Setting Up and Solving Division and Multiplication Problems

The Prototype was created to review multi-digit multiplication and division problems using 4th and 5th Grade South Carolina Standards of Mathematics. The Prototype reviewed the step-by-step procedures on solving multiplication and division problems, provided practice problems for the learner, and concluded with a posttest to determine the effectiveness of the prototype.

Transcript

1. Carolyn Boyce EDET 722-J50 December 5, 2019 hallce5@email.sc.edu Setting Up and Solving Whole Number Multiplication and Division Problems
2. Overview Ê Welcome to a multiplication and division module designed for 5th grade students. Ê The purpose of this module is to review multiplication and division strategies needed to find the speed, direction, and time in the 5th Grade Force and Motion Unit. Ê The module will walk the learner through the important steps of division and multiplication using examples and important vocabulary. The learner should have mastered grades 1 -4 mathematics before completing this course. Ê The learner will have time before the posttest to review each of the mathematical strategies covered in the module. Ê The module should take about 15-17 minutes to complete with 8-10 minutes left to complete the posttest. 2 of 101 2
3. Objectives Ê At the end of the module the learner should be able to: Ê Divide up to a four-digit dividend by a two-digit divisor Ê Multiply 4 digit by 1 digit and 2 digits using strategies to include a standard algorithm Ê Use subtraction in division problems Ê Set up Multiplication and Division problems with 2 digit numbers Ê Apply knowledge of multi-digit multiplication and division to patterns and real-world problems 3 3 of 101
4. Overview Ê The Module should be completed in order of the presentation. After completing the presentation, you can go back and review a certain unit by clicking on the specific objective on the right hand side flag ( ) . Ê Click on the Home Icon ( )to be taken back to the home screen and click on the arrow ( )to be taken to the next screen. Ê Click on the ( ) to end the module at any point. 4 4 of 101
5. Goal 1 Set up Multiplication and Division problems with 2 digit numbers 5 5 of 101
6. Important Vocabulary Ê Before we begin the module, you should know a few key vocabulary words. Ê Division is the opposite of multiplication. Division is dividing the dividend by the divisor Ê Dividend: the number that needs to be divided up into a smaller number Ê Divisor: the number being divided by Ê Divisor Ê Multiplication is a number added to itself a specific number of times Ê Number x the amount of times it is added to itself = product Dividend Goal 1 Goal 2 Goal 3 Goal 4 6 6 of 101
7. Goal 2 Divide up to a four-digit dividend by a two-digit divisor 7 7 of 101
8. How to set up and solve a four digit division problem Ê Step 1) Place the divisor before the division bracket and place the dividend under it. Ê Example: 4824 ÷ 24 Ê The divisor is the 24 and the dividend is 4824 4824 24 Goal 1 Goal 2 Goal 3 Goal 4 8 8 of 101
9. How to set up and solve a four digit division problem Ê Step 2) Examine the first two digits of the dividend and determine if it is greater or less than the divisor. If greater than divide the first two numbers of the dividend by the divisor. If less than look at the first three numbers of the dividend and divide by the divisor. Ê The first two numbers of the dividend are 48 so can you solve 48 ÷ 24? Yes the answer is 2 Goal 1 Goal 2 Goal 3 Goal 4 9 9 of 101
10. How to set up and solve a four digit division problem Ê Step 3) Place the answer above the third number if you divide by it or if you divide by the first two numbers then place the answer above the second number. Goal 1 Goal 2 Goal 3 Goal 4 4824 24 2 The two goes above the 8 in this example since 8 is the second number 10 10 of 101
11. How to set up and solve a four digit division problem Ê Step 3b) Multiple the answer to the divisor. Place the answer under the dividend Ê Multiply 24 x 2 and get 48 Ê Put 48 under the dividend Goal 1 Goal 2 Goal 3 Goal 4 4824 24 2 48 11 11 of 101
12. How to set up and solve a four digit division problem Ê Step 4) We use subtraction. Subtract the dividend by the answer of the divisor multiplied by the answer of the first part of the division problem. Ê Subtract 48 – 48 Goal 1 Goal 2 Goal 3 Goal 4 4824 24 2 - 48 12 12 of 101
13. How to set up and solve a four digit division problem Ê Step 5) Write the answer to the subtraction problem then drop down the next number of the dividend next to the subtraction answer. Ê The answer of 48 – 48 is zero so write that number the subtraction problem Goal 1 Goal 2 Goal 3 Goal 4 4824 24 2 - 48 0 13 13 of 101
14. How to set up and solve a four digit division problem Ê Now bring the 2 next to the zero. You cannot divide 2 ÷ 24 so drop down the 4 Goal 1 Goal 2 Goal 3 Goal 4 4824 24 2 - 48êê 0 2 4 14 14 of 101
15. How to set up and solve a four digit division problem Ê Step 6) Divide the new number by the divisor and then write the answer next to the first answer creating a two digit number Ê The new number is 24 so the new number by the divisor is 24 ÷ 24 and 24 ÷ 24 = 1 so write the 1 next to the 2 on top of the equation Goal 1 Goal 2 Goal 3 Goal 4 4824 24 21 - 48êê 0 2 4 15 15 of 101
16. How to set up and solve a four digit division problem Ê Step 7) Multiply the divisor and the second answer and write the answer under the first answer Ê Multiply 24 x1 since 24 is the divisor and 1 is the second answer then write 24 under the first 24 Goal 1 Goal 2 Goal 3 Goal 4 4824 24 21 - 48êê 0 2 4 - 2 4 16 16 of 101
17. How to set up and solve a four digit division problem Ê Step 8) Subtract the two answers and if you get zero than you have completed the problem. If you get something other than zero this is your remainder. We will not cover remainders in this module so all your problems should not have a remainder in this module. Ê Subtract 24 – 24 and 24 – 24 = 0 so you do not have a remainder Goal 1 Goal 2 Goal 3 Goal 4 4824 24 21 - 48êê 0 2 4 - 2 4 0 17 17 of 101
18. How to set up and solve a four digit division problem Ê You have found your answer to 4824 ÷ 24 = 21 Goal 1 Goal 2 Goal 3 Goal 4 18 18 of 101
19. Now that you have learned the steps, let’s practice a problem. 19 19 of 101
20. Practice Division Problem #1 Find the answer to 7670 ÷ 65 Click through the next slides to follow step by step on how to find the answer. Goal 1 Goal 2 Goal 3 Goal 4 20 20 of 101
21. Practice Division Problem #1 Goal 1 Goal 2 Goal 3 Goal 4 7670 65 21 21 of 101
22. Practice Division Problem #1 Goal 1 Goal 2 Goal 3 Goal 4 7670 65 1 - 65 11 22 22 of 101
23. Practice Division Problem #1 Goal 1 Goal 2 Goal 3 Goal 4 7670 65 1 - 65ê 11 7 23 23 of 101
24. Practice Division Problem #1 Goal 1 Goal 2 Goal 3 Goal 4 7670 65 11 - 65ê 11 7 - 6 5 ê 5 2 0 24 24 of 101
25. Practice Division Problem #1 Goal 1 Goal 2 Goal 3 Goal 4 7670 65 118 - 65ê 11 7 - 6 5 ê 5 2 0 - 5 2 0 0 25 25 of 101
26. Practice Division Problem #1 Therefore 7670 ÷ 65 = 118 Goal 1 Goal 2 Goal 3 Goal 4 26 26 of 101
27. Great Job with Long Division! 27 26b of 101
28. Now lets try some multiplication problems 28 27 of 101
29. Goal 3 Multiply 4 digit by 1 digit and 2 digits using strategies to include a standard algorithm 29 28 of 101
30. Multiplying 4 digit by 1 digit numbers Ê When Multiplying a 4 digit number by a 1 digit number the larger number is on top of the smaller number Ê For example 3628 x 4 is set up as 3628 x 4 Goal 1 Goal 2 Goal 3 Goal 4 30 29 of 101
31. Multiplying 4 digit by 1 digit numbers Ê Now we need to solve the problem so we multiply the single digit number to each of the numbers from the four digit number. Ê Start with the ones place: multiplying 8 x 4 from the example. 8 x 4 = 32 then place 2 in the ones place and carry the 3 to the top of the tens place on top of 2 3 3628 x 4 2 Goal 1 Goal 2 Goal 3 Goal 4 31 30 of 101
32. Multiplying 4 digit by 1 digit numbers Ê Now multiply 4 x 2 which equals 8 then add 3 more since you carried 3 so the answer in the ten place is 11. Put a 1 in the tens place and carry the other 1 from 11 to the top of 6 13 3628 x 4 12 Goal 1 Goal 2 Goal 3 Goal 4 32 31 of 101
33. Multiplying 4 digit by 1 digit numbers Ê Thirdly, multiply the single digit number to the hundred places. In the example, multiply 4 x 6 = 24. Place the 4 in the hundreds place answer and carry the 2 to the 3. 213 3628 x 4 412 Goal 1 Goal 2 Goal 3 Goal 4 33 32 of 101
34. Multiplying 4 digit by 1 digit numbers Ê Finally, multiply the single digit number to the thousandths place number. In the example, multiply 4 x 3 = 12 then add 3 since this was the number carried to the top so the answer is 15. Since this is the last number to multiply put the 1 and 5 in the answer. 213 3628 x 4 15412 Goal 1 Goal 2 Goal 3 Goal 4 34 33 of 101
35. Multiplying 4 digit by 1 digit numbers Ê Therefore 3628 x 4 = 15412. Ê DO NOT forget to carry the tens number and add it after multiplying when an answer is a double digit number. Goal 1 Goal 2 Goal 3 Goal 4 35 34 of 101
36. Now that you have learned the steps, lets practice a multiplication problem. 36 35 of 101
37. Practice Multiplication Problem #1 Find the answer to 8936 x 5 Click through the next slides to follow step by step on how to find the answer. Goal 1 Goal 2 Goal 3 Goal 4 37 36 of 101
38. Practice Multiplication Problem #1 8936 x 5 Goal 1 Goal 2 Goal 3 Goal 4 38 37 of 101
39. Practice Multiplication Problem #1 3 8936 x 5 0 Goal 1 Goal 2 Goal 3 Goal 4 39 38 of 101
40. Practice Multiplication Problem #1 3 8936 x 5 80 Goal 1 Goal 2 Goal 3 Goal 4 40 39 of 101
41. Practice Multiplication Problem #1 13 8936 x 5 680 Goal 1 Goal 2 Goal 3 Goal 4 41 40 of 101
42. Practice Multiplication Problem #1 413 8936 x 5 44680 Goal 1 Goal 2 Goal 3 Goal 4 42 41 of 101
43. Practice Multiplication Problem #1 Ê Therefore 8936 x 5 = 44,680 ÊWe will have more practice problems at the end. Goal 1 Goal 2 Goal 3 Goal 4 43 42 of 101
44. Multiplying 4 digit by 2 digit numbers Ê Now lets look at multiplying a 4 digit number by a 2 digit number. Ê When Multiplying a 4 digit number by a 2 digit number the larger number is on top of the smaller number just like a 4 digit number multiplied by a 1 digit number. Ê For example 3628 x 36 is set up as 3628 x 36 Goal 1 Goal 2 Goal 3 Goal 4 44 43 of 101
45. Multiplying 4 digit by 2 digit numbers Ê Now we need to solve the problem so we multiply. First we multiply the ones place from the 2 digit number to each of the numbers from the four digit number. Ê Start with the ones place: multiplying 8 x 6 from the example. 8 x 6 = 48 then place 8 in the ones place and carry the 4 to the top of the tens place on top of 2 4 3628 x 36 8 Goal 1 Goal 2 Goal 3 Goal 4 45 44 of 101
46. Multiplying 4 digit by 2 digit numbers Ê Now multiply 6 x 2 which equals 12 then add 4 more since you carried 4 so the answer in the tens place is 16. Put a 6 in the tens place and carry the other 1 from 16 to the top of 3 14 3628 x 36 68 Goal 1 Goal 2 Goal 3 Goal 4 46 45 of 101
47. Multiplying 4 digit by 2 digit numbers Ê Thirdly, multiply the single digit number to the hundred places. In the example, multiply 3 x 6 = 18 then add 1 which equals 19. Place the 9 in the hundreds place answer and carry the 1 to the 5. 114 3628 x 36 968 Goal 1 Goal 2 Goal 3 Goal 4 47 46 of 101
48. Multiplying 4 digit by 2 digit numbers Ê Finally, multiply the single digit number to the thousandths place number. In the example, multiply 6 x 5 = 30 then add 1 since this was the number carried to the top. Since this is the last number to multiply put the 3 and 1 in the answer. 114 3628 x 36 31968 Goal 1 Goal 2 Goal 3 Goal 4 48 47 of 101
49. Multiplying 4 digit by 2 digit numbers Ê Now that we have finished multiplying by the ones we have to multiply by the tens. When multiplying by the tens we place a 0 in the ones spot on the second row. 114 3628 x 36 31968 0 Goal 1 Goal 2 Goal 3 Goal 4 49 48 of 101
50. Multiplying 4 digit by 2 digit numbers Ê Now we multiply like we just did with the ones but now we use the 3 in the tens place. Ê First multiply 3 x 8 = 24. Place the 4 next to the 0 and carry the 2. When we carry number this time around we place them above the numbers we carried with the ones place. 2 114 3628 x 36 31968 40 Goal 1 Goal 2 Goal 3 Goal 4 50 49 of 101
51. Multiplying 4 digit by 2 digit numbers Ê Next we multiply 3 x 2 = 6 and add 2, which is 8. Since 8 is a single digit number we place it next to the 4. 2 114 3628 x 36 31968 840 Goal 1 Goal 2 Goal 3 Goal 4 51 50 of 101
52. Multiplying 4 digit by 2 digit numbers Ê Multiply 3 x 3 = 9. Since we did not carry any numbers from the last step we just write 9 next to the 8. 2 114 3628 x 36 31968 9840 Goal 1 Goal 2 Goal 3 Goal 4 52 51 of 101
53. Multiplying 4 digit by 2 digit numbers Ê Lastly, we multiply 3 x 5 = 15. Since this is the last number we multiply we write the 1 and 5 in the answer. 2 114 3628 x 36 31968 159840 Goal 1 Goal 2 Goal 3 Goal 4 53 52 of 101
54. Multiplying 4 digit by 2 digit numbers Ê Now we have to add the two answers together to get the final answer. 2 114 3628 x 36 31968 + 159840 191808 Goal 1 Goal 2 Goal 3 Goal 4 54 53 of 101
55. Multiplying 4 digit by 2 digit numbers Ê Therefore the answer to 5,328 x 36 = 191,808 Goal 1 Goal 2 Goal 3 Goal 4 55 54 of 101
56. Now that you have learned the steps, lets practice a multiplication problem. 56 55 of 101
57. Practice Multiplication Problem #2 Find the answer to 18936 x 52 Click through the next slides to follow step by step on how to find the answer. Goal 1 Goal 2 Goal 3 Goal 4 57 56 of 101
58. Practice Multiplication Problem #2 18936 x 52 Goal 1 Goal 2 Goal 3 Goal 4 58 57 of 101
59. Practice Multiplication Problem #2 1 18936 x 52 2 Goal 1 Goal 2 Goal 3 Goal 4 59 58 of 101
60. Practice Multiplication Problem #2 1 18936 x 52 72 Goal 1 Goal 2 Goal 3 Goal 4 60 59 of 101
61. Practice Multiplication Problem #2 1 1 18936 x 52 872 Goal 1 Goal 2 Goal 3 Goal 4 61 60 of 101
62. Practice Multiplication Problem #2 11 1 18936 x 52 7872 Goal 1 Goal 2 Goal 3 Goal 4 62 61 of 101
63. Practice Multiplication Problem #2 11 1 18936 x 52 37872 Goal 1 Goal 2 Goal 3 Goal 4 63 62 of 101
64. Practice Multiplication Problem #2 11 1 18936 x 52 37872 0 Goal 1 Goal 2 Goal 3 Goal 4 64 63 of 101
65. Practice Multiplication Problem #2 3 11 1 18936 x 52 37872 00 Goal 1 Goal 2 Goal 3 Goal 4 65 64 of 101
66. Practice Multiplication Problem #2 13 11 1 18936 x 52 37872 800 Goal 1 Goal 2 Goal 3 Goal 4 66 65 of 101
67. Practice Multiplication Problem #2 13 11 1 18936 x 52 37872 800 Goal 1 Goal 2 Goal 3 Goal 4 67 66 of 101
68. Practice Multiplication Problem #2 413 11 1 18936 x 52 37872 6800 Goal 1 Goal 2 Goal 3 Goal 4 68 67 of 101
69. Practice Multiplication Problem #2 4413 11 1 18936 x 52 37872 46800 Goal 1 Goal 2 Goal 3 Goal 4 69 68 of 101
70. Practice Multiplication Problem #2 4413 11 1 18936 x 52 37872 946800 Goal 1 Goal 2 Goal 3 Goal 4 70 69 of 101
71. Practice Multiplication Problem #2 4413 11 1 18936 x 52 37872 + 946800 984672 Goal 1 Goal 2 Goal 3 Goal 4 71 70 of 101
72. Practice Multiplication Problem #2 Therefore the answer to 18,936 x 52 = 984,672 Goal 1 Goal 2 Goal 3 Goal 4 72 71 of 101
73. Great Job with Multiplication 73 72 of 101
74. Goal 4 Apply knowledge of multi-digit multiplication and division to patterns and real-world problems. 74 73 of 101
75. Real World Problems using Multiplication and Division Ê Many students ask “Why are we learning multiplication and division?” Most jobs today require basic multiplication and division and many jobs require advanced multiplication and division. We are going to look at some real world problems involving the steps we just practiced in the previous slides. Goal 1 Goal 2 Goal 3 Goal 4 75 74 of 101
76. Real World Problems using Multiplication and Division Ê Example 1: A hotel has 7 floors. The lobby, restaurant and gym are located on the ground floor. The guestrooms are on 1st to 6th floors. 1. If there are 35 standard rooms on each floor, how many standard rooms are there? Ê Click on the question mark ( ) to bring you back to this page when you need to look back at the question. Goal 1 Goal 2 Goal 3 Goal 4 76 75 of 101
77. Real World Problems using Multiplication and Division Ê First we need to figure out what we are trying to solve. From the example we need to find how many standard rooms there are in the hotel. Ê Next we decide which numbers we need in order to solve the problem. Ê We know that there are 7 floors but only floors 1-6 have rooms. We also know there are 35 rooms on each floor. Ê Now that we have the numbers we need to create an equations. We need to multiply 6 floors by 35 rooms in order to find the total number of standard rooms. Goal 1 Goal 2 Goal 3 Goal 4 77 76 of 101
78. Real World Problems using Multiplication and Division Ê Like we practiced in the early problems the larger number goes on top and the smaller number on the bottom. 35 x 6 Goal 1 Goal 2 Goal 3 Goal 4 78 77 of 101
79. Real World Problems using Multiplication and Division Ê Now we do basic multiplication. Goal 1 Goal 2 Goal 3 Goal 4 3 35 x 6 0 3 35 x 6 210 Therefore there are 210 standard rooms in the hotel. 79 78 of 101
80. Real World Problems using Multiplication and Division Ê Now lets do a division word problem. Ê Example 2: In a car factory, there are 12 assembly lines. Each assembly line manufactures cars at the same speed. If the factory produces 2436 cars in a day, how many cars does each assembly line makes each day? Ê Click on the question mark to bring you back to this example. Goal 1 Goal 2 Goal 3 Goal 4 80 79 of 101
81. Real World Problems using Multiplication and Division Ê First we need to figure out what we are trying to solve. The example says we are trying to find how many cars each assembly line makes each day. Ê Next we need to decide which numbers are important from the word problem. Ê We know there are 12 assembly lines and the factory produces 2436 cars per day. Goal 1 Goal 2 Goal 3 Goal 4 81 80 of 101
82. Real World Problems using Multiplication and Division Ê To find how many cars each assembly line makes we need to divide 2436 cars per day by 12 assembly lines. Goal 1 Goal 2 Goal 3 Goal 4 2436 12 82 81 of 101
83. Real World Problems using Multiplication and Division Ê Step one is 2 ÷12 which cannot be solved so we do 24 ÷ 12 = 2 Ê Step Two is subtracting 24 – 24 = 0 Goal 1 Goal 2 Goal 3 Goal 4 2436 - 24 0 12 2 83 82 of 101
84. Real World Problems using Multiplication and Division Ê Step 3) we bring down the 3 and 6 because we cannot do 3 ÷ 12. We put a 0 in the tens place then we divide 36 ÷ 12 = 3 Goal 1 Goal 2 Goal 3 Goal 4 2436 - 24êê 0 3 6 - 3 6 0 12 203 84 83 of 101
85. Real World Problems using Multiplication and Division Ê Therefore each assembly line makes 203 cars per day Goal 1 Goal 2 Goal 3 Goal 4 2436 - 24êê 0 3 6 - 3 6 0 12 203 85 84 of 101
86. Now you will do some examples on your own. Once you have completed each step and found the answer then flip to the next slide to check your answer. If you miss a question or not sure what to do next go back and look at the previous slides to help you complete each problem. There are six review problems (2 from each section) then you will have a post-test. 86 85 of 101
87. Review Question 1) 9140 ÷ 20 Goal 1 Goal 2 Goal 3 Goal 4 9140 20 87 86 of 101
88. Review ÊQuestion 1) Check your work. Ê The answer should be 457 9140 ÷ 20 Goal 1 Goal 2 Goal 3 Goal 4 9140 - 80ê 11 4 - 10 0ê 1 40 - 1 40 0 20 457 88 87 of 101
89. Review Question 2) 4284 ÷ 18 Goal 1 Goal 2 Goal 3 Goal 4 4284 18 89 88 of 101
90. Review ÊQuestion 2) Check your work. Ê The answer should be 238 9140 ÷ 20 Goal 1 Goal 2 Goal 3 Goal 4 4284 - 36ê 6 8 - 5 4 ê 1 44 - 1 44 0 18 238 90 89 of 101
91. Review Question 3) 9483 x 7 9483 x 7 Goal 1 Goal 2 Goal 3 Goal 4 91 90 of 101
92. Review ÊQuestion 3) Check your work. Ê The answer should be 66381 352 9483 x 7 66381 Goal 1 Goal 2 Goal 3 Goal 4 92 91 of 101
93. Review Question 4) 8169 x 23 8169 x 23 Goal 1 Goal 2 Goal 3 Goal 4 93 92 of 101
94. Review Ê Question 4) Check your work. Ê The answer should be 187887 11 11 8169 x 23 24507 + 163380 187887 Goal 1 Goal 2 Goal 3 Goal 4 94 93 of 101
95. Review Question 5) In a hospital, there are 9 doctors, 101 nurses and 26 floors. On each floor, there are 6 beds. How many beds are there in total? Goal 1 Goal 2 Goal 3 Goal 4 95 94 of 101
96. Review ÊQuestion 5) Check your work. Ê The answer should be 156 3 26 x 6 156 Goal 1 Goal 2 Goal 3 Goal 4 96 95 of 101
97. Review Question 6) At the fire stations in Spartanburg there are 36 fire engines and there are 5472 firefighters on duty for each 12-hour shift. How many firefighters can be assigned equally to each fire engine? Goal 1 Goal 2 Goal 3 Goal 4 97 96 of 101
98. Review ÊQuestion 6) Check your work. Ê The answer should be 152 Goal 1 Goal 2 Goal 3 Goal 4 5472 - 36ê 187 - 180ê 72 - 72 0 36 152 98 97 of 101
99. Once you feel confident on the skills reviewed in this module, move to the next slide. If you are unsure on a section, go back and review it. 99 98 of 101
100. Now it is time to test your knowledge. Take the posttest so I can see what you know and what we need to continue to review. 100 99 of 101
101. Posttest The Posttest is on a Google Form. Read each question carefully and make sure to show your work on a scratch piece of paper to help you find the answer. Link to Posttest Goal 1 Goal 2 Goal 3 Goal 4 101 100 of 101
102. Congratulations! You have completed the module reviewing multiplication and division skills! You may now end the module. 102 101 of 101