!!!!!!!!!!!!!!! Rising 6 th Grade Summer Interactive Math Practice

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1 Rising 6 th Grade Summer Interactive Math Practice

2 Rising Sixth Grade Summer Math Packet I. Place Value Write each number in word form, in expanded form, expanded notation, name the place of the underlined digit, and give the value of the underlined digit. Use the following as an example: 856,904,229, Word Form: eight hundred fifty-six billion, nine hundred four million, two hundred twenty-nine thousand, one hundred seven and three hundred twenty-nine thousandths Expanded Form: 800,000,000, ,000,000,000, + 6,000,000, ,000, ,000, , , , /10 + 2/ /1000 Expanded Notation: (8 x 100,000,000,000) + (5 x 10,000,000,000) + (6 x 1,000,000,000) + (9 x 100,000,000) + (4 x 1,000,000) + (2 x 100,000) + (2 x 10,000) + (9 x 1000) + (1 x 100) + (7 x 1) + (3 x 1/10) + (2 x 1/100) + (9 x 1/1000) Place: billions Value: 6,000,000,000

3 23,509, Word Form: Expanded Form: Expanded Notation: Place: Value: 100,592,271, Word Form: Expanded Form: 3

4 Expanded Notation: Place: Value: Write the following numbers in standard form. four hundred three billion, nine hundred seventy-two million, eight hundred ninety-nine thousand, four hundred eight and twenty-two thousandths fifty-four million, two hundred two and eight thousandths seventy-three trillion, nine hundred nine thousand, six hundred fifty-two and one thousand two hundred twentythree ten thousandths* *Challenging 4

5 Order the following numbers from greatest to least in value. 54,710; 54,071; ; ; 5.041; 5.002; ; 7; 7.07; 0.07; Round the following numbers to the underlined digit. 7, ,060 1, , , ,192 5

6 Round the following numbers to the place indicated. 33,291,592 (hundred-thousands) 33,300, (tenths) (ones) 12,890 (ten-thousands) (hundredths) 43,927.2 (thousands) 506 (tens) II. Addition and Subtraction Find the sum or difference of the following whole number problems. Please show all work. 29, ,707 = 50,000-3,427 = 17,605 75,991-9,296-12,059 6

7 Find the sum or difference of the following decimal problems. Please show all work = = = = Estimate to solve. Show all work = , = 4,501-1,956 = 27,276-11,992 = 7

8 = 179, ,171 = III. Multiplication and Division Multiply and align if needed. Please show your work. 7 x 800 = 800 x 500 = 58 x 72 = 9,006 x 304 = 0.4 x 0.2 = 12 x 0.5 = 8

9 62 x = x 54.9 = 6.9 x 100 = x 70 = Estimate and show how you estimated. 42 x 28 = 4,832 x 332 = x = 0.9 x 1.2 = 5,941 x 83 = 68.4 x 52 = 9

10 Rewrite using a base and an exponent. 13 x 13 x 13 x 13 = 9 x 9 x 9 x 9 x 9 x 9 = Rewrite the exponent in standard form. 5 2 = 3 4 = 10 7 = 2 8 = 1 9 = 14 0 = Solve and show your work. Michelle is reading a book about the Civil War that is 243 pages long. She reads an average of 40 pages each day. She has 6 days to finish. Will she be able to finish the book? Explain why or why not. The hikers plan to travel an average of 9 miles a day. How many miles will they travel in 3 full weeks? 10

11 Sam bought 3.5 lbs. of sliced turkey to make sandwiches for a picnic. The turkey cost $5.91 per pound. About how much did Sam pay for the turkey? Divide and show your answer with a remainder if necessary. Show your work please = = 1, = = 11

12 Divide until your answer does not have a remainder. Show your work = = Solve the following word problems. Show your work. Julie has $5.40 to spend at the candy store. If her favorite candy costs $0.15 for each piece, how many pieces of candy can she buy? The bus drove 540 miles in 4.5 days, driving an equal number of miles each day. How many miles did the bus drive in a single day? 12

13 Mike has $11.25 to spend at the store, and he wants to buy as many trading cards as he can. Each card costs $0.75. How many cards can he buy? Estimate the quotient or use compatible numbers. Show how you estimated = = = = 13, = = = = 13

14 IV. Number Theory and Fractional Concepts Label each number either prime, composite, or neither List the factors of the following numbers. 12: 48: 72: 96: List the first seven multiples of the following numbers. 12: 15: 14

15 Directions: Using factor trees, write the prime factorization for each of the following numbers. Show work Find the greatest common factor of each set of numbers. 15 and and and and 51 8 and and 36 Find the least common multiple of each set of numbers. 3 and 7 4 and 12 2, 3 and 5 6 and 9 4, 5, 6 7 and 8 15

16 Create an equivalent fraction for each of the following fractions. 3/8 2/3 8/9 Reduce the following fractions to lowest terms. 45/60 16/32 48/72 Write the following mixed numbers as improper fractions and the improper fractions as mixed numbers. 48/7 43/9 83/9 8 ½ 7 ¼ 9 3/5 Order this set of numbers from greatest to least: 5 ½, 5 ⅘, 5, 5 2/3 9 ¾, 20/2, 10.1, 11 ⅓, ⅜, 2/9 ½, 4/14, 5/7 9/2, 6/3, 11/4 16

17 V. Addition and Subtraction of Fractions Solve and simplify your answers. ⅓ + ⅓ = ⅜ + ⅜ = 7 2/ /7 = 4/9 1/9 = 9/10 5/10 = 6 ¼ - 1 ¾ = Susan and Rebekah each ran 5 ¾ miles in a race. How much did they run together? James practiced his guitar for 5/8 of an hour. Luke practiced his for 3/8 of an hour. How much longer did James practice than Luke? 3/6 + 2/12 = ½ + 1/10 + 1/5 = 1/6 + 3/9 = 3/4 + 3/10 = 17

18 Mom bought 1/6 yard of blue ribbon and 2/3 yard of red ribbon. How much did she buy in all? 9/10 2/5 = 2/3 3/9 = 7/15 1/6 = ¾- 1/5 = Rusty did his math homework for 2/3 hour and then played video games for ½ hour. How much longer did he do math than play video games? When asked about their favorite flavor of ice cream, of the 5th graders who responded, 1/3 chose chocolate and 2/5 chose vanilla. How many more like vanilla than chocolate? 18

19 9 1/ /10= 7 3/5 + 6 ¼= 6 ¾ + 3 4/6 = 7 1/ /9 Molly s family waited 2 ½ hours for their flight to leave the airport and then spent 1 ¾ hour flying to New York. How much time did they spend altogether waiting for their flight and on their flight? Lauren had 10 ¼ inches cut off of her hair for Locks of Love and her friend Camille had 11 1/8 inches cut. How much did they have cut off together? 19

20 2 ½ - 2 5/16= 12 4/9 9 2/3= 4 5/14 1 3/7= 6 7/8 3 3/5= During the last month, Jacob spent 12 3/8 hours practicing his trumpet and 15 2/3 hours playing basketball. How much more time did he spend playing basketball than playing his trumpet? VI. Multiplication and Division of Fractions Solve and simplify the answer if possible. 5/8 x 2/3 = 11/13 x 4/5 = 20

21 8/9 x 5/7 = 7/12 x 6/7 = 1 1/2 x 3 2/5 = 5 ⅓ x 2 ¼ = 8 ⅓ x 6 ¼ = 4 ⅞ x 1 ⅓ = 6 x 4/9 = 7/9 x 14 = Three-fourths of students in your classroom listen to country music only. One-half of these students are boys. What fraction of students in your classroom are boys who listen to country music only? 21

22 A group of friends shared a dozen chocolate donuts. Each person ate 1 ½ donuts. How many friends shared the donuts? Maria needs 3 4 of a cup of sugar for one serving of her recipe. How many cups of sugar will she need for 5 servings? Estimate and show how you estimated. 4 4/5 x 8 3/7 = 8 ⅔ x 5 7/12 = 6 ½ x 4 5/12 = 9 3/4 x 33 1/3 = Solve and simplify if possible. Show your work. 2/3 4/5 = 5/10 10/15 = 22

23 3/7 9/14 = 4/5 6 = 7 2/3 = 4 ⅛ 3 ¼ = 3 ⅔ 1 ⅜ = 7/11 5 = The Hubba Bubba Bubble Gum Tape is 6 feet long*. How many 2 ¼ inch pieces can the tape be cut? *Hint: Convert feet to inches. On average, you have to replace your earphones every 4 ½ months. At this rate, how many earphones would you have to buy in 18 months? If a tortoise is timed traveling an average of 1/3 miles per hour, how long would it take the tortoise to travel 6 miles? 23

24 VII. Ratio and Probability Solve for x. Find the missing number in the proportion. 5 : 11 = 35 : x x = Find the missing number in the proportion. 25 to 3 = 100 to x x = Find the missing number in the proportion. 90 : 45 = 10 : x x = Find the missing number in the proportion. 40 : 8 = x : 32 x = Think about tossing a number cube with the numbers 1, 2, 3, 4, 5, and 6 on the faces. What is the probability of tossing a 2? What is the probability of tossing a number less than 3? Is tossing an odd number more likely than, less likely than, or equally likely as tossing a number greater than four? 24

25 Solve. Janet earns $22 for babysitting 5 ½ hours. At the same rate, what does she earn for babysitting four hours? Suzy put 20 marbles in a bag. Five of the marbles were red, seven were orange, four were green, and four were yellow. If she pulls a marble from the bag without looking, what is the probability that it will be orange? Solve the following rate problems using a ratio table. Jill had a summer job at her favorite ice cream store. She was to receive $8 per hour of work. Using that rate of pay, complete the table below. Hourly Pay Hours Worked $ $60 25

26 Mr. Smith s big SUV gets terrible gas mileage. Based on the rate given below, complete the rest of the table. Miles Traveled Gallons of Gas Used VIII. Geometry Solve the following area, perimeter, and volume problems. Show your work. Hint: Draw and label. What is the perimeter and area of a rectangular classroom floor that measures 34 feet in length and 22 feet in width? Make sure to label answers correctly. Perimeter = Area = 26

27 You are planting a garden for the summer. Your garden measures 12 feet by 9 feet. What s the perimeter and area of your garden? P = A = What is the volume of a cereal box that is 8 inches long, 12 inches tall, and 3 inches wide? Please label correctly. Volume = A box container is 4 feet long, 3 feet wide, and 2 feet high. What is the volume of the toy box? Label correctly. Volume = Tell the number of faces, edges, and vertices of the the above box. F = E = V = Find the area and perimeter of this figure. Perimeter = Area = 27

28 IX. Fractions, Decimals, and Percents Complete the following table. The first two have been done as examples for you. Simplest Fraction Form Decimal Number Percent 1/ or % 9/ % 1/ % % 3/ % 9/10 28

29 X. Additional Math Practice and Informational Links Website Khan Academy Math Drills Lite App IXL Math Play Math Playground The Art of Problem Solving Multiplication Great Schools K5 Learning Link videos worksheets/fifth-grade/math/