Summer Math Learning Packet

Summer Math Learning Packet Sixth grade math was a blast, The year just went by so fast! Let s keep everything fresh in your mind, So you can rely on it in a bind. Just complete two problems a day, And you will be on your way! **Resources From MyMath etools**

Use this sheet to record your answers to problems 1-90. Summer Math Packet Answer Sheet for students going into 6 th grade. 1.) 31.) 61.) 2.) 32.) 62.) 3.) 33.) 63.) 4.) 34.) 64.) 5.) 35.) 65.) 6.) 36.) 66.) 7.) 37.) 67.) 8.) 38.) 68.) 9.) 39.) 69.) 10.) 40.) 70.) 11.) 41.) 71.) 12.) 42.) 72.) 13.) 43.) 73.) 14.) 44.) 74.) 15.) 45.) 75.) 16.) 46.) 76.) 17.) 47.) 77.) 18.) 48.) 78.) 19.) 49.) 79.) 20.) 50.) 80.) 21.) 51.) 81.) 22.) 52.) 82.) 23.) 53.) 83.) 24.) 54.) 84.) 25.) 55.) 85.) 26.) 56.) 86.) 27.) 57.) 87.) 28.) 58.) 88.) 29.) 59.) 89.) 30.) 60.) 90.)

Indicate the answer choice that best completes the statement or answers the question. Find the greatest common factor of each set of numbers. 1.) 27, 36, 72 a. 9 b. 18 c. 8 d. 216 Find the least common multiple of each set of numbers. 2.) 4, 10, 12 a. 12 b. 120 c. 2 d. 60 3.) Aaron rides a bicycle 14 miles every 3 hours. At this rate, how many hours did Aaron ride if he rode 56 miles? a. 3 b. 6 c. 15 d. 12 4.) The ratio of juniors to seniors on the track team is 6 to 7. How many juniors are on the track team if there are 21 seniors on the team? a. 18 b. 20 c. 15 d. 19 5.) Out of 18 people surveyed at the mall, 10 have a motorcycle. Based on these results, of the 486 people at the mall, how many have a motorcycle? a. 27 b. 540 c. 270 d. 180

6.) Determine which pair of ratios or rates are equivalent. a. 10 hens produce 7 eggs; 5 hens produce 3.5 eggs b. 10 hens produce 7 eggs; 25 hens produce 14 eggs c. 10 hens produce 7 eggs; 30 hens produce 28 eggs d. 10 hens produce 7 eggs; 20 hens produce 10 eggs 7.) Stacy wants to throw a party. She needs $329 for food and $47 for gifts and decorations. She has saved $126. If she can save $25 each week, in how many weeks will she have enough money? a. 31 weeks b. 25 weeks c. 2 weeks d. 10 weeks 8.) 75% of Grant s coin collection is quarters. If Grant has 200 coins in his collection, how many are quarters? a. 50 b. 75 c. 150 d. 175 9.) Jeannine puts 10% of her paycheck into a savings account. If she makes $500 each week, how much does she put in her savings account each week? a. $5 b. $10 c. $50 d. $100 10.) What number is 80% of 50? a. 25 b. 40 c. 80 d. 160 11.) 20% of a store s sales are toys. If the store sells $1,200 in toys during one month, what are the store s total sales? a. $20 b. $60 c. $600 d. $6,000

12.) 60% of the students in marching band are girls. There are 30 girls in the marching band. How many students are there altogether? a. 50 b. 60 c. 160 d. 6,000 13.) 19 is 38% of what number? a. 2 b. 38 c. 50 d. 200 14.) 160 is 20% of what number? a. 12.5 b. 20 c. 800 d. 2,000 15.) Find 0.39% of 160 using decimals. a. 0.00624 b. 0.624 c. 62.4 d. 6.24 16.) Which statement is true? a. c. < 0.99 < 31% b. 31% > d. 0.99 < 31% 17.) 1.8 1.5 a. 1.3 b. 0.12 c. 12 d. 1.2

18.) Jenny bought 3.5 pounds of peanuts for $12.60. Her friend buys 6.25 pounds of walnuts for $23.75. Which is less expensive per pound? By how much? a. peanuts; $0.20 b. peanuts; $0.40 c. walnuts; $0.20 d. walnuts; $0.40 19.) 1231.14 51 a. 24.14 b. 24.3 c. 241.4 d. 2.414 Find each quotient. 20.) 4232 92 a. 46 b. 50 c. 45 d. 462 21.) 2.75 6.86 a. 1.8865 b. 18.865 c. 188.65 d. 19.865

Use estimation to determine whether the answer is reasonable. 22.) 31.73 9.5 = 3.34 a. Yes. The answer is reasonable. b. No. A reasonable estimate is 5.01. c. No. A reasonable estimate would be 2.23. d. No. A reasonable estimate is 32.33. Divide. Write in simplest form. 23.) a. b. c. d. Divide. 24.) a. b. c. d. Use the draw a diagram strategy. 25.) Jennifer s mom is putting a basketball hoop on the garage. The garage door is 8 feet high. There is 7 feet of wall between the top of the garage door to the garage roof. How far down from the garage roof should the hoop be placed so that it is 10 feet above the ground? a. 3 feet b. 2 feet c. 4 feet d. 5 feet

26.) Madeline is arranging stepping stones in a rectangular area of her garden. The stones are 1-foot squares and the area is 6.5 foot long and 5 foot wide. She intends to place the stones evenly apart, keeping them 0.5 foot from each other on all sides, as well as from the edge of the garden. How many stones will she use? a. 7 b. 10 c. 14 d. 12 27.) Terrence is making a octagonal sign which has 8 sides of equal length. He plans to draw diagonals from each vertex to all the other vertices. How many lines will he draw total? a. 18 b. 40 c. 35 d. 5 28.) 26 oz = lb a. b. c. d.

29.) Graph point K at ( 2, 1). Then graph its reflection over the y-axis. a. b.

30.) Graph point N at ( 5, 3). Then graph its reflection over the y-axis. a. b.

Graph each point on a coordinate system. 31.) W( 3, 2) a. b.

Identify the point located at each ordered pair. 32.) (4, 2) a. S b. T c. W d. Z Order the set of numbers from least to greatest. 33.) 2.61,, 2.69 a. 2.61,, 2.69 b., 2.69, 2.61 c. 2.69, 2.61, d., 2.61, 2.69 Simplify the expression. 34.) 4(4x + 7y) a. 16x + 11y b. 4x + 28y c. 16x + 7y d. 16x + 28y

35.) Factor 18a + 16b. a. 2(18a + 16b) b. 2(9a + 8b) c. 2ab(9 + 8) d. 34ab Use one or more properties to rewrite the expression as an equivalent expression that does not use parentheses. 36.) (7 f) 3 a. 21f b. 14f c. 28f d. 10f 37.) 7 + (x + 9) a. 7x + 63 b. x + 16 c. 16 x d. x 16 38.) Pamela bought a binder from the bookstore for $3.55. She gave the cashier four $1 bills. How many ways can Pamela be given change if the cashier has only quarters, dimes, and nickels? a. 8 different ways b. 7 different ways c. 10 different ways d. 9 different ways

Write each phrase as an algebraic expression. 39.) twelve more than three times a number a. b. c. d. Find the value of each expression. 40.) 5q 2 + 3m 4 if q = 7 and m = 1 a. 256 b. 22 c. 34 d. 244 41.) 7k + 2 c if k = 3 and c = 7 a. 245 b. 35 c. 7 d. 161 Solve each equation. Check your solution. 42.) 0.7 = a. 14 b. 21 c. 0.7 d. 10.29 Use the guess and check strategy to solve. 43.) Tamara is thinking of three different numbers from 1 to 20. The sum of the numbers is 33, and the differences between the numbers are multiples of 3. What are the numbers? a. 19, 10, and 4 b. 17, 15, and 11 c. 18, 9, and 3 d. 20, 9, and 4

44.) Solve. Graph the solution on a number line. a. b. c. d. 45.) Solve. Graph the solution on a number line. a. b. c. d. Solve the inequality. Graph the solution on a number line. 46.) a. b. c. d. Make a table to solve each problem. 47.) One tank has 43 gallons of water in it and is being filled at a rate of 4 gallons per minute. Another tank has 28 gallons of water in it and is being filled at a rate of 7 gallons per minute. After how many minutes will both tanks hold the same amount of water? a. 1 minute b. 3 minutes c. 4 minutes d. 5 minutes

Make a table to solve each problem. 48.) Chanda is collecting leaves for a school project. She has 10 leaves. She plans to collect 3 leaves per day for the next several days. What equation represents the number of leaves n that Chanda will have after d days? a. b. c. d. 49.) Christine is collecting leaves for a school project. She has 6 leaves. She plans to collect 3 leaves per day for the next several days. What equation represents the number of leaves n that Christine will have after d days? a. b. c. d.

50.) Chris is building a brick wall for his garden. It takes him 18 bricks to complete a single row. Complete the function table to show the relationship between the number of bricks b that it takes to make r rows. Rows, r 1 2 3 4 5 6 Bricks, b If Chris has 95 bricks, what is the greatest number of rows he can complete? a. 3 b. 6 c. 5 d. 4 51.) Which graph represents the equations and? a. b. c. d.

Use words and symbols to describe the value of each term as a function of its position. Then find the value of the indicated term. 52.) Find the value of the twenty-sixth term in the sequence. Position 12 14 16 18 n Value of Term 4 5 6 7 a. c. 2; 11 ; 9 b. n 9; 17 d. + 2; 15 Find the rule for each function table. 53.) n 6 3 12 6 18 9 a. b. c. d. Find the area of the shape below: 54.) a. 46.5 square yards b. 66.5 square yards c. 89 square yards d. 71 square yards

Find the area of the shape below: 55.) a. 37.25 square inches b. 39.75 square inches c. 45.25 square inches d. 35.75 square inches 56.) Lance is drawing a blueprint for his bedroom. His bedroom is a square. The coordinates of the vertices of his bedroom are G(4, 1), A(4, 6), R(9, 6), and D(9, 1). What is the perimeter of Lance s bedroom? a. 12 units b. 20 units c. 28 units d. 52 units 57.) Rectangle IJKL has vertices I (0, 5), J (0, 2), K (3, 2), and L (3, 5). Find the area of rectangle IJKL. a. 10 square units b. 20 units c. 21 square units d. 24 square units

58.) Vince drew the front view of a podium on a coordinate plane. The coordinates of the vertices of the podium are T (1, 3), U (3, 7), V (7, 7), and X (9, 3). Graph the figure. Then identify the shape of the podium. a. b. The podium is a parallelogram. c. The podium is a trapezoid. d. The podium is a trapezoid. The podium is a parallelogram.

59.) Graph the figure. Then identify the shape : F(5, 5), G(5, 9), H(9, 9), J(9, 5) a. b. The figure is a square. c. The figure is a square. d. The figure is a square. The figure is a square. 60.) A square has an area of 100 inches. If the side lengths of the square are each multiplied by 4, find the area of the new square. a. 160 inches b. 400 inches c. 1600 inches d. 600 inches

61.) Two rectangles are shown. How many times greater is the area of the larger rectangle than the smaller rectangle? a. 4 times b. 16 times c. 9 times d. 8 times 62.) Two triangles are shown. What factor would you multiply the perimeter of the larger triangle to determine the perimeter of the smaller triangle? a. b. c. 10 d. Use the draw a diagram strategy to solve the problems. 63.) Jamaica is building a clubhouse in her backyard. Her first three designs are too small; the first design has an area of 4 square feet, the second design has an area of 9 square feet, and the last design has an area of 16 square feet. Jamaica wants a clubhouse with an area of 36 square feet and a shape that is the same as her first three designs. What length should the clubhouse walls be? a. 7 feet b. 5 feet c. 6 feet d. 8 feet

Find the area of each trapezoid. Round to the nearest tenth if necessary. 64.) trapezoid: bases, 17 cm and 7 cm; height, 8 cm a. 32.5 cm 2 b. 192 cm 2 c. 96 cm 2 d. 28 cm 2 65.) trapezoid: bases, 16 cm and 8 cm; height, 4 cm a. 48 cm 2 b. 28.5 cm 2 c. 26 cm 2 d. 96 cm 2 66.) a. 132.6 b. 127.9 c. 255.8 d. 151 Find the missing dimension of the triangle. 67.) Area = 54 ft 2 base = 12 ft a. height = 18 ft b. height = 4.5 ft c. height = 9 ft d. height = 42 ft Find the area of each triangle. Round to the nearest tenth if necessary. 68.) height: ft; base: ft a. ft 2 b. ft 2 c. ft 2 d. ft 2

Find the missing dimension of the parallelogram. 69.) Area = 48 cm 2 base = 6 cm a. height = 4 cm b. height = 16 cm c. height = 42 cm d. height = 8 cm Find the area of each parallelogram. Round to the nearest tenth if necessary. 70.) base: in. height: in. a. c. in 2 b. in 2 d. in 2 in 2 71.) base: 7 m height: 6 m a. 42 m 2 b. 49 m 2 c. 13 m 2 d. 40 m 2 Find the surface area of each pyramid. Round to the nearest tenth if necessary. 72.) cube: side lengths, 4.1 ft a. 65.5 ft 2 b. 49.2 ft 2 c. 24.6 ft 2 d. 100.86 ft 2 73.) square pyramid: base side length, 7.2 cm; slant height, 14.8 cm a. 198.8 cm 2 b. 264.96 cm 2 c. 255.7 cm 2 d. 478.1 cm 2

74.) Use the formula to find the surface area of the triangular prism below. SA = A + (3/2)bh, where A = the area of the pyramid's base, b = the base of one of the faces, and h = height of one of the faces. a. 197.1 m 2 b. 232.2 m 2 c. 162.8 m 2 d. 359.1 m 2 Find the surface area of each triangular prism. Round to the nearest tenth if necessary. 75.) a. 441.7 cm 2 b. 420.4 cm 2 c. 508.5 cm 2 d. 405.7 cm 2

76.) a. 560 m 2 b. 476 m 2 c. 500 m 2 d. 660 m 2 Find the surface area of each rectangular prism. Round to the nearest tenth if necessary. 77.) a. 346 km 2 b. 415 km 2 c. 99.6 km 2 d. 173 km 2 78.) Find the volume of the prism described. triangular prism: base of triangle 7 cm, height of triangle 4 cm, height of prism 3 cm. a. 84 cm 3 b. 42 cm 2 c. 42 cm 3 d. 10.5 cm 3

Find the volume of each triangular prism. If necessary, round to the nearest tenth. 79.) a. 187.2 cm 3 b. 374.4 cm 3 c. 26.6 cm 3 d. 1,946.9 cm 3 Find the volume of each rectangular prism. Round to the nearest tenth if necessary. 80.) a. 275.2 ft 3 b. 229.3 ft 3 c. 114.7 ft 3 d. 19.3 ft 3 81.) Find the volume of the prism described. rectangular prism: length 9 ft, width 6 ft, height 5 ft. a. 135 ft 3 b. 270 ft 2 c. 45 ft 3 d. 270 ft 3

82.) Latonya created a table that lists the distances in miles from her house to several places where she enjoys spending her time. Favorite Places Place Distance (in miles) Beach 24 Park 30 Hiking Trail 25 Ally s House 28 Grandparent s House 18 Cousin s House 228 Dance School 33 Mall 34 Which measure of central tendency best represents the data? Explain. a. Since there is an extreme value, the mean best represents the data. b. Since there is an extreme value, the median best represents the data. c. Since there are no extreme values, the median best represents the data. d. Since there are no extreme values, the mean best represents the data. 83.) The table shows the weights of four elephants and lions. Weight of Animals (lb) Elephant Lion 9,200 7,500 10,800 8,100 500 476 485 510 Which statement correctly compares the mean absolute deviation of each set of data? a. The data for the weight of the elephants are same distance apart as the data for the weight of the lions. b. The data for the weight of the elephants are farther apart than the data for the weight of the lions. c. The data for the weight of the lions are farther apart than the data for the weight of the elephants. d. The data for the weight of the elephants are closer together than the data for the weight of the lions. Find the median, the first and third quartiles, the interquartile range, and any outliers for each set of data. 84.) 26.8, 15.5, 7.8, 10.9, 4.8, 13.9, 11.2, 12.4, 53.6, 15.4, 7, 20.1, 35, 10.4, 18.2 a. 13.9 median, 10.4 Q1, 18.1 Q3, 9.7 IQR, 53.6 and 35 outliers c. 13.9 median, 10.4 Q1, 20.1 Q3, 8.7 IQR, 53.6 and 35 outliers b. 13.9 median, 10.4 Q1, 20.1 Q3, 9.7 IQR, 53.6 and 35 outliers d. 13.9 median, 10.4 Q1, 20.1 Q3, 9.7 IQR, 4.8 outlier

Find the mean for each set of data. Round to the nearest tenth if necessary. 85.) Cost Tally Frequency $15 10 $17.50 8 $20 13 Indicate the answer choice that best completes the statement or answers the question. Draw a box plot for each set of data. 86.) 71, 60, 74, 84, 81, 62, 54, 57, 83, 95, 87, 68, 100, 89, 55 a. b. c. d. 87.) The box plot shows the height, in feet, of various tall buildings in America. What is the interquartile range of the data? a. 110 ft b. 190 ft c. 1,130 ft d. 80 ft

88.) The box plot shows the number of minutes Kia spent at trumpet practice. Describe the center and spread of the distribution using the appropriate measures. Minutes at Trumpet Practice a. The data are centered around 40. The spread of the data around the center is 40. b. The data are centered around 60. The spread of the data around the center is 40. c. The data are centered around 85. The spread of the data around the center is 40. d. The data are centered around 40. The spread of the data around the center is 85.

Display the set of data in a histogram. 89.) Daily Low Temperatures in January Temperature ( F) Tally Frequency 0 9 1 10 19 9 20 29 10 30 39 13 40 49 3 a. b. c. d.

90.) The line plot shows Micah s golf scores for different games. Which of the following statements is correct? a. The distribution is not symmetric and there are no outliers. The median and interquartile range are the appropriate measures to use. b. The distribution is not symmetric and there is an outlier at 3. The median and interquartile range are the appropriate measures to use. c. The distribution is not symmetric and there are no outliers. The mean and mean absolute deviation are the appropriate measures to use. d. The distribution is not symmetric and there is an outlier at 3. The mean and mean absolute deviation are the appropriate measures to use.