Quarter 4 Wee 3 MATHEMATICS POWERPOINT 5

Math 5 3rd Quarter

1. MATHEMATICS 5 QUARTER 4 WEEK 3 DAY 1 Finding the Volume of a given Cube and Rectangular Prism

2. Review:

3. Consider the problem below. Teacher Leny brought to her class a 3 × 3 × 3 Rubik’s cube. She told the class to determine the amount of space enclosed in the object. A Rubik’s cube is a solid figure which contains cubic units. If each is a cubic unit, how many cubic units are there in the figure? How many cubic units are there in one layer? How many layers are there? How many cubic units are there?

4. In this lesson, you are going to deal about finding the volume of a given cube and a rectangular prism using cubic centimeters (cu. cm or cm³) and cubic meters (cu. m or m³).

5. Study the answer of the given problem. Teacher Leny brought to her class a 3 × 3 × 3 Rubik’s cube. She told the class to determine the amount of space enclosed in the object. A Rubik’s cube is a solid figure which contains cubic units.

6. If each is a cubic unit, how many cubic units are there in the figure? How many cubic units are there in one layer? How many layers are there? How many cubic units are there?

7. In a rectangular prism, the base is always a rectangle. The area of the base is the product of its length (l) and width (w). Thus, to get the volume of the prism, we may multiply the area of the base with the height (h).

8. Volume of a rectangular prism = area of the base × height of the prism 𝑉 = l × w × h. Study the rectangular prism below and the computation for its volume on the right.

9. Note that 125 cm³ is read either as 125 cubic centimeters or 125 centimeters cube.

10. Example 3 What is the amount of space that is occupied by a rectangular pool which is 5.5 m in width, 10 m in height and 7 m in depth (height).

11. Complete Me! Direction: Find the volume of the cubes and rectangular prisms. On your answer sheet, copy and supply your answers for the following.

12. In your own words, explain how to find the volume of a cube and a rectangular prism.

13. What is the formula in getting the volume of a cube? How about rectangular prism?

14. Find Me! Directions: Find the volume of the solid figures below. Write your answers in your Math Activity notebook.

15. MATHEMATICS 5 QUARTER 4 WEEK 3 DAY 2 Estimating and using appropriate units of measure for volume

16. Review; Let us recall some of the different cubic units of measure in the metric system arranged from smallest to largest unit.   mm 3 cm 3 dm 3 m 3 dam 3 hm 3 km 3   Answer: mm 3 cm 3 dm 3 m 3 dam 3 hm 3 km 3

17. Look at the picture: What is in the picture? Have you ever measured the length, height and width of a book? Which of the following units of measure would be appropriate to use?

18. You already have an idea how big or small everyday objects are. You should have an idea of how big or small the different units of volume are so you can match these with the objects.

19. The common units of measure for lengths, width, and height are meter, centimeter, millimeter, foot, yard and inch. In our country, we are usually using the units in metric system like meters, kilometers, centimeters and millimeters. Other countries use the units in imperial system like feet, yards and inches. You may have seen people using feet, yards and inches for measuring lengths.

20. If we need to measure the dimensions of a small object, we can use centimeter, millimeter, decimeter, or inches. However, for bigger, longer or wider objects, the units that can be used are foot, yard, meter or kilometer.

21. You already know that volume is the amount of space that is enclosed in a 3-dimensional or solid figure. Since it is an amount of space, it has to be measured in cubes. For instance, if the dimensions of a solid figure are in meters, the volume would be measured in cubic meters or m3. If the 3-dimensional figure is measured in inches, the volume would be in cubic inches or in3.

22. Let’s consider the example in the previous part of the lesson. What do you think is an appropriate unit of measure to be used for finding the volume of the book?

23. A book may represent a solid figure. Its dimensions are small. Hence, the volume is also small. Therefore, you may use inches or centimeters as units of measure for the length, width and height of the book. The volume of the book can be in cubic inches or cubic centimeters.

24. Read and study the examples below. Example 1 For the volume of the water in an aquarium, the appropriate units of measure to use are cubic centimeters (c m 3 ) or cubic inches (in 3 ).

25. Example 2   The appropriate unit of measure for the amount of space enclosed in the tank is cubic meters or m 3 .

26. Another Examples Example 3 Let the volume of Figure A be 100 c m 3 . We can estimate the volumes of the other figures.

27. Figure B is almost half of the size of Figure A. Figure C is almost double the size of Figure A. Figure D is about the same size of Figure A.

28. Thus, the volumes of Figures B, C and D are approximately 50 cm 3 , 200 cm 3 and 100 cm 3 , respectively.

29. Example 4 A box is in the shape of rectangular prism. Its length, width and height are 2.8 m, 1.1 m and 0.95 m. Multiplying the dimensions, rounded off to the nearest whole numbers, gives a good estimate of the volume of the prism. Length: 2.8 m is rounded up to 3 m. Width: 1.1 m is rounded down to 1 m. Height: 0.95 m is rounded up to 1 m. Approximate volume = length × width × height = 3 m × 1 𝑚 × 1 𝑚 = 3 m3 Thus, an estimate for the volume of the box is 3 m3. It could also between 2 m3 and 3 m3.

30. Approximate volume = length × width × height = 3 m × 1 𝑚 × 1 𝑚 = 3 m 3   Thus, an estimate for the volume of the box is 3 m 3 . It could also between 2 m 3 and 3 m 3 .

31. Example 5 A piece of wood is in the shape of a cube. If its edge is 0.21 m, estimate the volume of the piece of wood.

32. Solution : If we are going to estimate the volume of the piece of wood, it is not logical to round it off to the nearest whole number, as that would be zero. This would give us a zero cubic meter for volume.   Since rounding off to the nearest whole number is not a good strategy, we may do it another way. You already know that 1 m = 100 cm. .

33. It follows that 0.21 m = 21 cm ≈ 21 cm.   Let us use 20 cm as our estimate. Approximate volume = 20 𝑐𝑚 × 20 𝑐𝑚 × 20 𝑐𝑚 = 8 000 cm 3   Thus, an estimate for the volume of the wood is 8 000 cm 3 . It must be less than a cubic meter.

34. Choose Me In! Directions: Select the appropriate unit of measure for the volumes of the following objects. Write your answers on a separate sheet of paper.

35. What are the appropriate unit of measure used for volumes of the following items in our kitchen. 1. Refrigerator 2. Kitchen Cabinet

36. What have you learned?

37. Pair Me Up! Directions: Match the items in column A with the units of measure in column B in finding the volume of the given objects. Write the letter of your answer on your answer sheet.

38. MATHEMATICS 5 QUARTER 4 WEEK 3 DAY 3 Solving routine problems involving volume of a cube and rectangular prism.

39. Review! Pair Me Up! Directions: Match the items in column A with the units of measure in column B in finding the volume of the given objects. Write the letter of your answer on your answer sheet.

40. Ask: What do you mean by the word “Routine”?

41. Routine problems are real life problems. - It involves at least one of the four operations to solve practical problems. - It requires basic skills and organized and sequenced steps. - Planned strategies and methods are needed to come up with the answer.

42. This Four-Step Method is used to solve the problem. 1. Understand: Know what is asked. Identify the given facts. 2. Plan: Choose the operation or the formula to be used. 3. Solve: Perform the strategy.

43. Suggested Strategies Drawing a model/diagram Using a formula and changing them to mathematical symbol. Working Backward 4. Check: Verify if the answer is correct.

44. Remember:  Volume (V) is the number of cubic units needed to fill the shape. It is the amount of space that is occupied by a solid figure.  Cube and rectangular prism are examples of a solid figure.

45. The formula in finding the volume of a cube: V= s x s x s or s 3 The formula in finding the volume of rectangular prism is V = l x w x h

46. Problem 1 Miguel made a rectangular prism picture frame with the family’s picture on its faces as his birthday gift to his father and mother who happens to have the same birthdate. Find the volume of Miguel’s picture frame with 4 inches long, 3 inches wide and 6 inches tall.

47. To solve the problem, we can use the 4-Step Method. Understand:  Know what is asked. The volume of Miguel’s picture frame  Know the given facts. 4 inches – length 3 inches width 6 inches height

48. Plan  Determine the operation or formula to be used. Formula: Volume of rectangular prism (V = l x w x h) Operation: Multiplication

49. Solve : Show how the solution is done.   Use and change the formula into mathematical sentence. (V = l x w x h) Substituting the formula: V = 4 in x 3 in x 6 in V = 72 in 3

50. Check: To check if you solve the problem correctly you can solve for either length, the width or the height. This time we are going to solve for length. Formula: V = l x w x h Substitute: 72 in 3 = l x 3 in x 6 in

51. Problem 2 Jules gift to his father’s birthday is a rubik’s cube because it was his favorite pastime. What is the volume of the Rubik’s cube if the edge is 5 centimeters?

52. To solve the problem, we can use the 4-step method. Understand;  Know what is asked. The volume of the Rubik’s cube  Know the given facts. 5 centimeters – edge

53. Plan Determine the operation or formula to be used. Formula: Volume of cube (V = s 3 ) Operation: Multiplication

54. Solve: Show how the solution is done. Use and change the formula into mathematical sentence. (V = s 3 )   V = 5cm 3 = 125 cm 3 Complete Answer: 125 cm 3 is the volume of the Rubik’s cube.

55. Check: To check if we solve the problem correctly just go back to your solution and check your computation.

56. PRACTICE EXERCISE 1. A rectangular tank measures 6 dm long, 5 dm wide and 20 dm tall. What is the volume of the tank? _____________________________________________________________ 2. What is the volume of the cube with an edge of 7 cm? __________________________

57. 3. The Town Engineer made a model of the building to house the patients of Covid 19. The model building has the length of 8 dm,5 dm as the width and 14 dm as the height. Find the volume of the building. ____________________________

58. What is the meaning of routine problem? Routine problems are real life problems. - It involves at least one of the four operations to solve practical problems. - It requires basic skills and organized and sequenced steps. - Planned strategies and methods are needed to come up with the answer.

59. Remember: Routine problems are practical problems and can be solved using the 4-step method. These methods are: understanding the problem- know what is asked and identify the given facts; planning-determine the formula or operation. solving-show how the solution is done; checking;

60. Directions : Read each problem carefully and encircle the letter of the correct answer. 1. How much space in a room will a cabinet occupy if it is 1.9 m long, 0.61 m wide, and 2.74 m high? 3.17566 m 3 3.28566 m 3 4.566 m 3 5.3216 m 3

61. 2. A box is 3.5 dm long and 6 dm high. Its volume is 210 dm 3 . How wide is it?   A) 6 B) 8 C) 10 D) 12

62. 3. A rectangular container is 0.4 m long, 0.3 m wide, and 1 m high. What is its volume? A) 5.12 m 3 B) 3 m 3 C) 1.12 m 3 D) 0.12 m 3

63. 4. Mother made a rectangular plot with 15 ft wide, 26 ft long and 4 ft high. Find the volume of mother’s plot? A) 1500 ft 3 B) 1560 ft 3 C) 1566 ft 3 D) 1570 ft 3

64. 5. A pit is 7 dm long, 5 dm wide, and 8 dm deep. How many cubic decimeters of sand will fill the pit? A) 310 dm 3 B) 300 dm 3 C) 290 dm 3 D) 280 dm 3

65. MATHEMATICS 5 QUARTER 4 WEEK 3 DAY 4 Solving non-routine problems involving volume of a cube and rectangular prism.

66. Review: What is the meaning of Routine Problems?

67. Our lesson will focus on solving non-routine problems. Do you still remember the formula in getting the volume of rectangular prism and cube? Here are they;   Volume of cube V= S 3 or S x S x S Volume of rectangular prism V= L x W x H

68. A non-routine problem is any complex problem that requires some degree of creativity or originality to solve. Non-routine problems typically do not have an immediately apparent strategy for solving them. Oftentimes, these problems can be solved in multiple ways.

69. TRY TO DISCOVER! An aquarium is 100 cm long, 50 cm wide and 80 cm high. If it is filled halfway through its height, how much volume of water is in it? We can apply the following steps in solving the given problem.

70. Step 1. Understand: Read and understand. No pencil or paper necessary for this step. Remember, you cannot solve a problem until you know what the problem is!

71. What is asked in the problem? The volume of water in the aquarium. What are the needed information? Length= 100 cm width = 50 cm height = 80 cm

72. Step 2. Plan: Now it’s time to decide on a plan of action! Choose a reasonable problem-solving strategy.

73. Several are listed below. You may only need to use one strategy or a combination of strategies. • draw a picture or diagram • make an organized list • make a table • solve a simpler related problem • find a pattern • guess and check

74. • act out a problem • work backward • write an equation • use manipulatives • break it into parts • use logical reasoning

75. In our problem, we will need to draw a picture of an aquarium. What is asked in the problem is only the amount of water inside the aquarium and not the volume of the aquarium but we need the dimensions of the aquarium.

76. Step 3. Solve or Execute: Now it’s time to dig in and get to work! V = L x W x H = 100 cm x 50 cm x 40 cm V = 200 000 cu.cm height of the water is only 40cm because it is only half filled

77. Step 4. Check or Review : Reviewing your work is just as important as the first 3 steps! Reread the problem and review all your work. V = (L x W x H) ÷ 2 = (100 cm x 50 cm x 80 cm) ÷ 2 V = 400 000 cu.cm ÷ 2 V = 200 000 cu.cm Therefore, the volume of water is 200 000 cm 3

78. Let’s try another one. What is the maximum number of cubes 5 cm on an edge that can be packed into a carton with dimensions 18 cm, 32 cm, 25 cm? The problem is asking for the number of cubes. To solve this problem, we can make a drawing or use manipulatives.

79. The number of cubes that can fill the box are 6 x 3 x 5 because each side of the cube is 5 cm long. Therefore, there are 90 cubes that can filled the carton box.

80. PRACTICE EXERCISE 1 Read the problem and do the needed steps. The width of a rectangular prism is doubled, its length is tripled, and its height is cut in half. If the volume of the original prism was V, what is its new volume?.

81. 1.What is asked? __________________________________________ 2. What are the given? __________________________________________ 3. What strategy will you do? __________________________________________ 4. What is the operation? ________________________________________ 5. What is the answer? __________________________________________

82. What is the meaning of non-routine problem? A non-routine problem is any complex problem that requires some degree of creativity or originality to solve. Non-routine problems typically do not have an immediately apparent strategy for solving them. Oftentimes, these problems can be solved in multiple ways.

83. REMEMBER In solving non routine problems we can used different strategies to be able to it . You may only need to use one strategy or a combination of strategies. • draw a picture or diagram • make an organized list • make a table

84. • solve a simpler related problem • find a pattern • guess and check • act out a problem • work backward • write an equation • use manipulatives • break it into parts • use logical reasoning

85. MATHEMATICS 5 QUARTER 4 WEEK 3 DAY 5 Catch-Up Friday