If less than 60-70% of the responses are correct

Transcription

1 Thomas Edison Energysmart Charter School Summer packet for students who have successfully completed 6 th Grade Math Student s name: 6 th Grade Math Teacher: I have checked for the completion of the packet. Parent/Guardian s signature The goal of Thomas Edison Energysmart Charter School is to assist your child in becoming a lifelong learner. The summer months provide the perfect opportunity to extend and enrich your child s learning experiences. Summer Reading/Writing and Math packets will help prepare your child for school year. All students are expected to read through and follow directions for both Reading/Writing and Math packets. Packets will be due by September 1, The math packet will count as 1 st marking period project grades in math and there would not any other math project during the first marking period. Submission can also be done online by ing/sharing the document with the previous year 6 th Grade Math teacher. Ten points will be taken out if the packet is late by a day, twenty points will be taken out if late by two days. The student would get 0 points if it is late by three or more days. Plagiarized work would receive a score of 0. Apart from the above, the following rubric will be used: Score of 100 Score of 90 Score of 80 Score of 70 Score of 0 If all 90 to 100% of the responses are correct If 80-90% of the responses are correct If 70-80% of the responses are correct If less than 60-70% of the responses are correct If less than 60% of the responses are correct Enjoy the break! 6th Grade Summer Math Packet Page 1 of 29

2 1. Alex rides a bicycle at a constant speed. He travels 13 kilometers in 30 minutes. Part A What is Alex s constant bicycle speed, in kilometers per minute, rounded to the nearest tenth? Show or explain your work. Part B Write an equation to express the distance Alex travels in terms of time. Use d to represent distance in kilometers and t to represent time in minutes. 2. Ms. Brown asked her class to evaluate 2(3) 2 5 and 2( 3) 2 5. Mona s work is shown below. Part A Identify the error Mona made when she evaluated both expressions. Part B Find the correct value for each of the two expressions. Show or explain your work for each of the two expressions. Part C Explain why the expressions do or do not have the same value. 6th Grade Summer Math Packet Page 2 of 29

3 3. Use substitution to determine which numbers from the set { 2, 1, 0, 1, 2} make the inequality 1 3x > 4 true. Show your work for each number from the set and explain why or why not the number makes the inequality true. 4. The bases of a baseball field form a square. Part A The area of a square can be approximated using the formula A = where is the length of the diagonal of the square. If the diagonal of the square formed by the bases is approximately feet, what is the area of the square? Round your answer to the nearest square foot. Show or explain your work. Part B The area of a square can also be approximated using the formula where is the perimeter of the square. If the perimeter of a different baseball field is 360 feet, what is the area of that field? Round your answer to the nearest square foot. Show or explain your work. 5. A store sells gift boxes. Their medium gift box is a cube with side lengths of s=5 Customers want to know how much the gift box will hold and how much wrapping paper will be needed. Part A Use the formula to label your answer. Show or explain your work. to find the volume of the gift box. Be sure Part B Use the formula to find the surface area of the gift box. Be sure to label your answer. Show or explain your work. Part C Wrapping paper costs $.05 per square inch. Assume the wrapping paper does not overlap any place on the gift box. How much will it cost to wrap the gift box? Show or explain your work. 6th Grade Summer Math Packet Page 3 of 29

4 6. Part A Write an expression for the following calculation: subtract 4 from 7, then multiply by z. Part B Write a different but equivalent expression for the expression you wrote in Part A. Explain why the two expressions are equivalent. 7. Part A Translate the expression 3(4 + x) into words using mathematical terms to identify the parts. Part B Name the property used to produce an equivalent expression for 3(4 + x). Part C What value of x makes the equation 3(4 + x) = 21 true? Show or explain your work. 8. There was a basket of strawberries on the table. The chef used 6 strawberries, which was of the total in the basket, for a recipe. Part A Write an equation to represent this situation and solve for the number of strawberries that were in the basket. Show or explain your work. Part B If of the strawberries used equals 11, what does this mean in terms of the original number of strawberries in the basket? Part C If x represents the total number of strawberries in a basket, write an expression that would represent one and a half baskets of strawberries. 6th Grade Summer Math Packet Page 4 of 29

5 9. Let S = Part B. be the specified set of values to use in Part A and Part A Which value(s) (if any) from set S is a solution to Show or explain your work. Part B Which value(s) (if any) from set S is a solution to Use substitution of a value for the variable x to determine whether the value is a solution to the equation. 10. Part A Write an expression for the product of 3 and the sum of x and 5. Part B Write an equivalent expression for your answer in Part A. Part C What is the value of the expression if x = 4? Show or explain your work. 11. Amelia earns $8 per hour babysitting for a family. Part A Write an equation that represents Amelia s earnings, A dollars, in terms of the time she babysits, n hours. Part B Make a table of values for integers from n = 1 to n = 7 for this situation. Part C Use either the < or > symbol to compare the money Amelia earns when n = 3 and n = 6. Use mathematical language to describe the relationship between these two amounts of money. 6th Grade Summer Math Packet Page 5 of 29

6 12. Part A Solve 2x + 5 < 17 for x. Show or explain your work. Part B Which of the value(s) {2, 5, 6} is a solution of the inequality 2x + 5 < 17? Use substitution to determine whether each value is a solution and show your work. Part C Explain why solving for x in Part A would have eliminated the need to use substitution to determine which values in Part B were solutions to the inequality. 13. Part A Write an equation to represent The sum of 9 and 3, multiplied by x equals 36. Part B Identify the product in the equation you wrote for Part A. Part C What are the factors in the equation you wrote for Part A? 14. Part A Identify the parts of the expression 3(x 5)using mathematical language. Part B Find an equivalent expression for 3(x 5). Give the name of the property of operations that will produce the equivalent expression for 3(x 5). 6th Grade Summer Math Packet Page 6 of 29

7 15. Joey wants to create a square pyramid and a rectangular prism by folding each from a piece of paper. The diagram below shows the dimensions in centimeters of the square pyramid and rectangular prism. Part A. Draw the net of the square pyramid. Be sure to label the edge lengths, in centimeters. Part B. Draw the net of the rectangular prism. Be sure to label the edge lengths, in centimeters. Part C. Use the nets to determine how many more square centimeters of paper Joey needs to construct the rectangular prism than the square pyramid. Use words, numbers, and/or pictures to show your work. 6th Grade Summer Math Packet Page 7 of 29

8 16. Miller s Packing Company makes and ships boxes in the shape of rightrectangular prisms. The company has two sizes of boxes and is working on making a third. The table below shows the details of each box. Use the table to help answer the questions. Part A. How many cubic feet larger is the capacity of box B than box A? Part B. Miller s Packing Company would like box C to have a capacity of 15 cubic feet. If the dimensions of the base are 2 feet by 3 feet, what will box C s height be? Part C. Christine is a silk-screener and needs 65 cubic feet of space to send an order of T-shirts. What combination of boxes, using the fewest number of boxes, could Christine buy to fit all her T-shirts? Part D. Christine also needs to ship small boxes of ink. Each ink box is foot long, foot wide, and foot high. How many ink boxes can Christine fit inside a Miller s box A? Use words, numbers, and/or pictures to show your work. 6th Grade Summer Math Packet Page 8 of 29

9 17. What is the area of the figure below? 18. Tina has developed two designs for painting the rectangular patio area in a courtyard. 6th Grade Summer Math Packet Page 9 of 29

10 Part A. What is the area, in square feet, of the shaded space in design A? Part B. What is the area, in square feet, of the shaded space in design B? Part C. Tina has enough paint to cover 300 square feet. Is this enough paint to complete either design? Explain your reasoning. Use words, numbers, and/or pictures to show your work. 6th Grade Summer Math Packet Page 10 of 29

11 19. Volume of Rectangular Prisms Part A. Each cube has an edge length of inch. What is the volume of a single cube? Part B. Use the unit cubes to determine the dimensions of the box. What is the length, the width, and the height of the box? Explain how you know. Part C. Now completely fill the box with the unit cubes. How many cubes fit inside the box? Use the volume of each unit cube to determine the volume of the box. Part D. Use the dimensions from part B to write an equation and calculate the volume of the box. Compare your answer with the answer from part C. Do these answers match? 6th Grade Summer Math Packet Page 11 of 29

12 20. Part A. Draw trapezoid CDEF with the following coordinates: Part B. What is the length of side EF? Part C. If point G is drawn at what would the length of DG be? Part D. If point H is drawn at how would you find the length of CH? Use words, numbers, and/or pictures to show your work. 21. Amelia earns $8 per hour babysitting for a family. Part A Write an equation that represents Amelia s earnings, A dollars, in terms of the time she babysits, n hours. Part B Make a table of values for integers from n = 1 to n = 7 for this situation. Part C Use either the < or > symbol to compare the money Amelia earns when n = 3 and n = 6. Use mathematical language to describe the relationship between these two amounts of money. 6th Grade Summer Math Packet Page 12 of 29

13 22. The daily low temperature in Anchorage, Alaska was 11 Fahrenheit (F) one day and 18 F the next day. Part A Write an inequality that compares these two temperatures. Part B Use the inequality you wrote in Part A to determine the positions of -11 and -18 on the number line. Part C Which of these values has a greater absolute value? Explain your answer. 23. Anton s car uses gallon of gas to drive to and from his sister s house. Part A If Anton has gallon of gas, how many times can he drive to and from his sister s house? Show or explain your work. Part B If Anton has gallons of gas, how many times can he drive to and from his sister s house? Show or explain your work. 6th Grade Summer Math Packet Page 13 of 29

14 24. Elaine drew a grid over the top of her city map. Part A What are the coordinates of point A? Part B What is the distance from point D to point A? Show or explain your work. Part C Give the coordinates of two different points that are exactly 3 units from point B. 6th Grade Summer Math Packet Page 14 of 29

15 25. Sean planted 90 daffodils and 84 tulips at the park. He planted the greatest possible number of rows that met both of these conditions: an equal number of tulips in each row an equal number of daisies in each row Part A How many rows of flowers did Sean plant? Show or explain your work. Part B How many tulips were planted in each row? 26. The table shows the costs of items at a book fair. Part A How much does it cost to buy 1 poster, 3 books, and 2 craft kits? Part B How much more does it cost to buy a craft kit and e-book than to buy a book and game? 6th Grade Summer Math Packet Page 15 of 29

16 27. The table below shows the ordered pairs which represent the locations of four towns on a coordinate plane. Graph and label each point with the name of the town it represents on the coordinate plane. For each of the 4 ordered pairs, explain how to find the point when you start at the origin. 6th Grade Summer Math Packet Page 16 of 29

17 28. The coordinate plane shows the locations of five art exhibits in the museum. The information desk is located at the origin. Part A What is the ordered pair that represents the Ceramics exhibit? Part B What is the ordered pair that represents the Photography exhibit? Part C Is the location of the Ceramics exhibit and Photography exhibit related by a reflection of the x-axis, y-axis, or both axes? 29. Part A What is the greatest common factor of 8 and 12? Part B What is the least common multiple of 8 and 12? Part C Name the property used to change the sum of to the equivalent expression 6(3 + 1). What does the number 6 represent? 6th Grade Summer Math Packet Page 17 of 29

18 30. Part A Graph the points ( 2, 1), (4, 3) and ( 2, 3) on the following coordinate plane. Draw lines to connect the points. What is the name for the polygon that is formed? Part B What is the area of the polygon in Part A? Be sure to label your answer with the correct units. Show or explain your work. 31. A worm is 10 inches below the surface of the earth. The worm crawls 5 inches up but falls back 2 inches. What integer represents the worm s location relative to the surface?show or explain your work. 32. The daily low temperature in Denver, Colorado was 9 Fahrenheit (F) Tuesday and 13 F Wednesday. Part A Write an inequality that compares these two temperatures. Part B Which daily low temperature in Denver, Colorado is to the right of 10 F on a number line? Part C Which of these temperatures has a greater absolute value? 6th Grade Summer Math Packet Page 18 of 29

19 33. The coordinate plane shows the locations of three buildings in relation to Jessie s house. Jessie s house is located at the origin. Each coordinate unit represents 1 block. Part A What is the ordered pair that represents the school? Explain how to find the coordinates for your answer. Part B What is the ordered pair that represents the hospital? Explain how to find the coordinates for your answer. Part C What reflection transforms the point that represents the school into the point that represents the hospital? Explain how you know your reflection is correct. 6th Grade Summer Math Packet Page 19 of 29

20 34. There is a 1:3 ratio of boys to girls in each class at a summer camp. The table below shows the numbers of some of the children in different classes. Part A. How many children are there in all in class 2? Part B. Which class has the most girls? Use words, numbers, and/or pictures to show your work. 35. This table shows the relationship between participants and judges for the district-wide spelling bee. Part A-Extend the table to determine the number of judges needed for 700 participants. Part B-State the ratio of participants to judges. Part C-How many judges are needed for 475 participants? Show your work. Use words, numbers, and/or pictures to show your work. 6th Grade Summer Math Packet Page 20 of 29

21 36. In a pet store there are a total of 25 animals; 15 of the animals are dogs. Determine the ratio of animals that are NOT dogs to the total animals in the store. Explain the reasoning for your answer. Use words, numbers, and/or pictures to show your work. Read the passage - 'Birthday Brownies' - and answer the question below: Birthday Brownies Birthday Brownies Jessica is looking forward to celebrating her birthday, which is coming up next week. To prepare, Jessica and her mom decide to spend Sunday afternoon making chocolate chip brownies to share with her friends. Jessica s mom has a special recipe she makes for Jessica each year on her birthday. This year, Jessica is looking forward to helping her mom and learning the recipe. Jessica wants to share some of the brownies with her basketball teammates on Monday and to share the rest with her class at school on Tuesday. To be sure that all of Jessica s friends in basketball and at school get at least one brownie, Jessica and her mom decide to double the recipe to make two batches of brownies. At basketball practice, Jessica s friends can t wait to eat the brownies. Jessica brings three-quarters of one batch to practice and shares the brownies with a total of 12 people. There are 30 people in Jessica s class at school. They eat the rest of the brownies when Jessica brings them to school. Her friend Marvin loves chocolate chips. When he thanks Jessica for bringing the chocolate chip brownies to school, he asks whether she will share the recipe. He wants to make chocolate chip brownies for his birthday, too. Jessica is happy to share the recipe she learned to make with her mom. She gives Marvin the recipe card below. 6th Grade Summer Math Packet Page 21 of 29

22 37. Read "Birthday Brownies" and answer the questions. Part A. Write a sentence describing the ratio of cups of sugar in the recipe to brownies. Part B. Write a sentence describing the ratio of the total number of brownies Jessica and her mother made to the total number of people served. Remember that Jessica counts as 1 of the 12 people on her basketball team. Show your work. 38. It takes Jolene 7 hours to knit 2 scarves. At this rate, how many scarves can Jolene knit in 1 hour? 6th Grade Summer Math Packet Page 22 of 29

23 39. John and Raul both bought the same style bike from a store. On Wednesday, John purchased the bike at a discount off the original price. On Friday, Raul bought the bike for off the original price. Part A-Who received the greater discount on the bike? Show your work. Part B-If John saved $24, what was the original price of the bike? Show your work. Use words, numbers and/or pictures to show your work. 40. Jaxon wants to buy a box of cereal. Two different boxes of one type of cereal are shown below. Part A. To the nearest penny, what is the unit price per ounce (oz) of each box of cereal? Part B. If Jaxon wants to get the best deal for his money, which box should he buy? Explain your answer. Use words, numbers, and/or pictures to show your work. 6th Grade Summer Math Packet Page 23 of 29

24 41. Chelsea is an artist who paints murals on underpasses in the city. She is making a table of how much paint she uses for each mural to help her predict how much paint she will use in the future. Based on the table, how much paint is required to cover an 8-foot-by- 8-foot area? What is the rate of paint coverage in square feet per gallon? Use words, numbers, and/or pictures to show your work. 6th Grade Summer Math Packet Page 24 of 29

25 42. Derek grows two different kinds of plants. He measures how many inches each plant grows and uses the data to make a growth chart for each plant. Plot the pairs of values on a coordinate plane like the one below. Assuming both plants continue to grow at a steady rate, extend the data by plotting a point for each plant at day 10. Connect the points for each plant using a solid line for plant A s growth and a dashed line for plant B s growth. 43. Thomas had race times of minutes and minutes. Part A. Label the number line on your answer sheet with a range of values appropriate for plotting Thomas's race times. Part B. On your answer sheet, plot and label points to represent each of Thomas's race times. 6th Grade Summer Math Packet Page 25 of 29

26 44. A school newspaper printed the graph below showing the number of votes received by four students in an election. After Greta looked at the graph, she claimed that she received as many votes as Terry and Amy together. Part A. Explain why Greta's claim is not true. Part B. On the grid on your answer sheet, redraw the graph so that it is not misleading. Do not change the number of votes per student. 6th Grade Summer Math Packet Page 26 of 29

27 45. Mr. Thomas took a survey of students who are good spellers. He made a table showing each student's name, the number of words they spelled correctly out of fifty words, and whether the student is righthanded or left-handed. Good Spellers Name Words Hand Ernie 45 Right Khalil 47 Left Chris 46 Right Alex 48 Right Adrian 50 Right Darla 49 Left Tom 46 Right Quinton 49 Right Xavier 48 Left Mr. Thomas made two statements about the survey results. Statement 1: "The median number of words correctly spelled is 48." Statement 2: "Most students who are good spellers are left-handed." Part A. Is Statement 1 supported by the data in the table? Show or explain how you got your answer. Part B. Is Statement 2 supported by the data in the table? Show or explain how you got your answer. 46. The chart shows the number of minutes Betty practiced playing the piano each day for ten days. Betty's Piano Practice (minutes) Part A. Use the data shown in the table to complete a stem-and-leaf plot. Include a key and title. Part B. Explain why a stem-and-leaf plot is a useful way to display data. 47. Solomon plotted point on the number line below. What number best represents the location of point? 6th Grade Summer Math Packet Page 27 of 29

28 48. Kathy prepared a report on past weather trends in her hometown. She listed the number of rainy days in April for 10 selected years, as shown in the table. Rainy Days in April Month/Year Number of Rainy Days April April April April April April April April April April What was the median number of rainy days in April for those 10 years? 49. The table shows the number of acres of land on each of five ranches. Part A. Find the number of acres on each ranch and write the numbers of acres as numerals. Part B. Using a number line, order the numbers of acres on each ranch from least to greatest. 6th Grade Summer Math Packet Page 28 of 29

29 50. Juan leads a volunteer club. The numbers of hours that members volunteered last month are shown below. 11, 15, 17, 20, 8, 21, 16, 9, 15, 18, 15, 11, 21, 9, 16 Part A. Use this data to complete the stem-and-leaf plot on your answer sheet. Part B. Explain how two identical numbers (for example: 21 and 21) should be entered in a stem-and-leaf plot. Part C. How does the number of pieces of data compare to the number of items in the "Leaf" column of your plot? 51. Marla is a salesperson for a large company. The number of days she spent traveling to different countries last year on business is shown in the table below. Marla's Business Travel Country Number of Days Brazil 6 Canada 5 China 14 France 3 Germany 11 Italy 8 Japan 3 United Kingdom 10 What was the mean number of days per country Marla spent traveling on business? 6th Grade Summer Math Packet Page 29 of 29