1. This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and teachers. These materials may not be used for any commercial purpose without the written permission of the owners. NJCTL maintains its website for the convenience of teachers who wish to make their work available to other teachers, participate in a virtual professional learning community, and/or provide access to course materials to parents, students and others. Click to go to website: www.njctl.org New Jersey Center for Teaching and Learning Progressive Mathematics Initiative

2. 4th Grade Addition and Subtraction www.njctl.org 2012-07-18

3. Setting the PowerPoint View Use Normal View for the Interactive Elements To use the interactive elements in this presentation, do not select the Slide Show view. Instead, select Normal view and follow these steps to set the view as large as possible: On the View menu, select Normal. Close the Slides tab on the left. In the upper right corner next to the Help button, click the ^ to minimize the ribbon at the top of the screen. On the View menu, confirm that Ruler is deselected. On the View tab, click Fit to Window. Use Slide Show View to Administer Assessment Items To administer the numbered assessment items in this presentation, use the Slide Show view. (See Slide 14 for an example.)

4. Table of Contents Vocabulary Multi-digit Addition Multi-digit Subtraction Subtraction across zeros Properties & Inverse Operations of Addition and Subtraction Click on a topic to go to that section

5. Vocabulary Click to Return to Table of Contents

6. Vocabulary Addends: Numbers you add Sum: The total after you add Plus sign: The sign + that tells you to add Equal sign: The sign = that means is equal to Difference: The result after a subtraction Subtract: To take away one quantity from another Minus sign: The sign - that tells you to subtract click to reveal

7. Review of addition and subtraction facts Addition is the "putting together" of two groups of objects and finding how many in all. Subtraction tells "how many are left" or "how many more or less." We say addition and subtraction are inverse operations because one operation can "undo" the other operation. Adding 3 and 5 to get 8 is the opposite of 8 minus 5 leaving 3. 3 + 5 = 8 and 8 - 5 = 3 addends sum difference

8. Multi-Digit Addition Click to Return to Table of Contents

9. There are 25 students in one fourth grade classroom and 22 in another. How many total students are in both classes? Solve the addition problem: 25 + 22 = Step 1: Line up place values of the numbers and write it vertically. 25 + 22 Step 2: Add working right to left (ones then tens)

10. 41 + 22 = 16 + 11 = 30 + 50 = 41 16 30 + 22 + 11 + 50 Rewrite the problems vertically and then add. click

11. There are 203 students in one school and 84 students in another. What is the total number of students in the two schools? Solve the addition problem: 203 + 84 = Step 1: Line up place values of the numbers and write it vertically. 203 + 84 Step 2: Add working right to left (ones, then tens, then hundreds) Be sure to line this 4 under the 3 (they are both in the ones column).

12. 426 + 71 = 4,105 + 62 = 54 + 704 = 426 4105 54 + 71 + 62 + 704 Rewrite the problems vertically and then add. click

13. Match the sum to the correct problem. 501 + 317 = 541 + 301 = 5,401 + 37 = 541 + 37 = 51 + 307 = 5,041 + 317 =

14. 1When you add 64 + 25 you get 89 Yes No

15. 2 When adding 340 + 9 the nine should be lined up under the zero, because they are both in the ones position. True False

16. 3 The sum of 30 + 33 is? 62 63 64 A B C

17. 4 The sum of 122 + 21 is?

18. 5 The sum of 230 + 35 is?

19. 6 If Noah buys 15 science fiction books and 11 puzzle books, how many books did Noah purchase in all?

20. 7 Miguel read 274 pages in his novel and Jeff read only 25 pages. How many pages did they read altogether?

21. 8 Violet ran 834 yards on Monday and 1,120 yards on Wednesday. How many total yards did she run?

22. 9 Larry made $46 raking leaves and $120 trimming trees. How much did he earn?

23. 10 A school collects labels to raise money. The total collected for two months is in the table. What is the total collected for the two months? MonthNumber of Labels Collected October1,358 November3,121

24. Addition with Regrouping Hundreds Tens Ones Add 135 + 278 When you add a column that has more than 10 blocks, such as the ones column, you change the ones into a ten block. Let's look to see what happens.

25. 10 of the 13 ones move left. 100 of the tens move left. 135 + 278 Now we will look at the new model. Hundreds Tens Ones

26. HundredsTens Ones 135 + 278 = 400 + 10 + 3 = 413 Click

27. National Library of Virtual Manipulatives Web Site shows exchange of base ten blocks. Click for link.

28. Steps for addition with regrouping 367 + 74 = 367 +74 Step 1: Line up the numbers vertically. step 2: Add the ones column. If the sum is more than 9 regroup to the tens column. Step 3: Add the tens column. If the sum is more that 9 regroup to the hundreds column. Step 4: Add the hundreds column.

29. Steps for addition with regrouping 367 + 74 = 1 367 + 74 1 Step 1: Line up the numbers vertically. Step 2: Add the ones column. If the sum is more than 9 regroup to the tens column. Step 3: Add the tens column. If the sum is more that 9 regroup to the hundreds column. Step 4: Add the hundreds column.

30. Steps for addition with regrouping 367 + 74 = 11 367 + 84 51 Step 1: Line up the numbers vertically. Step 2: Add the ones column. If the sum is more than 9 regroup to the tens column. Step 3: Add the tens column. If the sum is more that 9 regroup to the hundreds column. Step 4: Add the hundreds column.

31. Steps for addition with regrouping 367 + 74 = 11 367 + 84 451 Step 1: Line up the numbers vertically. Step 2: Add the ones column. If the sum is more than 9 regroup to the tens column. Step 3: Add the tens column. If the sum is more that 9 regroup to the hundreds column. Step 4: Add the hundreds column.

32. Find the sum. 1. 523 2. 8853. 278 +768 +107 +915 1291 992 1193 1 11

33. Solve each problem. 1 372 + 218 = 2 159 + 222 = 3 867 + 323 = 4 573 + 618 = 5 448 + 338 =

34. 11 True False 629 + 381 = 10,010

35. 12 847 + 223

36. 13 3,405 + 839 =

37. 14 73 + 946 =

38. 15 The answer to an addition problem is called? + sum difference product A B C

39. 16 Two groups of boy scouts are camping. There are 143 campers at one site and 219 at a second site. How many boy scouts are camping altogether?

40. 17 Jordan has 258 coins in his collection. His uncle gives him 71 more coins. How many coins does he have now?

41. 18 Look at the table. What is the total number of students in 4th grade? GradeBoysGirls 3rd Grade132159 4th Grade174153

42. 19 Tonia created a survey and asked her classmates which season is their favorite. How many students did she survey? SeasonFallWinterSpringSummer Number of Students 31125372

43. 20 Do you find it easier to add numbers vertically or horizontal? vertically (up and down) horizontal (across) either A B C

44. Multi-Digit Subtraction Click to Return to Table of Contents

45. Words to Remember Subtract: To take away one quantity from another 5 - 2 Difference: The result after subtraction 5 - 2 = 3 Minus sign: The sign - that tells you to subtract

46. Example 1 Finding How Many Are Left Hannah picks 14 flowers in her garden to put in vases. She puts 8 flowers in one vase. How many flowers are left for a second vase? Step 1 Draw how many you start with. Cross out the ones you subtract. Start with 14 flowers subtract 8 Step 2 Count how many are left. 14 - 8 = 6 Answer There are 6 flowers left for the second vase.

47. Example 2 Comparing with subtraction Diana has 19 friends listed in her instant messaging icon. Sixteen friends are currently online. How many more friends are online than offline?

48. Try this Fill in the missing information to solve the problem. Susan's family had eaten 11 of the 19 bananas she bought at the grocery store. How many are left? 19 - 11 = 8 bananas move remove

49. Fill in the missing operation signs. 14 15 = 29 95 4 = 91 29 8 = 2129 14 = 15 55 11 = 4430 8 = 22 22 8 = 3038 22 = 60 73 9 = 8259 44 = 103 23 33 = 5687 22 = 65

50. 21 62 - 41 =

51. 22 456 - 34 =

52. 23 3,524 - 1,220 =

53. 24 Gary has $368 in his savings account. He purchased a video game for $43. How much money does he have left in his savings account.

54. 25 There are 437 students in a school. One Monday 32 of them are absent. How many students are in school that Monday?

55. Subtraction with Regrouping HundredsTens Ones Subtract 243 - 128 When you can not subtract from a column, you regroup from the column to the left.

56. HundredsTens Ones Subtract 243 - 128 Take a ten and split it into ten ones.

57. HundredsTens Ones Subtract 243 - 128 Now we can subtract 8 from the ones column. X X X X X X X X X X X X X 3 13 243 - 128 115 /

58. National Library of Virtual Manipulatives Web Site shows splitting and moving of base ten blocks. Click for link.

59. Word Problems What number do you need to add to 13 to get 28? Hints: Solve 28 - 13 = _____ Answer 15 What number do you need to add to 24 to get 43? Answer 19 What number do you need to add to 45 to get 57? Answer 12 Remove

60. 26 455 - 318 = 143 773 137 A B C

61. 27 372 - 199 =

62. 28 1,257 - 182 =

63. 29 Xavier has 348 songs on his MP3 player and his brother has 284 songs on his. How many more songs does Xavier have than his brother?

64. 30 The park had 1,736 visitors on Saturday and 1,588 visitors on Sunday. How many more visitors were there on Saturday?

65. Subtraction Across Zeros Click to Return to Table of Contents

66. Subtraction Across Zeros Example: What is 600- 243 Step-1 Are there enough ones in 600 to subtract 3 ones? No (3 > 0) 600 - 243 5 10 Since there are 0 tens, we can't borrow from tens. So, borrow 1 hundred and regroup as 10 tens. 6 hundreds 0 tens = 5 hundreds 10 tens. Math Concept: While subtracting across zeros, you may need to regroup the hundreds first.

67. Step-2 Borrow 1 ten and regroup as 10 ones 600 - 243 5 10 10 10 tens 0 ones = 9 tens 10 ones 9 Step-3 Subtract the hundreds (5 - 2 = 3) Subtract the ones (10 - 3 = 7) Subtract the tens (9 - 4 = 5) 600 - 243 5 10 10 9

68. Solve the problems on the next page using the web site. Click for web site.

69. Subtract using the web site. Show your work 600 900 700 - 236 - 748 - 645

70. 300 800 400 - 200 - 425 - 174

71. 31 600 - 457 = 143 247 253 A B C

72. 32 800 - 506

73. 33 400 - 235

74. 34 500 - 406 =

75. 35 700 - 431

76. 36 300 - 113 =

77. 37 There are 500 students at an elementary school, 229 of those students are involved in sports. How many are not involved in sports?

78. 38 What is 3,500 – 1,875 1,625 2,375 2,425 A B C

79. 39 There are 201 members of the soccer club. 155 of them sold items for the fundraiser. How many soccer players did not fund raise?

80. 40 One thousand kids were surveyed. 287 of them do not enjoy cooking. How many kids do enjoy cooking?

81. Another way to think of it.... 600 - 461 Step 1: Underline the 0 in the tens place, since there is nothing to regroup with, keep going to the 6. Step 2: Now you have 60 underlined, regroup 60 into 59 + 1, put the 1 with the 0 in the ones place. Step 3: Subtract.

82. 600 - 461 Step 1: Underline the 0 in the tens place, since there is nothing to regroup with, keep going to the 6. Step 2: Now you have 60 underlined, regroup 60 into 59 + 1, put the 1 with the 0 in the ones place. Step 3: Subtract. 59 1

83. Step 1: Underline the 0 in the tens place, since there is nothing to regroup with, keep going to the 6. Step 2: Now you have 60 underlined, regroup 60 into 59 + 1, put the 1 with the 0 in the ones place. Step 3: Subtract. 600 - 461 139 59 1

84. 41 300 - 173 = 300 - 173 29 1

85. 42 6,000 - 328 = 1 599 6000 - 328

86. 43 9,000 - 2,481 =

87. 44 There are 600 students in the school district. Each morning, 482 students come early to have breakfast. How many students do not come early?

88. 45 The distance across the United States is about 3,000 miles. If you drive 372 miles in one day, how many more miles do you have to drive?

89. Properties & Inverse Operations of Addition and Subtraction Click to Return to Table of Contents

90. Number Properties Identity Property of Addition When you add zero to a number, the sum is that same number. 7 + 0 = 7

91. Number Properties Commutative Property The order of the numbers does not change the sum of an addition problem. Addition a + b = b + a 6 + 3 = 3 + 6 9 = 9

92. Associative Property The grouping of the numbers does not change the sum of an addition problem. Addition (a + b) + c = a + (b + c) (2 + 3) + 4 = 2 + (3 + 4) 5 + 4 = 2 + 7 9 = 9 Number Properties

93. 2 + 0 = 2 0 + 3 = 3 Identity (Zero) Number in Flight Addition Property Shown "Stick People" in Flight 3 + 2 = 5 2 + 3 = 5 Commutative (Order) (3 + 2) + 4 = 9 3 + (2 + 4) = 9 Associative (Grouping)

94. Use the indicated property to complete the following. 1. Identity 7 + 0 = __7__ 2. Commutative 6 + 2 = __2__ + 6 3. Associative (1 + 6) + 3 = __10__ 1 + (6 + _3_) = __10__ 4. Identity 0 + 11 = 11 5. Commutative _15_ + 2 = _2_ + 15 6. Associative _8_ + (5 + 4) = _17_ (8 + 5) + 4 = _17_

95. 46 The property of 7 + 4 = 4 + 7 is _________ identity (zero) commutative (order) associative (grouping) A B C

96. 47 The property of (8+ 2) + 4 = 8 + (2 + 4) is ___________ identity commutative associative A B C

97. 48 The property of 9 + (5 + 3) = (9 + 5) + 3 is ________ identity commutative associative A B C

98. 49The property to 7 + 4 = 4 + 7 is _______ identity commutative associative A B C

99. Addition and subtraction are related operations. 7 + 4 = 11 Addition sentences 4 + 7 = 11 11 - 7 = 4 Related subtraction 11 - 4 = 4 sentences Use a related subtraction sentence to find a missing addend. ___ + 9 = 12 12 - 9 = 3 3 + 9 = 12 Missing addend Related subtraction sentence Check to be sure

100. Undoing an Addition Problem If 19 + 7 = 25, what is 25 - 7? Solution Ask yourself, what number added to 7 has a sum of 25? 18 + 7 = 25, so the opposite must be true: 25 - 7 = 18. X

101. Related Addition Related Subtraction 7 + 4 = 11 20 + 40 = 60 120-50 = 70 225 - 25 = 200 Fill in the blanks. Addition

102. 50 Which is related to this addition sentence? 19 + 6 = 25 19 - 6 = 25 25 - 6 = 19 19 - 6 = 25 A B C

103. 51Which is a related subtraction sentence? 120 + 30 = 150 120 - 30 = 150 150 - 20 = 120 150 - 30 = 120 A B C

104. Since addition and subtraction are "opposite" operation, they are call fact families. If you add any two numbers, then subtract one of the addends from the sum, the difference will be the other addend. These 3 numbers, along with the operations of addition and subtraction, form a fact family. Example: Write the addition and subtraction fact family for 7, 2, and 9 7 + 2 = 9 9 - 7 = 2 2 + 7 = 9 9 - 2 = 7

105. Directions: For numbers 1 through 4, fill in the blanks to complete the fact familty. 1. 4 + 6 = 102. ____________________ ___________________ _____________________ ___________________ 8 - 3 = 5 3. ___________________ 4. _____________________ 3 + 2 = 5 ______________________ ____________________ 16 - 7 = 9 ____________________ _____________________

106. 52Which is the missing fact for this family? 539 + 76 = 615 615 - 539 = 76 615 - 76 = 539 539 + 76 = 615 615 - 15 = 600 539 - 76 = 615 A B C D 76 + 539 = 615

107. 53 Which is the missing fact for this family? 123 + 88 = 211 211 - 123 = 88 211 - 88 = 123 88 + 88 = 176 123 - 211 = 88 88 + 123 = 211 A B C D 123 + 0 = 123

108. 54Which is the missing fact for this family? 25 + 38 = 63 38 + 25 = 63 63 - 25 = 38 0 + 63 = 63 63 - 38 = 25 25 + 25 = 50 A B C D 63 - 33 = 30

109. 55 Philip solved a subtraction problem this way: 4,003 –2,564 1,439 Which number sentence shows the inverse of his subtraction problem? 1439 + 2564 = 4003 4003 - 1439 = 2564 1439 + 4003 = 2564 A B C

110. 56 Jerry solved the following problem on his math test: 12,462 + 5,980 18,442 Which equation shows the inverse of addition? 12,462 - 5980 = 6,482 18,442 - 5,980 = 12,462 18,442 + 5.980 = 24,422 A B C

111. 57Fill in the missing addend by relating the addition to subtraction. ___ + 146 = 156

112. 58 Fill the missing addend by relating the addition to subtraction. 8 + ___ = 15

113. 59Fill in the missing addend by relating the addition to subtraction. 1507 + ____ = 1653

114. 60Fill in the missing addend by relating the addition to subtraction. 843 + ____ = 8,000

115. 61Fill in the missing number by relating the subtraction to addition. 7,032 - ____ = 4,392

116. 62Matt has saved $12 to buy a video game. The video game costs $34. How much more will Matt have to save to buy the video game? Use the following open number sentence to find the answer. 34 = m + 12 $16 $18 $22 A B C

117. 63 Linda completed 102 math problems last week. Linda and Sal completed a total of 238 math problems altogether. How many math problems did Sal complete last week? Which equation will help solve this problem? (Let n = the number of math problems completed by Sal last week.) 102 + n = 238 102 - n = 238 102 × n = 238 A B C

118. 64 Lorraine received $30 for her birthday. She bought earrings for $12.63 pocketbook and a T-shirt for $12.80. How much of her birthday money does Lorraine have left? 30 = 12.63 + 12.80 + m $17.37 $14.57 $ 4.57 A B C

119. 65 Abe has saved $13 to buy a new soccer ball. The soccer ball costs $37. How much more will Abe have to save to buy the ball? Use the following open number sentence to find the answer. 37 = m + 13 $22 $23 $24 A B C

120. 66 The hot dog stand at the carnival had 2,000 hot dogs. They sold 1,259 of them. How many hot dogs do they have left? 1,259 + h = 2,000

121. 67 You purchase a toy train and a drum. You hand the cashier a ten dollar bill. What will be your change be? $2.23 $5.03 $4.67

122. 45 -12 12 33+33 45 When checking a subtraction problem with addition, add the number that is subtracted and the answer. You should end up with the original number you started with. 451 -122 122 329 +329 451

123. Sometimes, mistakes are made when we subtract. Estimating is one way to check the reasonableness of our work. But, we can also use addition to check our subtraction. You already know that you can use fact families. For example: The subtraction problem 9 - 5 = 4 can be checked with the addition problem 4 + 5 = 9. The same can be done with larger numbers.

124. When a student adds 543 + 328 the answer gotten is 861. Is the student correct? Check the addition with subtraction. 861 - 543 318 This should be 328, so the answer is wrong. 11 5

125. When a student subtracts 3,471 - 1,850 the answer gotten is 1,621. Is the student correct? Check the subtraction with addition. 1621 + 1850 3471 This is what was subtracted from, so the answer is correct

126. 68Use inverse operations to figure out if the following problem is correct? Yes It is correct No It is wrong 453 + 3,271 = 3,624 3624 - 3271 ______ check

127. 69 Use inverse operations to figure out if the following problem is correct? 4,300 - 1,283 = 3183 3183 + 1283 ______ check Yes NoIt is wrong It is correct

128. 70 Use inverse operations to figure out if the following problem is correct? 23,521 + 6,356 = 29,877 29877 - 6356 ________ check Yes NoIt is wrong It is correct

129. 71 You have $729 in your bank account. You rake leaves for several of your neighbors and then deposit $134 into your account. The bank teller says you now have a balance of $853. Is this correct? Yes No

130. 72 You combine trading cards with your friend. You have 341 cards and your friend has 492 cards. Together you will have 833 cards. Is this correct? Yes No

131. 73 Soccer camp is 524 miles away. If you drive 385 miles the first day, you will need to drive 139 miles on the second day. Is this correct? Yes No

132. 74 The football team ran for 253 yards during the game one Saturday. The next Saturday they ran 198 yards. They ran for a total of 341 yards during these two games. Is this correct? Yes No

133. For the next set of responder questions, check your answer before responding.

134. 75Many of the students at Lake Elementary buy school lunch. 367 of the students ordered chicken nuggets on Monday, while 189 of the students ordered peanut butter and jelly. How many students ordered lunch on Monday? 178 556 546 A B C

135. 76The Jones Middle School was having a school dance on Friday night. Only 350 students were allowed to sign up for the dance. 147 signed up to go. How many more students were able to sign up before Friday night?

136. 77Massachsetts occupies 10,655 square miles of land and water. If 2,673 square miles is water, how many square miles of Massachsetts is land?

137. 78 Rudy uses 156 ml of salad dressing for his salad. Mike uses 208 ml on his salad. How much dressing do they use altogether?

138. 79 Ivan is putting books in his bookcase. He has put 134 on the shelves. He has 408 books in all. How many more books does he need to put on the shelves?

139. 80 You have paid the cashier at the store with four $20 bills. The item you want to buy is $67. How much change will you get back?

140. 81Kenny went to the Boardwalk for a week in July. His mom bought 400 tickets for him for the amusement rides. He used 315 of them. How many tickets does Kenny have left?

141. 82 The football stadium holds 80,000 people. 65,876 people bought tickets to go to the game. How many more tickets can be sold to fill the stadium?

142. 83 Benny had a collection of marbles. He has exactly 450 marbles. For Christmas, his uncle Fred gave him 37 more marbles. How many marbles does Benny have in his collection now?