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Name ___________________________ Date _________ Grade 4 Summer Packet – Going into 5th Grade For questions 3-6, which symbol belongs in the box to make a true comparison? (use <, =, or >). Write your answer in the box. 3. 4. 5. Twenty-seven thousand, four hundred ninety 20,000 7,000 400 10 9 6. For questions 7-8, fill in the missing digit in the blank in each number that will make each statement true. 7. Four hundred twenty-six thousand, seven hundred nine = 426,7__9 8. 835,__14 > Eight hundred thirty-five thousand, eight hundred fourteen 9. Which number when rounded to the nearest ten thousand has a value of 290,000? a. 286,314 b. 298,947 c. 281,769 d. 295,986 10. Round 759,048 to the nearest hundred thousand. 11. Circle the numbers below that have a value of 950,000 when rounded to the nearest ten thousand. 944,806 12. 953,782 956,270 945,867 947,603 The area of a building is 709,650 square feet. What is this number rounded to the nearest thousand square feet? a. 700,000 b. 709,000 c. 709,700 d. 710,000 13. 14. Which of the following is NOT equivalent to 8 7 56? a. 56 is 7 added to itself 8 times. b. 56 is 8 multiplied 7 times. c. 56 is 7 times as many as 8. d. 56 is 8 times as many as 7. Use the equation 72 8 9 to complete the following statement. 72 is 8 times as many as ______ and 9 times as many as ______. 15. Write a multiplication equation that is equivalent to the verbal statement below. Verbal statement: 16. 48 is 8 times as much as 6 Raja worked 40 hours per week for 4 weeks. Frank worked half the amount of time Raja worked. How many hours did Frank work during the 4 weeks? Show your work. 17. The students in the fourth grade sold 684 erasers for a fund-raiser. They sold 4 times as many erasers as the students in the fifth grade. How many erasers did the students in the fifth grade sell? 18. The workers at a farm collected 837 chicken eggs and 9 duck eggs. The number of chicken eggs collected was how many times the number of duck eggs collected? 19. Eight buses are available for a class trip. Each bus can seat 56 students. The letter n represents the number of students that can go on the class trip. Which equation can be used to find n ? Put a check mark in the oval if the equation can be used. Can be used 56 8 n 8 n 56 n 8 56 n 8 56 56 8 n 20. A school auditorium has 32 rows of seats. Each row has 15 seats. The letter k represents the total number of seats. Write an equation that can be used to find k. 21. Write an equation with a variable that could be solved to find the answer to the word problem below. Do not solve the word problem. Word problem: There are 133 paper cups at a party, and that is 7 times the number of people at the party. How many people are there? 22. Represent the word problem below by writing an equation with a variable. The variable should represent the number of trees that Mr. Wong’s students planted. Do not solve the word problem. Word problem: The students in Ms. Shah’s class planted 4 more trees than the students in Mr. Wong’s class planted. Ms. Shah’s students planted 36 trees. What is the number of trees that Mr. Wong’s students planted? In questions 1-4, use the standard algorithm to add or subtract. 1) 2,746 23,694 3) 62,114 49,586 2) 92,318 23, 027 4) 4,591 1,985 5. Which expression is equal to 3, 452 6 ? a. 2,000 6 300 6 40 6 5 6 b. 2,000 6 400 6 30 6 5 6 c. 3,000 6 400 6 50 6 2 6 d. 3,000 6 500 6 40 6 2 6 7. Marbles are arranged in an array that has 318 columns and 7 rows. How many total marbles are in the array? 8. Find 42 25. Show your work. 9. Show how to find 288 4. 10. A rectangular array of cabbage plants in a field has 6,489 plants arranged in 9 rows. How many columns are in the array? Explain your reasoning. 11. Find 708 6. 12. Use an area model to explain how to find 192 8. 13. Fill in the missing numbers in the boxes below to make equivalent fractions. 1 14. 2 10 100 Which is an equivalent fraction for a. 1 2 b. 2 6 c. 4 6 d. 3 2 2 ? 3 4 2 is equivalent to . 10 5 15. Draw a model and use it to explain why 16. The 24 counters below are arranged in groups of 4 to show that 4 of the 6 total number of counters are black. Arrange the 24 counters in groups of a different size to show another fraction that is equivalent to 4 . 6 17. Ms. Lucas drew the model below for 3 . 4 Then she asked her students to find a fraction that is equivalent to and draw their own model for that fraction. For each model below, choose Yes or No to indicate whether the 3 shaded portion represents a fraction that is equivalent to . 4 Yes No Yes No Yes No Yes No 3 4 18. 19. A group of students picked up 4 bags of litter in a park. Each bag contained n pieces of litter. The students collected 120 pieces of litter in all. Which equation can be solved to find the number of pieces of litter in each bag? a. 4 n 120 b. 4 120 n c. 4 n 120 d. 4 n 120 Four cousins collected bottle caps for a school fund-raiser. Adam, Selina, and Fiona counted the number of bottle caps they collected, as shown in the table below. Darius did not count his bottle caps. They all placed their bottle caps in a pile on the teacher’s desk. The teacher counted 2,000 bottle caps in all. Student Adam Number of Bottle Caps 367 Selina 922 Fiona 442 Let the number of bottle caps that Darius collected be represented as n. Write an equation that could be used to find n. Do not solve the equation. 20. Jenny decides to buy two cans of juice for each guest she has invited to a party. She buys the cans and puts 21 cans in each of 4 rooms in her house. Represent the number of invited guests with the letter g and write an equation with g that could be solved to find the number of invited guests. 21. Which number is a prime number? 22. a. 21 b. 39 c. 43 d. 49 Is 57 a prime or composite number? Explain your answer. 23. Put a check mark in the oval to indicate whether the number is prime or composite. Number Prime Composite 99 51 41 23 24. List all the factor pairs for 72. 25. The number 64 is a multiple of which of the following numbers? 26. a. 9 c. 6 b. 8 d. 3 Which number is a multiple of 7 ? a. 1 c. 63 b. 17 d. 89 1. Complete the table below by filling in the missing values of B using the rule: add 15. A B 11 26 12 13 14 15 What pattern do you see in the sequence of numbers in the B column? ____________________________________________________ 2. The first six terms of a sequence of symbols are shown. What symbol will be the 10th symbol? a. b. c. d. 3. Sunila described a number pattern below. Part A: The starting number is 13. The rule is to add 5. Fill in the blanks below with the first six numbers in the number pattern that Sunila described. _______, _______, _______, _______, _______, _______ Part B: Describe one thing you notice about the pattern. ___________________________________________________________________________ 4. Which symbol (<, =, or >) belongs in the box below to make a true comparison? Write your answer in the box. 2 3 1 4 Draw a picture and use it to explain your answer. 5. Name the fraction that represents each shaded region. _____________________ ___________________ Which is greater, the fraction of Figure A that is shaded or the fraction of Figure B that is shaded? Explain your response. _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 6. Write the two numbers in the boxes to make a true comparison. Use 3 and 10. 7. 2 ____ 4 ____ Shade a fractional part of each drawing. Write the fractions in the comparison to make it true. > ____ 8. > Is each sum equivalent to 2 yes or no. 2 ? Put a check mark in the oval to select 5 Yes 2 2 5 5 5 5 1 1 5 5 5 5 5 5 5 5 1 1 5 5 5 5 5 5 5 3 4 5 5 5 ____ No 9. Write an equation to show 5 as a sum of two or more fractions. 8 Draw a model that represents the equation. Equation: _________________ Model: 10. A pizza was cut into 6 equal slices. Andrew and Robert will share 5 of the pizza. 6 Use fractions to write two different ways that Andrew and Robert could share the pizza between them. They do not each get the same amount. A: __________________________ B: __________________________ In questions 11-14, add or subtract each. Write answers as proper fractions or mixed numbers. Show all work that leads to your answer. 11. 2 5 1 4 6 6 12. 5 7 1 4 12 12 3 3 4 4 13. 2 15. In two weeks a flower grew 14. 9 3 7 4 10 10 11 3 of a foot. The first week it grew of a foot. 12 12 How much did the flower grow in the second week? Show your work with a model or expression. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ 16. Train A and train B left a train station at the same time and headed in the same direction. After five minutes, train A was 5 1 7 miles from the station and train B was 2 miles from the 10 10 station. How much farther from the station is train A than train B? Show your work with an equation or a model. Complete the missing amounts in the following table so that the two measurements are equivalent. Measurement Measurement 17. 1 ft ______ in 18. 1 kg ______ g 19. 1 hr ______ min 20. 1L ______ mL In questions 21-23, use a letter to represent the unknown, and then write an equation and use it to solve the word problem. 21. Brooke read 3,237 pages during the fourth grade. She read 8,421 pages in fourth and fifth grades combined. How many pages did Brooke read in fifth grade? Write an equation using a letter to represent the unknown. _________________________ Use your equation to answer the question. _____________________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ 22. Lane rode his bike 340 miles in April. In May he rode his bike 100 miles more than in April. Lane rode a total of 960 miles in May and June. How many miles did Lane ride in June? Write an equation using a letter to represent the unknown. _________________________ Use your equation to answer the question. ______________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 23. Kyle swam 40 minutes on Monday, 20 minutes on Tuesday, and 30 minutes on Wednesday. Over the same days, Lavar swam for a total of 20 minutes less than Kyle. What is the total amount of time, in minutes, that Lavar swam? Write an equation using a letter to represent the unknown. _________________________ Use your equation to answer the question. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ___________________________________________________ In questions 24-25, use the standard algorithm to add or subtract each. 24. 2,346 1,768 25. 34,234 27,318 1. Use the number line below to show which whole number can be multiplied by 1 7 to get . 8 8 2. Each circle in the model below represents one whole. Write a product to represent the shaded parts shown in the model. Product: ____________________________ 3. Which of the following fraction models can be used to show 3 a. b. c. d. What is the value of 3 2 ? ________________ 5 2 ? 5 4. Holly gives 1 cup of cat food to each of her 4 cats every morning. How much 3 food does Holly need each morning to feed her 4 cats? Part A: Draw a model for the problem. Part B: How much food does Holly need each morning to feed her 4 cats? __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ 5. The label on a box of cookies states that one serving is 1 of the box. Each of 8 the 6 people in a family ate one serving of the cookies. What fraction of the box of cookies did the family eat? _____________________ 6. The distance of one lap around a track is 1 mile. Casey ran 12 laps. 4 Part A: Write an expression that can be used to find the total number of miles that Casey ran. _____________________ Part B: How many miles did Casey run? Show your work. ______________________ 7. Jake wants to find the value of 4 27 . 10 100 Part A: What fraction can Jake write that is equal to 4 and has a 10 denominator of 100? ___________________ Part B: Show how you can use the fraction from Part A to find the value of 4 27 . 10 100 _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ 8. Kelly finds 7 11 . Her work is shown in the box below. 10 100 Since the two fractions have different denominators, I wrote with a denominator of 100. 7 10 7 7 , so I added 10 100 7 11 18 . 100 100 100 Kelly’s work contains an error. State the error that Kelly made. Show how to find 7 11 correctly. 10 100 _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ For questions 9–11, add the fractions. Write each sum as a fraction with a denominator of 100. 9. 2 43 10 100 10. 8 6 10 100 12. Howard placed 100 pennies in a pile. He removed 48 pennies from the pile. Part A: Write a fraction to represent the part of the pile of pennies that Howard removed. ______________ Part B: Write a decimal to represent the part of the pile of pennies that Howard removed. _______________ 13. Complete the table below with the decimal number that is equal to each fraction. Fraction 18 100 3 10 7 100 76 100 Decimal Number 14. Part A: Write a fraction that represents the shaded part of the large square. ________________ Part B: Write a decimal number that represents the shaded part large square. of the ________________ 15. How many square inches of felt is needed to cover the top of a rectangular table that has a length of 92 inches and a width of 46 inches? Show your work. 16. Mo bought a rectangular piece of carpet for his living room, which has an area of 96 square feet. The length of his rectangular living room is 12 feet. What is the width, in feet, of Mo’s living room? Show your work. 18. Student The table shows the lengths, in inches, of the shoes of the students in Lisa’s class. Length of Student’s Shoe Student Length of Student’s Shoe (in inches) (in inches) Lisa 6 1 4 Diane 6 1 2 Sangam 5 1 8 Fred 7 1 4 Melissa 6 1 2 Hal 7 1 8 Justin 8 1 8 Monique 6 1 2 Ray 7 1 4 Briyona Connie 6 1 4 6 Part A: Make a lineplot of the data. Be sure to include labels. Part B: What is the difference between the length of the longest shoe and the length of the shortest shoe? _____________ 19. The students in a study group each measured the thickness of notebooks. The results are shown in the lineplot below. their math If the students stack their notebooks one on top the other, what will be the total thickness of the stack? a. b. c. d. 7 8 3 2 8 1 2 2 7 2 8 1 inches inches inches inches 20. Mr. Bruno ordered 78 pencils for the students in his class. He ordered enough pencils for each student to have exactly 3 pencils. How many students are in Mr. Bruno’s class? Mr. Bruno ordered 78 pencils for the students in his class. He ordered enough pencils for each student to have 3 pencils. How many students are in Mr. Bruno’s class? Use a letter to represent the number of students in Mr. Bruno’s class. Write an equation and use it to solve the word problem. __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ ____________________________________________________ 21. A group of 5 friends has a total of 74 marbles. Each of the friends is given an equal number of marbles and there are 4 marbles left over. How many marbles did each friend get? Use a letter to represent the number of marbles each friend got. Write an equation and use it to solve the word problem. _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ 22. Leah scored 26 points in a basketball game. She made 7 baskets worth 2 points each, and she also made some baskets worth 3 points each. How many 3-point baskets did Leah make in the game? Use a letter to represent the number of 3-point baskets Leah made. Write an equation and use it to solve the word problem. _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ 23. The mass of one green block is 450 grams. The mass of one yellow block is 0.7 kilograms. Part A: Which block has a greater mass? How much greater is the mass, in kilograms? ___________________________________________ ___________________________________________ Part B: What is the total mass, in kilograms, of 3 green blocks and 2 yellow blocks? __________________________________________________________ ___________________________________________________________ 24. 25. On the first day of summer, the height of a plant was 9 inches. At the 3 end of the summer, the height of the plant was 3 feet. The height of 4 the plant at the end of the summer is how many times the height of the plant at the beginning of the summer? a. 3 b. 4 c. 5 d. 6 1 hours playing computer games. His younger sister 3 spends 45 minutes playing computer games. How many more minutes does Jeff spend playing computer games than his sister spends? Jeff spends 1 ____________________