5. The common factors of 15 and 20 are 1 and 5. The o nly common prime factor of 15 and 20 is 5. The GCF of 15 and 20 is 5. So, the GCF of 15 and 20 is 5. Choose a strategy to find the greatest common factor of 21 and 25! 20
3
5
2
2
s 1, If the GCF i
e no b
there will me ri
p
common ! factors
GCF 21, 25 = Practice to remember… Choose a strategy. Find the greatest common factor of the numbers. Show your thinking. 1. GCF (16, 42) = 2. GCF 24, 56 = 3. GCF (12, 30) = 4. GCF 25, 75 = © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Practice to remember, continued… Answer the question. Number Theory RE 9.3C 5. Tia made 50 cupcakes and 160 cookies for a bake sale. She uses all the items to make treat boxes that have both cupcakes and cookies. If she puts an equal number of cupcakes and an equal number of cookies in each treat box, what is the greatest number of treat boxes can she make? How many of each item will be in a box? Remembering Practice for fluency… 6. The bookstore received a delivery of 8 boxes. Each box contained 65 books. Nine books were damaged and returned. How many books did the bookstore keep? 7. Multiply. a. 520 b. 511 a. 18,990 b. 18,960 c. 480 d. 471 c. 18,690 d. 18,660 3,165 • 6
Complete. 8. 55 m = dm Compare. Write >, <, or = for each 9. . cm = 20 mm 10. 50 cm 5 dm 11.
8 km 9,000 m Use the graph to answer the question. 12. At the end of 2 hours, what was the difference in distance biked by N ell and Jose? Explain. © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Least Common Multiple Number Theory HW 9.4A Practice to review…I can find common multiples and the least common multiple of two or more numbers! Multiples that two or more numbers have in common are called common multiples of those numbers. The least common multiple (LCM) of two or more numbers is the common multiple that is less than all other common multiples of the numbers. Example: The first several multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, … The first several multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, … Some common multiples of 6 and 9 are 18, 36, and 54. The least common multiple (LCM) of 6 and 9 is 18. I can list multiples of whole numbers to find common multiples and the least common multiple! The first several multiples of 4 are: The first several multiples of 12 are: The least common multiple of 4 and 12 is ____________ . Practice to remember… List multiples of each number. Find the least common multiple of the numbers. 1. 4: ______________________________________ 2. 12: ____________________________________ 10: _____________________________________ 14: ____________________________________ LCM (4, 10) = LCM 12, 14 = 3. 9: ______________________________________ 4. 20: ____________________________________ 15: _____________________________________ 30: ____________________________________ LCM 9, 15 = LCM 20, 30 = Answer the question. Show your thinking. 5. Will has a guitar lesson every 3 days and a piano lesson every 5 days. How often does he have a guitar and a piano lesson on the same day? Show how you know. © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Remembering Practice for fluency… Number Theory RE 9.4A Use the graph to answer the questions.
6. Which activity was more popular with girls than boys? a. E-­‐mail b. Web Search c. Games d. Word Processing 7. How many boys are represented in the graph? a. 48 boys b. 52 boys c. 56 boys d. 60 boys List all common factors for the numbers. Find the greatest common factor of the numbers. 12, 30 _______________________________ 9. 10. 35, 70 _______________________________ 11. GCF 35, 70 = 8. GCF 21, 30 = Answer the questions. Show your thinking. 12. Park rangers are cutting 7-­‐foot lengths of rope. How many lengths c an they make from 85 feet of rope? Explain. 13. Scott has 72 baseball cards. He wants to display them in rows with an equal number of cards. How many different ways can Scott set up the rows? Explain. © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Number Theory HW 9.4B Name: _______________________________________ Date: __________________ Least Common Multiple Practice to review… I can find common multiples and the least common multiple of two or more numbers! Multiples that two or more numbers have in common are called common multiples of those numbers. The least common multiple (LCM) of two or more numbers is the common multiple that is less than all other common multiples of the numbers. !
18
Example: The prime factorization of 18 is 2 • 3 • 3. !
!!!!!!!!!!!!!!!!
The prime factorization of 24 is 2 • 2 • 2 • 3. !!!!!!!!!!!!!!!
3
The least common multiple (LCM) of 18 and 24 is the product of all the prime factors of the two numbers (using common factors only once). 24
2
2
3
2
So, LCM 18, 24 = 2 • 2 • 2 • 3 • 3 = 72. I can use the prime factorization to find the greatest common factor of two numbers! 40 50 !
Organize the prime factors in the diagram. 40
50
!
!!!!!!!!!!!!!!!!
40 = 50 = !!!!!!!!!!!!!!!
The least common multiple of 40 and 50 is ________________________ . Practice to remember… Write the prime factorization of each number. Then find the least common multiple of the numbers. 1. 6 = ______________________ 2. 4: ________________________ 8 = ______________________ 7: ________________________ LCM (6, 8) = _______________ LCM 4, 7 = _______________ 3. 3: ________________________ 4. 30: _______________________ 12: _______________________ 40: _______________________ LCM 3, 12 = _____________ LCM 30, 40 = _____________ © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Remembering Practice for fluency… Number Theory RE 9.4B 5. What is the value of the digit 7 in 370,465? 6. What is the value of the digit 3 in 536,407,089?
a. 7 tens b. 7 hundreds a. 30 b. 30,000 c. 7 thousands d. 7 ten-­‐thousands c. 300,000 d. 30,000,000 List all the factors for each number. List the first five multiples of each number. 7. 36 _____________________________ 8. 9 _____________________________ 9. 100 _____________________________ 10. 12 _____________________________ Use the data from the table to answer the questions. 11. Kareem and Dylan have 45 trading cards. Kareem has 2 times as many cards as Dylan. How many trading cards does Dylan have? Show how you know. 12. Sally spends about $20 a week on school lunches. About how much m
oney does she spend on lunches during the 39-­‐week school year? Show your thinking. © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Least Common Multiple Number Theory HW 9.4C Practice to review… I can find common multiples and the least common multiple of two or more numbers! Multiples that two or more numbers have in common are called common multiples of those numbers. The least common multiple (LCM) of two or more numbers is the common multiple that is less than all other common multiples of the numbers. 12
We can use different strategies to find the LCM of 12 and 28. 28
!
!!!!!!!!!!!!!!!!
WAY 1: Make a list. WAY 2: Use prime factorization. Some multiples of 12 are 12, 24, 48, 60, 72, 84, … The prime factorization of 12 is 2 • 2 • 3. Some multiples of 28 are 28, 56, 84, 112, … The prime factorization of 28 is 2 • 2 • 7. LCM 24, 36 = LCM (24, 36) = 3
!!!!!!!!!!!!!!!
2
2
7
Choose a strategy to find the least common multiple of 5 and 21! LCM 5, 21 = Practice to remember… Choose a strategy. Find the least common multiple of the numbers. Show your thinking. 1. LCM (15, 25) = 2. LCM 6, 7 = 3. LCM (2, 17) = 4. LCM 12, 90 = © Lincoln Public Schools, 2014 5th Grade Math Chapter 9, Part 1 Name: _______________________________________ Date: __________________ Practice to remember, continued… Answer the question. Number Theory RE 9.4C 5. The downtown bus leaves the station every 15 minutes. The uptown bus leaves the station every 35 minutes. Both buses start the day leaving the station at 7: 00 A.M. When is the next time both buses will leave the station at the same time? Show how you know. Remembering Practice for fluency… 6. Write forty-­‐seven hundredths in standard form. 7. Which is a true statement?
a. 4,700 a. 2546,000 = 2,545,000 b. 0.47 b. 14,350,000 < 1,435,000 c. 0.047 c. 73,000,009 < 73,000,090 d. 0.0047 d. 1,062,400 > 1,064,200 Round to the nearest whole number. 8. 17.343 10. 0.635 Compare. Write >, <, or = for each _________________________ 9. 0.7 _________________________ 11. 1.475 . 0.008 1.494 Use the data to complete the graph. 12. The Wildlife Club has many books on wild animals. Rolf counted 250 books on birds, 50 books on snakes, 275 books on wild cats, 150 books on gorillas, and 100 books on elephants. © Lincoln Public Schools, 2014 5th Grade Math