1. 5-3 Dividing by
One-Digit Divisor
Math Notes
Number Sense 2.2

2. What you’re learning today...
Number Sense 2.2 - Demonstrate proficiency
with division ... including long division with
multi-digit divisors.

3. What you’re learning today...
Number Sense 2.2 - Demonstrate proficiency
with division ... including long division with
multi-digit divisors.
1 r1
8 9
8
1

4. What you’re learning today...
Number Sense 2.2 - Demonstrate proficiency
with division ... including long division with
multi-digit divisors.
1 r1
8 9
8
1
WHAT YOU’VE
LEARNED ALREADY

5. What you’re learning today...
Number Sense 2.2 - Demonstrate proficiency
with division ... including long division with
multi-digit divisors.
1 r1
8 9
8
1 WHAT YOU’RE
LEARNING TO DO TODAY
WHAT YOU’VE
LEARNED ALREADY

6. What you’re learning today...
Number Sense 2.2 - Demonstrate proficiency
with division ... including long division with
multi-digit divisors.
1 r1
8 9
8 8 983
1 WHAT YOU’RE
LEARNING TO DO TODAY
WHAT YOU’VE
LEARNED ALREADY

7. What you’re learning today...
Number Sense 2.2 - Demonstrate proficiency
with division ... including long division with
multi-digit divisors.
1 r1
8 9
8 8 983
1 WHAT YOU’RE
LEARNING TO DO TODAY
WHAT YOU’VE
LEARNED ALREADY

8. Long Division Mnemonic

9. Long Division Mnemonic
DAD

10. Long Division Mnemonic
DAD
MOM

11. Long Division Mnemonic
DAD
MOM
SISTER

12. Long Division Mnemonic
DAD
MOM
SISTER
BROTHER

13. Long Division Mnemonic
DAD
MOM
SISTER
BROTHER
ROVER

14. Long Division Mnemonic
DAD DIVIDE
MOM
SISTER
BROTHER
ROVER

15. Long Division Mnemonic
DAD DIVIDE
MOM MULTIPLY
SISTER
BROTHER
ROVER

16. Long Division Mnemonic
DAD DIVIDE
MOM MULTIPLY
SISTER SUBTRACT
BROTHER
ROVER

17. Long Division Mnemonic
DAD DIVIDE
MOM MULTIPLY
SISTER SUBTRACT
BROTHER BRING DOWN
ROVER

18. Long Division Mnemonic
DAD DIVIDE
MOM MULTIPLY
SISTER SUBTRACT
BROTHER BRING DOWN
ROVER REPEAT OR
REMAINDER

19. DAD
MOM
SISTER
BROTHER
ROVER

20. DAD
MOM
SISTER
BROTHER
ROVER

21. DAD
MOM
96
SISTER
BROTHER
ROVER

22. DAD
MOM
8 96
SISTER
BROTHER
ROVER

23. STEP 0: Use
DAD
guidelines
MOM
8 96
SISTER
BROTHER
ROVER

24. STEP 0: Use
DAD
guidelines
MOM
8 96
SISTER
BROTHER
ROVER

25. STEP 0: Use
DAD
guidelines
MOM
STEP 1: DIVIDE
8 96
SISTER
9 by 8
BROTHER
ROVER

26. STEP 0: Use
1
DAD
guidelines
MOM
STEP 1: DIVIDE
8 96
SISTER
9 by 8
BROTHER
ROVER

27. STEP 0: Use
1
DAD
guidelines
MOM
STEP 1: DIVIDE
8 96
SISTER
9 by 8
BROTHER
STEP 2:
ROVER
MULTIPLY
8 by 1

28. STEP 0: Use
1
DAD
guidelines
MOM
STEP 1: DIVIDE
8 96
SISTER
9 by 8
BROTHER
STEP 2:
8
ROVER
MULTIPLY
8 by 1

29. STEP 0: Use
1
DAD
guidelines
MOM
STEP 1: DIVIDE
8 96
SISTER
9 by 8
BROTHER
STEP 2:
8
ROVER
MULTIPLY
8 by 1
STEP 3:
SUBTRACT 9 - 8

30. STEP 0: Use
1
DAD
guidelines
MOM
STEP 1: DIVIDE
8 96
SISTER
9 by 8
BROTHER
STEP 2:
8
ROVER
MULTIPLY
8 by 1
1 STEP 3:
SUBTRACT 9 - 8

31. STEP 0: Use
1
DAD
guidelines
MOM
STEP 1: DIVIDE
8 96
SISTER
9 by 8
BROTHER
STEP 2:
8
ROVER
MULTIPLY
8 by 1
1 STEP 3:
SUBTRACT 9 - 8
STEP 4:
BRING DOWN the 6

32. STEP 0: Use
1
DAD
guidelines
MOM
STEP 1: DIVIDE
8 96
SISTER
9 by 8
BROTHER
STEP 2:
8
ROVER
MULTIPLY
8 by 1
16 STEP 3:
SUBTRACT 9 - 8
STEP 4:
BRING DOWN the 6

33. STEP 0: Use
1
DAD
guidelines
MOM
STEP 1: DIVIDE
8 96
SISTER
9 by 8
BROTHER
STEP 2:
8
ROVER
MULTIPLY
8 by 1
STEP 5:
REPEAT or
16 STEP 3:
SUBTRACT 9 - 8
REMAINDER
STEP 4:
BRING DOWN the 6

34. STEP 0: Use
1
DAD
guidelines
MOM
STEP 1: DIVIDE
8 96
SISTER
9 by 8
BROTHER
STEP 2:
8
ROVER
MULTIPLY
8 by 1
STEP 5:
REPEAT or
16 STEP 3:
SUBTRACT 9 - 8
REMAINDER
STEP 4:
BRING DOWN the 6

35. 1
DAD
MOM
8 96
SISTER
BROTHER
8
ROVER
16

36. STEP 1: DIVIDE
1
DAD
16 by 8
MOM
8 96
SISTER
BROTHER
8
ROVER
16

37. STEP 1: DIVIDE
12
DAD
16 by 8
MOM
8 96
SISTER
BROTHER
8
ROVER
16

38. STEP 1: DIVIDE
12
DAD
16 by 8
MOM
STEP 2:
8 96
SISTER
MULTIPLY
BROTHER 8 by 2
8
ROVER
16

39. STEP 1: DIVIDE
12
DAD
16 by 8
MOM
STEP 2:
8 96
SISTER
MULTIPLY
BROTHER 8 by 2
8
ROVER
16
16

40. STEP 1: DIVIDE
12
DAD
16 by 8
MOM
STEP 2:
8 96
SISTER
MULTIPLY
BROTHER 8 by 2
8
ROVER
STEP 3:
16
SUBTRACT
16 - 16
16

41. STEP 1: DIVIDE
12
DAD
16 by 8
MOM
STEP 2:
8 96
SISTER
MULTIPLY
BROTHER 8 by 2
8
ROVER
STEP 3:
16
SUBTRACT
16 - 16
16
00

42. STEP 1: DIVIDE
12
DAD
16 by 8
MOM
STEP 2:
8 96
SISTER
MULTIPLY
BROTHER 8 by 2
8
ROVER
STEP 3:
16
SUBTRACT
16 - 16
16 STEP 4:
00 Nothing to
BRING DOWN

43. STEP 1: DIVIDE
12
DAD
16 by 8
MOM
STEP 2:
8 96
SISTER
MULTIPLY
BROTHER 8 by 2
8
ROVER
STEP 3:
16
SUBTRACT
STEP 5:
16 - 16
REPEAT or
REMAINDER
16 STEP 4:
00 Nothing to
BRING DOWN

44. STEP 1: DIVIDE
12
DAD
16 by 8
MOM
STEP 2:
8 96
SISTER
MULTIPLY
BROTHER 8 by 2
8
ROVER
STEP 3:
16
SUBTRACT
STEP 5:
16 - 16
REPEAT or
REMAINDER
16 STEP 4:
00 Nothing to
BRING DOWN

45. STEP 1: DIVIDE
12
DAD
16 by 8
MOM
STEP 2:
8 96
SISTER
MULTIPLY
BROTHER 8 by 2
8
ROVER
STEP 3:
16
SUBTRACT
STEP 5:
16 - 16
REPEAT or
REMAINDER
16 STEP 4:
NO REMAINDER
00 Nothing to
BRING DOWN

46. Check By Multiplying
12
x 8

47. Check By Multiplying
12
x 8

48. Check By Multiplying
12
x 8
6

49. Check By Multiplying
1
12
x 8
6

50. Check By Multiplying
1
12
x 8
6

51. Check By Multiplying
1
12
x 8
96

52. DAD
MOM
SISTER
BROTHER
ROVER

53. DAD
MOM
SISTER
BROTHER
ROVER

54. DAD
MOM
SISTER
230
BROTHER
ROVER

55. DAD
MOM
SISTER
8 230
BROTHER
ROVER

56. STEP 0: Use
DAD
guidelines
MOM
SISTER
8 230
BROTHER
ROVER

57. STEP 0: Use
DAD
guidelines
MOM
SISTER
8 230
BROTHER
ROVER

58. STEP 0: Use
DAD
guidelines
MOM
SISTER
8 230 STEP 1: Because 8
cannot go into 2,
BROTHER DIVIDE 23 by 8
ROVER

59. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
8 230 STEP 1: Because 8
cannot go into 2,
BROTHER DIVIDE 23 by 8
ROVER

60. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
8 230 STEP 1: Because 8
cannot go into 2,
BROTHER DIVIDE 23 by 8
ROVER
STEP 2:
MULTIPLY
8 by 2

61. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
8 230 STEP 1: Because 8
cannot go into 2,
BROTHER
ROVER
16 DIVIDE 23 by 8
STEP 2:
MULTIPLY
8 by 2

62. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
8 230 STEP 1: Because 8
cannot go into 2,
BROTHER
ROVER
16 DIVIDE 23 by 8
STEP 2:
MULTIPLY
8 by 2
STEP 3:
SUBTRACT 23 - 16

63. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
8 230 STEP 1: Because 8
cannot go into 2,
BROTHER
16 DIVIDE 23 by 8
7
ROVER
STEP 2:
MULTIPLY
8 by 2
STEP 3:
SUBTRACT 23 - 16

64. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
8 230 STEP 1: Because 8
cannot go into 2,
BROTHER
16 DIVIDE 23 by 8
7
ROVER
STEP 2:
MULTIPLY
8 by 2
STEP 3:
SUBTRACT 23 - 16
STEP 4:
BRING DOWN the 0

65. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
8 230 STEP 1: Because 8
cannot go into 2,
BROTHER
16 DIVIDE 23 by 8
70
ROVER
STEP 2:
MULTIPLY
8 by 2
STEP 3:
SUBTRACT 23 - 16
STEP 4:
BRING DOWN the 0

66. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
8 230 STEP 1: Because 8
cannot go into 2,
BROTHER
16 DIVIDE 23 by 8
70
ROVER
STEP 2:
MULTIPLY
8 by 2
STEP 5: STEP 3:
REPEAT or SUBTRACT 23 - 16
REMAINDER
STEP 4:
BRING DOWN the 0

67. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
8 230 STEP 1: Because 8
cannot go into 2,
BROTHER
16 DIVIDE 23 by 8
70
ROVER
STEP 2:
MULTIPLY
8 by 2
STEP 5: STEP 3:
REPEAT or SUBTRACT 23 - 16
REMAINDER
STEP 4:
BRING DOWN the 0

68. 2
DAD
MOM
SISTER
8 230
BROTHER
16
70
ROVER

69. STEP 1: DIVIDE
2
DAD
70 by 8
MOM
SISTER
8 230
BROTHER
16
70
ROVER

70. STEP 1: DIVIDE
28
DAD
70 by 8
MOM
SISTER
8 230
BROTHER
16
70
ROVER

71. STEP 1: DIVIDE
28
DAD
70 by 8
MOM
8 230
STEP 2:
SISTER
MULTIPLY
BROTHER
16 8 by 8
70
ROVER

72. STEP 1: DIVIDE
28
DAD
70 by 8
MOM
8 230
STEP 2:
SISTER
MULTIPLY
BROTHER
16 8 by 8
70
ROVER
64

73. STEP 1: DIVIDE
28
DAD
70 by 8
MOM
8 230
STEP 2:
SISTER
MULTIPLY
BROTHER
16 8 by 8
70
ROVER STEP 3:
SUBTRACT
64 70 - 64

74. STEP 1: DIVIDE
28
DAD
70 by 8
MOM
8 230
STEP 2:
SISTER
MULTIPLY
BROTHER
16 8 by 8
70
ROVER STEP 3:
SUBTRACT
64 70 - 64
06

75. STEP 1: DIVIDE
28
DAD
70 by 8
MOM
8 230
STEP 2:
SISTER
MULTIPLY
BROTHER
16 8 by 8
70
ROVER STEP 3:
SUBTRACT
64 70 - 64
06 STEP 4:
Nothing to
BRING DOWN

76. STEP 1: DIVIDE
28
DAD
70 by 8
MOM
8 230
STEP 2:
SISTER
MULTIPLY
BROTHER
16 8 by 8
70
ROVER STEP 3:
SUBTRACT
64 70 - 64
STEP 5:
REPEAT or 06 STEP 4:
Nothing to
REMAINDER BRING DOWN

77. STEP 1: DIVIDE
28r6
DAD
70 by 8
MOM
8 230
STEP 2:
SISTER
MULTIPLY
BROTHER
16 8 by 8
70
ROVER STEP 3:
SUBTRACT
64 70 - 64
STEP 5:
REPEAT or 06 STEP 4:
Nothing to
REMAINDER BRING DOWN

78. Check By Multiplying
28
x 8

79. Check By Multiplying
28
x 8

80. Check By Multiplying
6
28
x 8
4

81. Check By Multiplying
6
28
x 8
4

82. Check By Multiplying
6
28
x 8
22 4

83. Check By Multiplying
6
28
x 8
22 4
6

84. Check By Multiplying
6
28
x 8
22 4
+ 6

85. Check By Multiplying
6
28
x 8
22 4
+ 6
230

86. DAD
MOM
SISTER
BROTHER
ROVER

87. DAD
MOM
SISTER
BROTHER
ROVER

88. DAD
MOM
SISTER
1810
BROTHER
ROVER

89. DAD
MOM
SISTER
9 1810
BROTHER
ROVER

90. STEP 0: Use
DAD
guidelines
MOM
SISTER
9 1810
BROTHER
ROVER

91. STEP 0: Use
DAD
guidelines
MOM
SISTER
9 1810
BROTHER
ROVER

92. STEP 0: Use
DAD
guidelines
MOM
SISTER
9 1810 STEP 1: Because 9
cannot go into 1,
BROTHER DIVIDE 18 by 9
ROVER

93. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
9 1810 STEP 1: Because 9
cannot go into 1,
BROTHER DIVIDE 18 by 9
ROVER

94. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
9 1810 STEP 1: Because 9
cannot go into 1,
BROTHER DIVIDE 18 by 9
ROVER STEP 2:
MULTIPLY
9 by 2

95. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
9 1810 STEP 1: Because 9
BROTHER
18 cannot go into 1,
DIVIDE 18 by 9
ROVER STEP 2:
MULTIPLY
9 by 2

96. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
9 1810 STEP 1: Because 9
BROTHER
18 cannot go into 1,
DIVIDE 18 by 9
ROVER STEP 2:
MULTIPLY
9 by 2
STEP 3:
SUBTRACT 18 - 18

97. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
9 1810 STEP 1: Because 9
BROTHER
18 cannot go into 1,
DIVIDE 18 by 9
ROVER 0 STEP 2:
MULTIPLY
9 by 2
STEP 3:
SUBTRACT 18 - 18

98. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
9 1810 STEP 1: Because 9
BROTHER
18 cannot go into 1,
DIVIDE 18 by 9
ROVER 0 STEP 2:
MULTIPLY
9 by 2
STEP 3:
SUBTRACT 18 - 18
STEP 4:
BRING DOWN the 1

99. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
9 1810 STEP 1: Because 9
BROTHER
18 cannot go into 1,
DIVIDE 18 by 9
ROVER 01 STEP 2:
MULTIPLY
9 by 2
STEP 3:
SUBTRACT 18 - 18
STEP 4:
BRING DOWN the 1

100. STEP 0: Use
2
DAD
guidelines
MOM
SISTER
9 1810 STEP 1: Because 9
BROTHER
18 cannot go into 1,
DIVIDE 18 by 9
ROVER 01 STEP 2:
MULTIPLY
9 by 2
STEP 3:
SUBTRACT 18 - 18
STEP 4a:
Since 9 cannot go into 1, place STEP 4:
0 in the quotient. Bring down 0 BRING DOWN the 1

101. STEP 0: Use
20
DAD
guidelines
MOM
SISTER
9 1810 STEP 1: Because 9
BROTHER
18 cannot go into 1,
DIVIDE 18 by 9
ROVER 01 STEP 2:
MULTIPLY
9 by 2
STEP 3:
SUBTRACT 18 - 18
STEP 4a:
Since 9 cannot go into 1, place STEP 4:
0 in the quotient. Bring down 0 BRING DOWN the 1

102. STEP 0: Use
20
DAD
guidelines
MOM
SISTER
9 1810 STEP 1: Because 9
BROTHER
18 cannot go into 1,
DIVIDE 18 by 9
ROVER 0 10 STEP 2:
MULTIPLY
9 by 2
STEP 3:
SUBTRACT 18 - 18
STEP 4a:
Since 9 cannot go into 1, place STEP 4:
0 in the quotient. Bring down 0 BRING DOWN the 1

103. STEP 0: Use
20
DAD
guidelines
MOM
SISTER
9 1810 STEP 1: Because 9
BROTHER
18 cannot go into 1,
DIVIDE 18 by 9
ROVER 0 10 STEP 2:
MULTIPLY
STEP 5: 9 by 2
REPEAT or STEP 3:
REMAINDER SUBTRACT 18 - 18
STEP 4a:
Since 9 cannot go into 1, place STEP 4:
0 in the quotient. Bring down 0 BRING DOWN the 1

104. STEP 0: Use
20
DAD
guidelines
MOM
SISTER
9 1810 STEP 1: Because 9
BROTHER
18 cannot go into 1,
DIVIDE 18 by 9
ROVER 0 10 STEP 2:
MULTIPLY
STEP 5: 9 by 2
REPEAT or STEP 3:
REMAINDER SUBTRACT 18 - 18
STEP 4a:
Since 9 cannot go into 1, place STEP 4:
0 in the quotient. Bring down 0 BRING DOWN the 1

105. 20
DAD
MOM
SISTER
9 1810
BROTHER
18
ROVER 0 10

106. STEP 1: DIVIDE
20
DAD
10 by 9
MOM
SISTER
9 1810
BROTHER
18
ROVER 0 10

107. STEP 1: DIVIDE
20 1
DAD
10 by 9
MOM
SISTER
9 1810
BROTHER
18
ROVER 0 10

108. STEP 1: DIVIDE
20 1
DAD
10 by 9
MOM
SISTER
9 1810 STEP 2:
BROTHER
18 MULTIPLY
9 by 1
ROVER 0 10
9

109. STEP 1: DIVIDE
20 1
DAD
10 by 9
MOM
SISTER
9 1810 STEP 2:
BROTHER
18 MULTIPLY
9 by 1
ROVER 0 10 STEP 3:
9 SUBTRACT
10 - 9

110. STEP 1: DIVIDE
20 1
DAD
10 by 9
MOM
SISTER
9 1810 STEP 2:
BROTHER
18 MULTIPLY
9 by 1
ROVER 0 10 STEP 3:
9 SUBTRACT
1 10 - 9

111. STEP 1: DIVIDE
20 1
DAD
10 by 9
MOM
SISTER
9 1810 STEP 2:
BROTHER
18 MULTIPLY
9 by 1
ROVER 0 10 STEP 3:
9 SUBTRACT
1 10 - 9
STEP 4:
Nothing to
BRING DOWN

112. STEP 1: DIVIDE
20 1
DAD
10 by 9
MOM
SISTER
9 1810 STEP 2:
BROTHER
18 MULTIPLY
9 by 1
ROVER 0 10 STEP 3:
9 SUBTRACT
STEP 5: 1 10 - 9
REPEAT or STEP 4:
REMAINDER Nothing to
BRING DOWN

113. STEP 1: DIVIDE
2 0 1 r1
DAD
10 by 9
MOM
SISTER
9 1810 STEP 2:
BROTHER
18 MULTIPLY
9 by 1
ROVER 0 10 STEP 3:
9 SUBTRACT
STEP 5: 1 10 - 9
REPEAT or STEP 4:
REMAINDER Nothing to
BRING DOWN

114. Check By Multiplying
201
x 9

115. Check By Multiplying
201
x 9

116. Check By Multiplying
201
x 9
9

117. Check By Multiplying
201
x 9
9

118. Check By Multiplying
201
x 9
09

119. Check By Multiplying
201
x 9
09

120. Check By Multiplying
201
x 9
1809

121. Check By Multiplying
201
x 9
1809
+ 1

122. Check By Multiplying
201
x 9
1809
+ 1
1810