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Name _________________ Period_____ Date _________ Grade 3 Summer Packet – Going into 4th Grade 3. Jenelle doesn’t know all the multiplication facts. Which could Jenelle use to help find 8 7 ? a. 6 4 plus 2 3 b. 5 2 plus 3 6 c. 8 2 plus 8 4 d. 8 2 plus 8 5 4. Which equals 2 6 ? a. The sum of 2 1 and 2 6 b. The sum of 2 2 and 2 4 22 d. The sum of 2 5 and 2 0 c. The sum of 2 3 and 5. Which would be the best first step to help find 2 3 8 6 7 quickly? a. 2 3 5 and 3 8 11 c. 3 8 11 and 6 7 13 6. b. 2 8 10 and 3 7 10 d. 2 6 8 and 3 6 9 Two students explained how they found the product 2 3 5 using different methods. Jamar’s Method 2 times 3 is 6, and 6 times 5 is 30. Anita’s Method The product of 3 and 5 is 15, and the product of 2 and 15 is 30. Part A: Explain why both methods are correct. _______________________________ __________________________________________________________________ __________________________________________________________________ Part B: Show another way to find the product using a different way of thinking from Jamar’s or Anita’s method. 5. Write a multiplication equation that could be used to find 35 7 6. Ken knows that 4 6 24. Write the numbers 4, 6, and 24 in the boxes below to give a related division equation. 7. . = The answer to 32 4 can be found by thinking of which of the following equations? a. 32 4 36 b. 32 4 28 c. 4 8 32 d. 2 16 32 8. Which of the following equations is another way to find the value of 56 8 a. ? 8 56 b. 8 56 8 56 c. d. 8 56 in 9. Find the product of the numbers given. 10. a. 8 5 b. 3 9 c. 7 4 d. 2 7 Find the quotient of the numbers given. a. 35 5 b. 24 3 c. 16 8 d. 28 7 Use a drawing or an array to solve the word problems in questions 11–12. 11. Shirley needs 3 pieces of rope for a project. Each piece of rope must be 12 feet long. How much rope does Shirley need for the project altogether? Use a drawing or an array to show your work. 12. Sam ran 21 miles total on Friday, Saturday, and Sunday. He ran the same number of miles on each day. How far did Sam run on Friday? Use a drawing or an array to show your work. Write an equation to solve the word problems in questions 14–17. 14. Sue put 24 toy cars into 4 equal rows. How many toy cars are in each row? Write an equation to solve the problem. 15. Tina uses 7 beads to make a bracelet. She made 4 bracelets. How many total beads did she use? Write an equation to solve the problem. 17. An electronic game has 35 spaceships arranged in equal rows of 5 spaceships. How many rows will there be? Write an equation to solve the problem. Use the multiplication table below for questions 18–20. 18. 1 2 3 4 5 6 1 1 2 3 4 5 6 2 2 4 6 8 10 12 3 3 6 9 12 15 18 4 4 8 12 16 20 24 5 5 10 15 20 25 30 6 6 12 18 24 30 36 Explain what happens when any number is multiplied by 1. _______________________________ __________________________________________________________________ 19. Explain what happens when any number is multiplied by 2. _______________________________ __________________________________________________________________ 20. Look at the multiplication facts for the number 4. Explain how those multiplication facts compare to the multiplication facts for the number 2. _______________________________ __________________________________________________________________ Use the addition table below for questions 21–23. + 1 2 3 4 5 6 7 8 9 10 21. 1 2 3 4 5 6 7 8 9 10 11 2 3 4 5 6 7 8 9 10 11 12 3 4 5 6 7 8 9 10 11 12 13 4 5 6 7 8 9 10 11 12 13 14 5 6 7 8 9 10 11 12 13 14 15 6 7 8 9 10 11 12 13 14 15 16 7 8 9 10 11 12 13 14 15 16 17 8 9 10 11 12 13 14 15 16 17 18 9 10 11 12 13 14 15 16 17 18 19 10 11 12 13 14 15 16 17 18 19 20 Explain the pattern that happens every time two even numbers are added. _______________________________ __________________________________________________________________ 22. Explain the pattern that happens every time two odd numbers are added. _______________________________ 23. __________________________________________________________________ Explain the pattern that happens every time an odd number and an even number are added. _______________________________ __________________________________________________________________ 24. + 1 2 3 4 5 6 7 8 9 10 Explain why the numbers on each diagonal in the table are the same, such as the shaded numbers shown in the table below. 1 2 3 4 5 6 7 8 9 10 11 2 3 4 5 6 7 8 9 10 11 12 3 4 5 6 7 8 9 10 11 12 13 4 5 6 7 8 9 10 11 12 13 14 5 6 7 8 9 10 11 12 13 14 15 6 7 8 9 10 11 12 13 14 15 16 7 8 9 10 11 12 13 14 15 16 17 8 9 10 11 12 13 14 15 16 17 18 9 10 11 12 13 14 15 16 17 18 19 10 11 12 13 14 15 16 17 18 19 20 _______________________________ __________________________________________________________________ __________________________________________________________________ 25. What is the area, in square units, of the rectangular array shown below? = 1 square unit Area = _________________ Write the lengths of the sides of the array. Width = ________________ Length = _______________ Explain how the width and length relate to the area. 26. A rectangular array has a length of 4 units and a width of 2 units. Draw the array and find its area. Explain your answer. 27. The area of a rectangular array is 20 square units. What are possible values of the length and width of the array? Width = ____________________ Length = ____________________ In questions 1-6, multiply each. 1. 77 4. 7 6 2. 59 5. 12 3 3. 48 6. 18 2 In questions 7-11, divide each. 7. 48 8 10. 35 7 12. 8. 11. 50 2 9. 44 4 36 4 Part A: What is 34 2 ? Part B: What multiplication fact can you use to check your answer? ________________ Use the clock below to answer questions 13 and 14. 13. Aja got on the school bus at 7:15 A.M. It took 37 minutes to get to school. What time did she arrive at school? _____________________ 14. Pablo took a trip from New York to Florida. His plane left New York at 10:30 A.M. and arrived in Florida at 1:00 P.M. How long, in minutes, was Pablo’s flight? Use the number line below to help answer the question. __________________ 15. The table below shows Jennifer’s schedule each school day. School begins at 8:30 A.M. with reading class. Use the clock below to help find the time that Jennifer’s lunch begins. ACTIVITY Reading Art Math Lunch Gym Science & Social Studies 16. JENNIFER’S SCHOOL SCHEDULE AMOUNT OF TIME 1 hour 45 minutes 1 hour and 15 minutes 30 minutes 45 minutes 2 hours and 20 minutes Marcus compares the amount of water in the two containers with the amount of milk. He says the amount of water is greater than the amount of milk. Is Marcus correct? Circle yes or no. Yes No Show your work and explain your answer. __________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ _______________________________________________________________________ 17. Ali put books on one scale and a pumpkin on another scale. Which of the following statements are true? For each statement, put a check in the oval to choose true or false. True False The mass of the pumpkin is 4 kilograms more than the mass of the books. The mass of the pumpkin is 33 kilograms more than the mass of the books. The mass of the pumpkin is 4 times the mass of the books. The mass of the pumpkin is 33 times the mass of the books. 18. Which is the best estimate for the total amount of water in the two containers? a. 9 liters b. 10 liters c. 11 liters d. 12 liters 19. A whole is divided into 5 equal parts. Write the fraction that represents 3 parts of the whole. ________________ 20. 4 of a cup of flour to make muffins. She will measure the flour using 5 1 1 a -cup scoop. How many times will Cara need to fill the -cup scoop in order 5 5 4 to measure of a cup of flour? 5 Cara needs ________________ 21. Jenny cut her jump rope into 3 pieces that are the same length. The length of one piece of rope is what fraction of the length of the jump rope? ________________ 22. Which of the following could be used to show a. C. b. d. 1 ? 6 23. Show how to cut the apple pie into 4 equal slices. What fraction represents one slice? __________ 24. The chocolate bar is made of smaller rectangular pieces that are equal in size. Write a fraction to represent one of the smaller pieces of the chocolate bar. _____________ 25. Mark the number line to show 1 . Label 0 and 1 on the number line. 4 26. Label the marks on the number line. Place a point at the location of a fraction. Label 0 and 1 on the number line. Explain why the point located has the number labeled. ____________________________________________ ____________________________________________ ____________________________________________ 27. The point on the number line below represents the fraction 1 . Label 0 and 1 on the number line. 6 Explain why the number at the point must be named 5 . 6 ____________________________________________ ____________________________________________ ____________________________________________ 5 . Locate and label 6 28. Brian’s music player can hold 5 songs. Brian has put 1 song on the player. Mark on the number line to show what fraction 1 song is of the 5 songs. Label 0 and 1 on the number line. 29. The point on the number line represents what fraction? _____________ 30. Label the number line to show the point where 2 is located. Label 0 and 1 on 3 the number line. 31. Label the number line and place a point where the fraction 0 and 1 on the number line. 3 is located. Label 6 32. Sing Li had 120 baseball cards. After Sing Li bought 50 more cards, Sing Li had 35 more cards than Ray. Which of the following equations shows how to find the number of cards that Ray has? n is the number of cards Ray has. 33. a. n 120 50 35 b. n 120 35 50 c. n 120 50 35 d. n 120 50 35 There are 51 books on a bookshelf. There are 7 books on the top shelf. There are 4 lower shelves that each have the same number of books. k is the number of books on each lower shelf. Part A: Write an equation that can be used to find the value of k. ___________________ Part B: How many books are on each lower shelf? ______________ 34. Mary had 10 carrots. She ate 5 carrots, and then Joe gave her some more carrots. Mary then had 8 carrots. Write an equation that can be used to find how many carrots Joe gave Mary. ___________________________ How many carrots did Joe give Mary? ___________ 35. A word problem is shown in the box. Ray had $50. He bought 2 shirts that cost $19 each. How much money did Ray have after buying the shirts? Alex’s answer to the word problem is $29. Is Alex’s answer reasonable? Circle YES or NO. YES NO Explain your choice using estimation. ____________________________________________ ____________________________________________ ___________________________________________ In questions 1–8, multiply or divide. 1. 5 9 5. 42 7 2. 8 6 3. 97 6. 81 9 7. 72 9 In questions 9–10, add or subtract. 9. 192 749 10. 651 376 4. 8. 69 56 7 13. Which figure above is not a quadrilateral? 14. a. I b. II c. III d. IV Which of the figures below have both of the properties listed? List all that have both properties. Properties: 1) All side lengths appear to be equal. figure is a quadrilateral. Answer(s): _____________ What is the name of one of the quadrilaterals chosen? ___________________ 15. Find an equivalent fraction for 3 6. 2) The In questions 15–16, there may be one or more common features shared by the figures. 15. Name a feature that appears to be shared by figures B and C but is not shared by figures A and D. _________________________________________________________________ _________________________________________________________________ What name describes figures B and C but does not describe figures A and D? Answer: ______________ 16. Name a feature that is shared by all of the figures A, B, C, and D. __________________________________________________________________ __________________________________________________________________ What name describes all of the figures A, B, C, and D? Answer: ______________ 17. Draw a polygon on the dot grid below that meets both of the following properties. The polygon is a rectangle has all sides of equal length List 3 other names for the rectangle drawn. 18. Circle all words that can describe the shape of the computer screen (not including the base) below. More than one word may be circled. Square 19. 20. Parallelogram Rectangle Rhombus Trapezoid A rectangle is formed by bending a wire that is 32 centimeters long. The length of the rectangle is 12 centimeters. What is the width, in centimeters, of the rectangle? a. 2 c. 6 b. 4 d. 8 The figure below shows the outline of the floor of Rita’s house. What is the perimeter of the floor of the house? Answer: Perimeter = _________________ units 21. Part A: Fill in the blanks below. The area of the figure above is ______ square units, and the perimeter is _______ units. Part B: Draw a rectangle on the grid below that has the same area as the rectangle in Part A but has a different perimeter. What is the perimeter of the new rectangle? Answer: Perimeter = _________ units 22. 1 5 1 8 23. 4 7 6 7 22. Part A: Draw a figure in the grid below that has 3 rows of squares with 6 squares in each row. What is the area, in square units, of the figure? Answer: Area = __________ square units Part B: Explain how the area of the figure drawn above could be calculated without counting the small squares? ________________________________________________________________________ ________________________________________________________________________ ___________________________________________________________________ 23. The rectangle above is partially filled with square tiles. Explain how the area of the rectangle above can be found without counting the rest of the square tiles that would be needed to fill the rectangle. ____________________________________________ ____________________________________________ ____________________________________________ 24. Meghan would like to practice cheerleading in her home’s basement, which is 9 feet by 8 feet. The local hardware store has a sale on square pads that have sides that are 1 foot in length. In order to cover the floor, what is the minimum number of square pads that must be used? Explain your answer. __________________________________________________________________ __________________________________________________________________ 25. Which of the following equations represents the total area of the shaded region shown above? 26. a. Area = 3 2 5 c. Area = 3 2 5 b. Area = 3 2 5 d. Area = 3 2 5 Use an area model to show whether 3 8 equals 3 (6 2). Explain why or why not. ______________________________________________________________________ ________________________________________________________________________ 27. Which of the following area models represents the expression 6 (3 5) ? a. b. c. 28. d. Which of the following gives the area, in square units, of the figure below? a. 32 4 4 b. 32 73 c. 36 4 4 d. 37 47 30. Which of the following two figures has the greater area? Explain your answer. Figure I Figure II __________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ 31. Find the area, in square units, of the rectangle shown below. The area of each small square is 1 square unit. Answer: Area = __________________ square units 32. 33. Derek tiles a path that is 1-foot wide on each side around a pool, as shown by the diagram below. The area of each tile is 1 square foot. Which of the following will be the total area of the path? a. 4 square feet b. 20 square feet c. 24 square feet d. 112 square feet What is the total area, in square centimeters, of the figure shown below? The area of each small square is 1 square centimeter. a. 15 b. 20 c. 60 d. 75