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Rising 6th Grade Level Math Summer Work Packet Name ____________ Date _________ Rising 6th Grade Level Math Summer Work Dear student: Included here is your summer math work. Work thoughtfully throughout the summer to complete the problems, showing your work and labeling your answers. Many of the problems are review and application of the ideas and skills worked on this past school year. A few problems may need you to use a hint or outside resource (internet or other mathematician) to help you solve the problem. There may be one or two problems that are meant to stretch you mathematically. TRY them anyway. Leave no problem blank. Bring this packet to your math teacher on the first day of school in September. If you have any questions, please email me at [email protected] Name _______________________ Operations and Properties Practice A: Estimating with Whole Numbers Round each number to the greatest place value. 1. 67 _____ 2. 81 _____ 3. 24 _____ 4. 115 _____ 5. 575 _____ 6. 1,852 _____ Estimate each sum or difference. 7. 42 19 _______________________ 10. 93 14 _______________________ 8. 63 28 ________________________ 11. 104 178 ________________________ 9. 37 34 ________________________ 12. 112 9 ________________________ Estimate each product. 13. 2 19 _______________________ 14. 87 2 ________________________ 15. 26 3 ________________________ Rewrite each problem using compatible numbers. Then divide. 16. 148 5 _______________________ 19. 62 3 _______________________ 17. 412 4 ________________________ 20. 40 7 ________________________ 18. 70 6 ________________________ 21. 29 4 ________________________ 22. A fin whale weighs 44 tons. A gray whale weighs 32 tons. About how much more does a fin whale weigh than a gray whale? ________________________________________________________________________________________ 23. The Suez Canal in Egypt is 108 miles long. The Erie Canal in New York is 363 miles long. About how long are the two canals together? ________________________________________________________________________________________ Operations and Properties Practice A: Order of Operations (PEMDAS) Name the operation you should perform first. 1. 5 6 2 2. 18 3 1 _______________________ 4. 32 6 3. 4 (7 1) ________________________ 5. (15 38) 6 _______________________ ________________________ 6. 5 10 12 ________________________ ________________________ Match each expression to its value. Expression Value _________________ 7. 7 8 2 A. 9 _________________ 8. 9 (12 10) B. 40 _________________ 9. (20 15) 2 C. 12 _________________ 10. 10 5 7 D. 0 _________________ 11. 6 2 3 E. 16 _________________ 12. (2 4) 8 F. 11 _________________ 13. 14 2 0 G. 13 _________________ 14. (5 1) 10 H. 10 15. Sam bought two CDs for $13 each. Sales tax for both CDs was $3. Write an expression to show how much Sam paid in all. ________________________________________________________________________________________ 16. Alicia made 24 chocolate chip cookies and 36 sugar cookies. Then she divided all the cookies into 10 bags to sell at the bake sale. Write an expression to show how many cookies she put into each bag. ________________________________________________________________________________________ Operations and Properties Practice A: Divide Multi-Digit Whole Numbers Find each quotient. 1. 585 13 2. 2,756 53 _______________ _______________ 3. 7,790 20 _______________ 4. 3,072 25 ________________ _______________ 5. 22,528 88 6. 17,658 36 _______________ _______________ 7. 37,674 69 _______________ 8. 45,619 50 ________________ Write the correct answer. 9. A marketing firm has 636 surveys to take. They have 12 analysts to administer the surveys. If the firm splits the surveys evenly among the analysts, how many surveys will each analyst administer? _____________________________________ 10. At the museum, there were 4,050 students in attendance from a total of 15 different school districts. How many people, on average, were attending from each school district? _____________________________________ 11. Hannah earned $40,860 last year. She earned the same amount each month. How much did she earn per month? _____________________________________ 12. The health lab has to test 21,432 specimens. If there are 24 technicians in the lab sharing the work load, how many specimens, on average, will each lab technician have to test? _____________________________________ 13. Ben is taking a week-long bike excursion. He will be taking a route that is 1,178 miles in length. How many miles per day, on average, will Ben have to bike in order to complete his route? _____________________________________ Decimals Review for Mastery: Multiplying Decimals You can use a model to help you multiply a decimal by a whole number. Find the product of 0.12 and 4, using a 10 by 10 grid. Shade 4 groups of 12 squares. Count the number of shaded squares. Since you have shaded 48 of the 100 squares, 0.12 • 4 0.48. Find each product. 1. 0.23 • 3 _______________ 5. 0.15 • 3 _______________ 2. 0.41 • 2 _______________ 6. 0.42 • 2 _______________ 3. 0.011 • 5 4. 0.32 • 2 _______________ 7. 0.04 • 8 ________________ 8. 0.22 • 4 _______________ ________________ You can also use a model to help you multiply a decimal by a decimal. Find the product of 0.4 and 0.6. 0.4 • 0.6 0.24 Find each product. 9. 0.2 • 0.8 _______________ 13. 0.5 • 0.2 _______________ 10. 0.7 • 0.9 _______________ 14. 0.4 • 0.4 _______________ 11. 0.5 • 0.5 _______________ 15. 0.1 • 0.9 _______________ 12. 0.3 • 0.6 ________________ 16. 0.4 • 0.7 ________________ Name _______________________________________ Date __________________ Class __________________ Decimals Practice A: Multiplying Decimals Find each product. 1. 2. _______________________ 4. 3. ________________________ 5. _______________________ 7. 0.4 • 0.5 10. 6.7 • 0.4 6. ________________________ 8. 1.2 • 1.5 _______________________ ________________________ 9. 1.7 • 0.3 ________________________ 11. 9.6 • 0.2 _______________________ ________________________ ________________________ 12. 0.8 • 0.8 ________________________ ________________________ Evaluate 2x for each value of x. 13. x 0.1 _______________________ 16. x 1.2 _______________________ 14. x 0.5 15. x 0.9 ________________________ 17. x 1.7 18. x 2.4 ________________________ 19. Each box can hold 2.5 pounds of apples. How many pounds can 3 boxes hold? _______________________________________ ________________________ ________________________ 20. Each pie costs $5.60. How much will it cost to buy 2 pies? ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Mathematics Name _______________________________________ Date __________________ Class __________________ Decimals Practice A: Adding and Subtracting Decimals Find each sum or difference. 1. 1.5 2.3 2. 6.5 1.4 _______________________ 3. 8.9 5.1 ________________________ 4. 12.6 3.4 5. 8.16 7.02 _______________________ 6. 7.25 8.75 ________________________ 7. 11.4 8.6 8. 16.5 4.3 _______________________ 11. 8.9 3.05 _______________________ ________________________ 9. 9.55 1.2 ________________________ 10. 25.6 5.1 ________________________ ________________________ 12. 10.64 8.5 ________________________ ________________________ Circle the letter of the correct answer. 13. If x 2.3, what is the value of the expression 5.4 x? Think 5.4 + 2.3 A 3.1 C 7.1 B 7.7 D 3.7 15. If m 1.9, what is the value of the expression m 4.2? Think 1.9 + 4.2 A 2.3 C 6.1 B 2.2 D 7.1 G 1.7 J 13.1 18. Jennifer brought $14.75 to the baseball game. She spent $3.45 for a hot dog and soda. How much money does she have left? ________________________________________ 17. Marcus is 1.5 meters tall. His sister, Carol, is 0.1 meter taller than Marcus. Their father is 0.2 meter taller than Carol. How tall is Carol? How tall is their father? _______________________________________ 14. If a 4.2, what is the value of the expression 8.7 a? Think 8.7 – 4.2 F 12.9 H 4.5 G 4.9 J 12.5 16. If y 5.9, what is the value of the expression 7.2 y? Think 7.2 – 5.9 F 1.3 H 13.3 Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Mathematics Name _______________________________________ Date __________________ Class __________________ Practice A: Dividing Decimals by Whole Numbers Find each quotient. 1. 2.8 4 _______________________ 4. 7.2 9 _______________________ 7. 0.8 4 _______________________ 10. 5.4 9 _______________________ 2. 1.8 2 ________________________ 5. 0.15 3 ________________________ 8. 2.1 7 ________________________ 11. 3.5 5 ________________________ 3. 3.6 6 ________________________ 6. 4.8 8 ________________________ 9. 0.32 4 ________________________ 12. 0.2 2 ________________________ Evaluate 2.4 x for each given value of x. 13. x 8 _______________________ 16. x 4 _______________________ 14. x 2 ________________________ 17. x 6 ________________________ 15. x 3 ________________________ 18. x 12 ________________________ 19. A six-pack of orange soda costs $4.20. How much does each can in the pack cost? _______________________________________ 20. It rained 2.7 inches in July and 2.1 inches in August. What was the average rainfall for those two months? _______________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Mathematics Name _______________________________________ Date __________________ Class __________________ Decimals Review for Mastery: Dividing by Decimals You can use powers of ten to help you divide a decimal by a decimal. To divide 0.048 by 0.12, first multiply each number by the least power of ten that makes the divisor a whole number. 0.048 0.12 0.12 • 102 12 Move the decimal point 2 places to the right. 0.048 • 102 4.8 Move the decimal point 2 places to the right. Then divide. 4.8 12 Step 1: Divide as you would divide a whole number by a whole number. Step 2: Think 48 12 4. Step 3: Bring the decimal into the quotient and add a zero placeholder if necessary. So, 0.048 0.12 0.4. Find each quotient. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Mathematics Name _______________________________________ Date __________________ Class __________________ Decimals Practice A: Dividing by Decimals Find each quotient. 1. 2.4 0.4 _______________________ 4. 8.1 0.9 _______________________ 7. 3.3 0.3 _______________________ 10. 7.5 1.5 _______________________ 2. 1.4 0.2 3. 4.8 0.6 ________________________ 5. 1.8 0.3 ________________________ 6. 6.4 0.8 ________________________ 8. 2.6 1.3 ________________________ 9. 7.2 1.2 ________________________ 11. 6.0 0.5 ________________________ 12. 9.9 1.1 ________________________ ________________________ Evaluate 4.8 x for each value of x. 13. x 0.2 (Think 4.8 0.2) _______________________ 16. x 0.6 _______________________ 14. x 0.4 15. x 0.3 ________________________ 17. x 0.8 18. x 1.2 ________________________ 19. Antonio spent $5.60 on cashews. They cost $1.40 per pound. How many pounds of cashews did Antonio buy? _______________________________________ ________________________ ________________________ 20. Over several months, a scientist measured a total of 6.3 inches of snow. The average snowfall each month was 2.1 inches. How many months did the scientist measure the snow? ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Mathematics Name _______________________________________ Date __________________ Class __________________ Decimals Practice A: Interpreting the Quotient: Round Quotient Up, Down, or Leave with decimal number (remainder) Circle the letter of the correct answer. 1. Hamburger rolls come in packs of 8. How many packs should you buy to have 60 rolls? 2. Each pack of hamburger rolls costs $1.50. How many packs can you buy with $8.00? (8.00 1.50) A 8 F 6 B 6 G 5 C 5 H 4 D 7 J 8 3. How many 0.6-pound hamburgers can you make with 7.8 pounds of ground beef? 4. You spend a total of $5.10 for 3 pounds of ground beef. How much does the ground beef cost per pound? A 13 F $0.70 B 14 G $0.17 C 10 H $15.30 D 16 J $1.70 Write the correct answer. 5. Four friends equally shared the cost of buying supplies for the class picnic. The supplies cost a total of $12.40. How much did they each pay? 8. You spent a total of $9.60 on paper plates for the picnic. Each pack costs $1.20. How many packs of paper plates did you buy? _______________________________________ 7. Plastic forks come in packs of 6. If you need 40 forks for the picnic, how many packs should you buy? _______________________________________ 6. In all, 20 people are going to the picnic. Each van seats 6 people. How many vans are needed to take everyone to the picnic? _______________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Mathematics