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2. NUMBER SENSE AT A FLIP

3. NUMBER SENSE AT A FLIP

4. Number Sense
Number Sense is memorization and practice. The secret to getting good at number sense is to learn how to recognize and then do the rules accurately . Then learn how to do them quickly. Every practice should be under a time limit.

5. The First Step
The first step in learning number sense should be to memorize the PERFECT SQUARES from 12 = 1 to = 1600 and the PERFECT CUBES from 13 = 1 to 253 = These squares and cubes should be learned in both directions. ie = and the is 17.

6. Used when you forget a rule about 2x2 multiplication
2x2 Foil (LIOF) 23 x 12
The Rainbow Method
Work Backwards
Used when you forget a rule about 2x2 multiplication
45 x 31=
31 x 62=
64 x 73=
62 x 87=
96 x74=

7. Consecutive Decades 35 x 45 45 x 55= 65 x 55= 25 x 35= 95 x 85=

8. Ending in 5…Ten’s Digits Both Even 45 x 85

9. Ending in 5…Ten’s Digits Both Odd 35 x 75

10. Ending in 5…Ten’s Digits Odd&Even 35 x 85

11. Squaring Numbers Ending In 5 752
45 x 45=
952=
652=
352=
15 x 15=

12. Multiplying By 12 ½ 32 x 12 ½ (1/8 rule) 12 ½ x 48= 12 ½ x 88 =

13. Multiplying By 16 2/3 42 x 16 2/3 (1/6 rule) 16 2/3 x 42 =

14. Multiplying By 33 1/3 24 x 33 1/3 (1/3 rule) 33 1/3 x 45= 33 1/3 x 66=

15. Multiplying By 25 32 x 25 (1/4 rule) 24 x 44= 444 x 25= 25 x 88=

16. Multiplying By 50 32 x 50 (1/2 rule) 50 x 44= 50 x 126= 50 x 424=

17. Multiplying By 75 32 x 75 (3/4 rule) 75 x 44= 75 x 120= 75 x 24=

18. Multiplying By 125 32 x 125 (1/8 rule) 125 x 48= 125 x 88= 125 x 408=

19. Multiplying When Tens Digits Are Equal And The Unit Digits Add To 10 32 x 38

20. Multiplying When Tens Digits Add To 10 And The Units Digits Are Equal 67 x 47

21. Multiplying Two Numbers in the 90’s 97 x 94

22. Multiplying Two Numbers Near 100 109 x 106

23. Multiplying Two Numbers With 1st Numbers = And A “0” In The Middle 402 x 405

24. Multiplying By 3367 18 x 3367 3367 x 33= 3367 x123= 3367 x 66=
10101 Rule
Multiplying By x 3367
3367 x 33=
3367 x123=
3367 x 66=
3367 x 93=
3367 x 24=

25. Multiplying A 2-Digit # By 11 92 x 11
121 Pattern
Multiplying A 2-Digit # By x 11
(ALWAYS WORK FROM RIGHT TO LEFT)
11 x 34=
11 x 98=
65 x 11=
11 x 69=
27 x 11=

26. Multiplying A 3-Digit # By 11 192 x 11
1221 Pattern
Multiplying A 3-Digit # By x 11
(ALWAYS WORK FROM RIGHT TO LEFT)
11 x 231=
11 x 687=
265 x 112=
879x 11=
11 x 912=

27. Multiplying A 3-Digit # By 111 192 x 111
12321 Pattern
Multiplying A 3-Digit # By x 111
(ALWAYS WORK FROM RIGHT TO LEFT)
111 x 213=
111 x 548=
111 x825=
936 x 111=
903 x 111=

28. Multiplying A 2-Digit # By 111 41 x 111
1221 Pattern
Multiplying A 2-Digit # By x 111
(ALWAYS WORK FROM RIGHT TO LEFT)
45 x 111=
111 x 57=
111 x93=
78 x 111=
83 x 1111=

29. Multiplying A 2-Digit # By 101 93 x 101

30. Multiplying A 3-Digit # By 101 934 x 101

31. Multiplying A 2-Digit # By 1001 87 x 1001

32. Halving And Doubling 52 x 13 14 x 56= 16 x 64= 8 x 32= 17 x 68=

33. One Number in the Hundreds And One Number In The 90’s 95 x 108

34. Fraction Foil (Type 1) 8 ½ x 6 ¼

35. Fraction Foil (Type 2) 7 ½ x 5 ½

36. Fraction Foil (Type 3) 7 ¼ x 7 ¾

37. Adding Reciprocals 7/8 + 8/7
5/6 + 6/5
11/ /11
7/2 + 2/7
7/ /7
11/15 +15/11

38. Percent Missing the Of 36 is 9% of __

39. Base N to Base 10 Of 426 =____10 546=_____10 347=_____7 769=_____9
1245=_____5
2346=_____6

40. Multiplying in Bases 4 x 536=___6

41. N/40 to a % or Decimal 21/40___decimal
31/40=
27/40=
51/40=
3/40=
129/40=

42. Remainder When Dividing By 9 867/9=___remainder
3251/9=
264/9=
6235/9=
456/9=
6935/9=

43. Base 8 to Base 2 7328 =____2 3548= _____2 3258=_____2 1568=_____2
421 Method
3548= _____2
3258=_____2
1568=_____2
3548=_____2
5748=_____2

44. Base 2 to Base 8 Of 1110110102 =___8 1100012= _____8 1111002=_____8
421 Method
= _____8
=_____8
=_____8
110112=_____8
=_____8

45. Cubic Feet to Cubic Yards 3ft x 6ft x 12ft=__yds3

46. Ft/sec to mph 44 ft/sec __mph

47. Subset Problems {F,R,O,N,T}=______
SUBSETS
{A,B,C}=
{D,G,H,J,U,N}=
{!!, $, ^^^, *}=
{AB, FC,GH,DE,BM}=
{M,A,T,H}=

48. Repeating Decimals to Fractions .18=___fraction
.25
.123
.74
.031 .8

49. Repeating Decimals to Fractions .18=___fraction
.16
.583
.123
.55
.92

50. Gallons Cubic Inches 2 gallons=__in3
½ gallon =______in3
77 in3=_______gallons
33 in3=_______gallons
1/5 gallon=______in

51. Finding Pentagonal Numbers 5th Pentagonal # =__
3rd pentagonal number=
6th pentagonal number=
10th pentagonal number=
4th pentagonal number=

52. Finding Triangular Numbers 6th Triangular # =__
3rd triangular number=
10th triangular number=
5th triangular number=
8th triangular number=
40th triangular number=

53. Pi To An Odd Power 13=____approximation

54. Pi To An Even Power 12=____approximation

55. The More Problem 17/15 x 17 19/17 x 19= 15/13 x 15= 21/17 x 21=

56. The Less Problem 15/17 x 15 13/17 x 13= 21/23 x 21= 5/7 x 5= 4/7 x4=

57. Multiplying Two Numbers Near 1000 994 x 998

58. The (Reciprocal) Work Problem 1/6 + 1/5 = 1/X
Two Things Helping
1/3 + 1/5 = 1/x
1/2 + 1/6 =1/x
1/4 + 1/7 = 1/x
1/8 + 1/6 =1/x
1/10 + 1/4 = 1/x

59. The (Reciprocal) Work Problem 1/6 - 1/8 = 1/X
Two Things working Against Each Other
1/8 – 1/5 = 1/x
1/11 – 1/3 = 1/x
1/8 – 1/10 = 1/x
1/7 / 1/8 – 1/x
1/30 – 1/12 = 1/x

60. The Inverse Variation % Problem 30% of 12 = 20% of ___

61. Sum of Consecutive Integers 1+2+3+…..+20
1+2+3+….+30=
1+2+3+….+16=
1+2+3+….+19=
1+2+3+…+49=
1+2+3+….100=

62. Sum of Consecutive Even Integers 2+4+6+…..+20
2+4+6+….+16=
2+4+6+….+40=
2+4+6+….+28=
2+4+6+….+48=
2+4+6+….+398=

63. Sum of Consecutive Odd Integers 1+3+5+…..+19
1+3+5+….+33=
1+3+5+….+49=
1+3+5+….+67=
1+3+5+….+27=
1+3+5+….+47=

64. Finding Hexagonal Numbers Find the 5th Hexagonal Number
Find the 3rd hexagonal number=
Find the 10th hexagonal number=
Find the 4th hexagonal number=
Find the 2nd hexagonal number=
Find the 6th hexagonal number=

65. Cube Properties Find the Surface Area of a Cube Given the Space Diagonal of 12

66. Find S, Then Use It To Find Volume or Surface Area
Cube Properties
Find S, Then Use It To Find Volume or Surface Area 2 S 3

67. Finding Slope From An Equation 3X+2Y=10
Y = 2X + 8
Y = -7X + 6
2Y = 8X - 12
2X + 3Y = 12
10X – 4Y = 13

68. Hidden Pythagorean Theorem Find The Distance Between These Points (6,2) and (9,6)

69. Finding Diagonals Find The Number Of Diagonals In An Octagon
# of Diagonals in a pentagon
# of diagonals of a hexagon
# of diagonals of a decagon
# of diagonals of a dodecagon
# of diagonal of a heptagon

70. Finding the total number of factors 24= ________
12=
30=
120=
50=
36=

71. Estimating a 4-digit square root
7549 = _______ 1.
3165 2.
6189 3.
1796 4.
9268 5.
5396

72. Estimating a 5-digit square root
37485 = _______ 1.
31651 2.
61893 3.
17964 4.
92682 5.
53966

73. 59C = _______F C F 4500C=______F 410C =_____F 630C =_____F 680C=_____F

74. C F
50F = _______C
650F=
350F=
750F=
800F=
450F=

75. Finding The Product of the Roots
4X2 + 5X + 6 a b c
5x2 + 6x + 2
2x2 + -7x +1
3x2 + 4x -1
-3x2 +2x -4
-8x2 -6x +1

76. Finding The Sum of the Roots
4X2 + 5X + 6 a b c
5x2 + 6x + 2
2x2 + -7x +1
3x2 + 4x -1
-3x2 +2x -4
-8x2 -6x +1

77. Estimation
Rule
x 26 =
x 38
x 54
x 17
x 31
x 64

78. Area of a Square Given the Diagonal
Find the area of a square with a diagonal of 12
Diagonal = 14
Diagonal = 8
Diagonal = 20
Diagonal = 26
Diagonal = 17

79. Estimation of a 3 x 3 Multiplication

80. Dividing by 11 and finding the remainder
7258 / 11=_____
Remainder
16235 / 11
/ 11
/ 11
26543 / 11
/ 11

81. 2994 x 6 = Multiply By Rounding 3994 x 7 5991 x 6 4997 x 8 6994 x 4

82. 122 + 242= The Sum of Squares 142 + 282 172 + 342 112 + 222 252 + 502
(factor of 2) =

83. 122 + 362= The Sum of Squares 142 + 422 172 + 512 112 + 332 252 + 752
(factor of 3) =

84. The Difference of Squares
(Sum x the Difference) =

85. 2989 + 456= Addition by Rounding 2994 + 658 3899 x 310 294 + 498 + 28

86. 123…x9 + A Constant
(1111…Problem)
123 x 9 + 4
1234 x 9 + 5
12345 x 9 + 6
1234 x 9 + 7
x 9 + 6
12 x 9 + 3

87. Supplement and Complement
Find The Difference Of The Supplement And The Complement Of An Angle Of 40.
angle of 70
angle of 30
angle of 13.8
angle of 63
angle of 71 ½

88. Supplement and Complement
Find The Sum Of The Supplement And The Complement Of An Angle Of 40.
angle of 70
angle of 30
angle of 13.8
angle of 63
angle of 71 ½

89. Larger or Smaller 55 52 +

90. Two Step Equations (Christmas Present Problem)3 -
= 11 1
2x -1 =8
x/ =6
5x -12 = 33
x/ =8
x/12 +5 = 3

91. How Many #s less than 20 are relatively prime to 20?
Relatively Prime (No common Factors Problem) * One is relatively prime to all numbers
How Many #s less than 20 are relatively prime to 20?
less than 18
less than 50
less than 12
less than 22
less than 100

92. Find the Product of the GCF and the LCM of 6 and 15
Product of LCM and GCF
Find the Product of the GCF and the LCM of 6 and 15
21 and 40
38 and 50
25 and 44
12 and 48
29 and 31

93. Estimation
15 x 17 x 19
7 x 8 x 9
11 x 13 x 15
19 x 20 x 21
38 x 40 x 42
9 x 11 x 13

94. Sequences-Finding the Pattern
7, 2, 5, 8, 3, 14
Find the next number in this pattern
5,10,15,20,25…..
11, 12, 14, 17,…..
8,9,7,8,6……
7,13,14,10,21,7…..
2,8,5,4,6,10,6,4,15…

95. Sequences-Finding the Pattern
1, 4, 5, 9, 14, 23
Find the next number in this pattern
1,4,5,9,14,23……
2,3,5,10,18,33,……
1,4,9,16,25…….
8, 27,64,125….
10,8,6,4,….

96. Degrees Radians
900= _____
Radians
1800=
450=
2700=
1350=