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This is a new powerpoint. If you find any errors
please let me know at kenneth.lee2_at_fortbendisd.com

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
402 1600 and the PERFECT CUBES from 13 1 to
253 15625. These squares and cubes should be
learned in both directions. ie. 172 289
and the 289 is 17.
6
2x2 Foil (LIOF)23 x 12
The Rainbow Method
Work Backwards
Used when you forget a rule about 2x2
multiplication

• The last number is the units digit of the
  
  product of the units
  digits
• Multiply the outside, multiply the inside
• Add the outside and the inside together plus any
  
  carry and write down the units digit
• Multiply the first digits together and add
  
  and carry. Write down the number

3(2)
2(2)3(1)
2(1)
6
7
2
276
7
2x2 Foil (LIOF)23 x 12
The Rainbow Method
Work Backwards
Used when you forget a rule about 2x2
multiplication

1. 45 x 31
2. 31 x 62
3. 64 x 73
4. 62 x 87
5. 96 x74

8
Squaring Numbers Ending In 5752

• First two digits the tens digit times one more
  than the tens digit.
• Last two digits are always 25
• 7(71) 25
• 56 25

9
Squaring Numbers Ending In 5752

1. 45 x 45
2. 952
3. 652
4. 352
5. 15 x 15

10
Consecutive Decades35 x 45

• First two digits the small tens digit times
  one more than the large tens digit.
• Last two digits are always 75
• 3(41) 75
• 15 75

11
Consecutive Decades35 x 45

1. 45 x 55
2. 65 x 55
3. 25 x 35
4. 95 x 85
5. 85 x75

12
Ending in 5Tens Digits Both Even45 x 85

• First two digits the product of the tens
  digits plus ½ the sum of the tens digits.
• Last two digits are always 25
• 4(8) ½ (48) 25
• 38 25

13
Ending in 5Tens Digits Both Even45 x 85

1. 45 x 65
2. 65 x 25
3. 85 x 65
4. 85 x 25
5. 65 x65

14
Ending in 5Tens Digits Both Odd35 x 75

• First two digits the product of the tens
  digits plus ½ the sum of the tens digits.
• Last two digits are always 25
• 3(7) ½ (37) 25
• 26 25

15
Ending in 5Tens Digits Both Odd35 x 75

1. 35 x 75
2. 55 x 15
3. 15 x 95
4. 95 x 55
5. 35 x 95

16
Ending in 5Tens Digits OddEven35 x 85

• First two digits the product of the tens
  digits plus ½ the sum of the tens digits.
  Always drop the remainder.
• Last two digits are always 75
• 3(8) ½ (38) 75
• 29 75

17
Ending in 5Tens Digits OddEven35 x 85

1. 45 x 75
2. 35 x 65
3. 65 x 15
4. 15 x 85
5. 55 x 85

18
Multiplying By 12 ½ 32 x 12 ½
(1/8 rule)

• Divide the non-12 ½ number by 8.
• Add two zeroes.

32
400

8
4 00
19
Multiplying By 12 ½ 32 x 12 ½
(1/8 rule)

1. 12 ½ x 48
2. 12 ½ x 88
3. 888 x 12 ½
4. 12 ½ x 24
5. 12 ½ x 16

20
Multiplying By 16 2/3 42 x 16 2/3
(1/6 rule)

• Divide the non-16 2/3 number by 6.
• Add two zeroes.

42
700

6
7 00
21
Multiplying By 16 2/3 42 x 16 2/3
(1/6 rule)

1. 16 2/3 x 42
2. 16 2/3 x 66
3. 78 x 16 2/3
4. 16 2/3 x 48
5. 16 2/3 x 120

22
Multiplying By 33 1/3 24 x 33 1/3
(1/3 rule)

• Divide the non-33 1/3 number by 3.
• Add two zeroes.

• 24

800

3
8 00
23
Multiplying By 33 1/3 24 x 33 1/3
(1/3 rule)

1. 33 1/3 x 45
2. 33 1/3 x 66
3. 33 1/3 x 123
4. 33 1/3 x 48
5. 243 x 33 1/3

24
Multiplying By 2532 x 25
(1/4 rule)

• Divide the non-25 number by 4.
• Add two zeroes.

32
8
00

4
8 00
25
Multiplying By 2532 x 25
(1/4 rule)

1. 25 x 44
2. 444 x 25
3. 25 x 88
4. 25 x 36
5. 25 x 12

26
Multiplying By 5032 x 50
(1/2 rule)

• Divide the non-50 number by 2.
• Add two zeroes.

32
16

00
2
16 00
27
Multiplying By 5032 x 50
(1/2 rule)

1. 50 x 44
2. 50 x 126
3. 50 x 424
4. 50 x 78
5. 50 x 14

28
Multiplying By 7532 x 75
(3/4 rule)

• Divide the non-75 number by 4.
• Multiply by 3.
• Add two zeroes.

32

8x32400
4
24 00
29
Multiplying By 7532 x 75
(3/4 rule)

1. 75 x 44
2. 75 x 120
3. 75 x 24
4. 48 x 75
5. 84 x 75

30
Multiplying By 37 1/237 1/2 x 24
(3/8 rule)

9 00
00
(3/8)24
31
Multiplying By 62 1/262 1/2 x 56
(5/8 rule)

35 00
00
(5/8)56
32
Multiplying By 87 1/287 1/2 x 48
(7/8 rule)

42 00
00
(7/8)48
33
Multiplying By 83 1/383 1/3 x 36
(5/6 rule)

30 00
00
(5/6)36
34
Multiplying By 66 2/366 2/3 x 66
(2/3 rule)

44 00
00
(2/3)66
35
Multiplying By 12532 x 125
(1/8 rule)

• Divide the non-125 number by 8.
• Add three zeroes.
• 32

4000

8
4 000
36
Multiplying By 12532 x 125
(1/8 rule)

1. 125 x 48
2. 125 x 88
3. 125 x 408
4. 125 x 24
5. 125 x 160

37
Multiplying When Tens Digits Are Equal And The
Unit Digits Add To 1032 x 38

• First two digits are the tens digit
  times one more than the tens digit
• Last two digits are the product
  of the units digits.

3(31)
2(8)
12 16
38
Multiplying When Tens Digits Are Equal And The
Unit Digits Add To 1032 x 38

1. 34 x 36
2. 73 x 77
3. 28 x 22
4. 47 x 43
5. 83 x 87

39
Multiplying When Tens Digits Add To 10 And The
Units Digits Are Equal67 x 47

• First two digits are the product of the tens
  digit plus the units digit
• Last two digits are the product
  of the units digits.

6(4)7
7(7)
31 49
40
Multiplying When Tens Digits Add To 10 And The
Units Digits Are Equal67 x 47

1. 45 x 65
2. 38 x 78
3. 51 x 51
4. 93 x 13
5. 24 x 84

41
Multiplying Two Numbers in the 90s97 x 94

• Find out how far each number is from 100
• The 1st two numbers equal the sum of the
  differences subtracted from 100
• The last two numbers equal the
  product of the differences

100-(36)
3(6)
91 18
42
Multiplying Two Numbers in the 90s97 x 94

1. 98 x 93
2. 92 x 94
3. 91 x 96
4. 96 x 99
5. 98 x 98

43
Multiplying Two Numbers Near 100109 x 106

• First Number is always 1
• The middle two numbers
  the sum on the units digits
• The last two digits the
  product of the units digits

1
96
9(6)
1 15 54
44
Multiplying Two Numbers Near 100109 x 106

1. 106 x109
2. 103 x 105
3. 108 x 101
4. 107 x 106
5. 108 x 109

45
Multiplying Two Numbers With 1st Numbers And A
0 In The Middle402 x 405

• The 1st two numbers the product of the hundreds
  digits
• The middle two numbers the sum of the
  units x the hundreds digit
• The last two digits the product of the units
  digits

4(4)
4(25)
2(5)
16 28 10
46
Multiplying Two Numbers With 1st Numbers And A
0 In The Middle402 x 405

1. 405 x 405
2. 205 x 206
3. 703 x 706
4. 603 x 607
5. 801 x 805

47
Multiplying By 336718 x 3367
10101 Rule

• Divide the non-3367 by 3
• Multiply by 10101

18/3 6 x 10101
60606
48
Multiplying By 336718 x 3367
10101 Rule

1. 3367 x 33
2. 3367 x123
3. 3367 x 66
4. 3367 x 93
5. 3367 x 24

49
Multiplying A 2-Digit By 1192 x 11
121 Pattern
(ALWAYS WORK FROM RIGHT TO LEFT)

• Last digit is the units digit
• The middle digit is the sum of the tens and the
  units digits
• The first digit is the tens digit any carry

91
92
2
10 1 2
50
Multiplying A 2-Digit By 1192 x 11
121 Pattern
(ALWAYS WORK FROM RIGHT TO LEFT)

1. 11 x 34
2. 11 x 98
3. 65 x 11
4. 11 x 69
5. 27 x 11

51
Multiplying A 3-Digit By 11192 x 11
1221 Pattern
(ALWAYS WORK FROM RIGHT TO LEFT)

• Last digit is the units digit
• The next digit is the sum of the tens and the
  units digits
• The next digit is the sum of the tens and the
  hundreds digit carry
• The first digit is the hundreds digit any carry

191
92
2
11
2 1 1 2
52
Multiplying A 3-Digit By 11192 x 11
1221 Pattern
(ALWAYS WORK FROM RIGHT TO LEFT)

1. 11 x 231
2. 11 x 687
3. 265 x 11
4. 879x 11
5. 11 x 912

53
Multiplying A 3-Digit By 111192 x 111
12321 Pattern
(ALWAYS WORK FROM RIGHT TO LEFT)

• Last digit is the units digit
• The next digit is the sum of the tens and the
  units digits
• The next digit is the sum of the units, tens and
  the hundreds digit carry
• The next digit is the sum of the tens and
  hundreds digits carry
• The next digit is the hundreds digit carry

191
92
2
11
1921
2 1 3 1 2
54
Multiplying A 3-Digit By 111192 x 111
12321 Pattern
(ALWAYS WORK FROM RIGHT TO LEFT)

1. 111 x 213
2. 111 x 548
3. 111 x825
4. 936 x 111
5. 903 x 111

55
Multiplying A 2-Digit By 11141 x 111
1221 Pattern
(ALWAYS WORK FROM RIGHT TO LEFT)

1. Last digit is the units digit
2. The next digit is the sum of the tens and the
   units digits
3. The next digit is the sum of the tens and the
   units digits carry
4. The next digit is the tens digit carry

4
41
1
41
4 5 5 1
56
Multiplying A 2-Digit By 11141 x 111
1221 Pattern
(ALWAYS WORK FROM RIGHT TO LEFT)

1. 45 x 111
2. 111 x 57
3. 111 x93
4. 78 x 111
5. 83 x 111

57
Multiplying A 2-Digit By 10193 x 101

1. The first two digits are the 2-digit number x1
2. The last two digits are the 2-digit number x1

93(1)
93(1)
93 93
58
Multiplying A 2-Digit By 10193 x 101

1. 45 x 101
2. 62 x 101
3. 101 x 72
4. 101 x 69
5. 101 x 94

59
Multiplying A 3-Digit By 101934 x 101

1. The last two digits are the last two digits
   of the 3-digit number
2. The first three numbers are the 3-digit
   number plus the hundreds digit

9349
34
943 34
60
Multiplying A 3-Digit By 101934 x 101

1. 101 x 658
2. 963 x 101
3. 101 x 584
4. 381 x 101
5. 101 x 369

61
Multiplying A 2-Digit By 100187 x 1001

1. The first 2 digits are the 2-digit number x 1
2. The middle digit is always 0
3. The last two digits are the 2-digit number x 1

87(1)
0
87(1)
87 0 87
62
Multiplying A 2-Digit By 100187 x 1001

1. 1001 x 66
2. 91 x 1001
3. 1001 x 53
4. 1001 x 76
5. 5.2 x 1001

63
Halving And Doubling52 x 13

1. Take half of one number
2. Double the other number
3. Multiply together

52/2
13(2)
26(26) 676
64
Halving And Doubling52 x 13

1. 14 x 56
2. 16 x 64
3. 8 x 32
4. 17 x 68
5. 19 x 76

65
One Number in the Hundreds And One Number In The
90s95 x 108

1. Find how far each number is from 100
2. The last two numbers are the product of
   the
   differences subtracted from 100
3. The first numbers the difference (from the
   90s) from 100 increased by 1 and subtracted from
   the larger number

108-(51)
100-(5x8)
102 60
66
One Number in the Hundreds And One Number In The
90s95 x 108

1. 105 x 96
2. 98 x 104
3. 109 x 97
4. 98 x 105
5. 97 x 107

67
Fraction Foil (Type 1)8 ½ x 6 ¼

1. Multiply the fractions together
2. Multiply the outside two number
3. Multiply the inside two numbers
4. Add the results and then add to the
   product of the whole numbers

(8)(6)1/2(6)1/4(8)
(1/2x1/4)
53 1/8
68
Fraction Foil (Type 1)8 ½ x 6 ¼

1. 9 1/2 x 8 1/3
2. 5 1/5 x 10 2/5
3. 10 1/7 x 14 1/2
4. 3 1/4 x 8 1/3
5. 6 1/4 x 8 1/2

69
Fraction Foil (same fraction)7 ½ x 5 ½

1. Multiply the fractions together
2. Add the whole numbers and
   divide by the
   denominator
3. Multiply the whole numbers and
   add to previous step

(7x5)6
(1/2x1/2)
41 1/4
70
Fraction Foil (Type 2)7 ½ x 5 ½

1. 9 1/2 x 7 1/2
2. 4 1/5 x 11 1/5
3. 10 1/6 x 14 1/6
4. 2 1/3 x 10 1/3
5. 6 1/7 x 8 1/7

71
Fraction Foil (fraction adds to 1)7 ¼ x 7 ¾

1. Multiply the fractions together
2. Multiply the whole number by
   one more than the whole number

(7)(71)
(1/4x3/4)
56 3/16
72
Fraction Foil (Type 3)7 ¼ x 7 ¾

1. 8 1/2 x 8 1/2
2. 10 1/5 x 10 4/5
3. 9 1/7 x 9 6/7
4. 5 3/4 x 5 1/4
5. 2 1/4 x 2 3/4

73
Adding Reciprocals7/8 8/7

• Keep the common denominator
• The numerator is the difference of
  the two numbers squared
• The whole number is always two plus
  any carry from the fraction.

74
Adding Reciprocals7/8 8/7

1. 5/6 6/5
2. 11/13 13/11
3. 7/2 2/7
4. 7/10 10/7
5. 11/15 15/11

75
Percent Missing the Of36 is 9 of __

• Divide the first number by
  the percent number
• Add 2 zeros or move the
  decimal two places to the right

36/9
00

400
76
Percent Missing the Of36 is 9 of __

1. 40 is 3 of ______
2. 27 is 9 of ______
3. 800 is 25 of ____
4. 70 is 4 of ______
5. 10 is 2 1/2 of _____

77
Percent Missing the Of36 is 9 of __

1. 40 is 3 of ______
2. 27 is 9 of ______
3. 800 is 25 of ____
4. 70 is 4 of ______
5. 10 is 2 1/2 of _____

78
Base N to Base 10 426 ____10

• Multiply the left digit times the base
• Add the number in the units column

4(6)2

2610
79
Base N to Base 10 Of426 ____10

1. 546_____10
2. 347_____10
3. 769_____10
4. 1245_____10
5. 2346_____10

80
Multiplying in Bases4 x 536___6

• Multiply the units digit by the multiplier
• If number cannot be written in base n subtract
  base n until the digit
  can be written
• Continue until you have the answer

4x312 subtract 12 Write 0

4x520222 subtract 18 Write 4
Write 3
3406
81
Multiplying in Bases4 x 536___6

1. 2 x 426 _____6
2. 3 x 547_____7
3. 4 x 678_____8
4. 5 x 345_____5
5. 3 x 278_____8

82
N/40 to a or Decimal21/40___decimal

• Mentally take off the zero
• Divide the numerator by the denominator
  and write down the digit
• Put the remainder over the 4 and write the
  decimal without the decimal point
• Put the decimal point in front of the numbers

5
25
.
21/4
1/4
83
N/40 to a or Decimal21/40___decimal

1. 31/40
2. 27/40
3. 51/40
4. 3/40
5. 129/40

84
Remainder When Dividing By 9867/9___remainder

• Add the digits until you get a single digit
• Write the remainder

86721213

3
85
Remainder When Dividing By 9867/9___remainder

1. 3251/9
2. 264/9
3. 6235/9
4. 456/9
5. 6935/9

86
Base 8 to Base 27328 ____2
421 Method

• Mentally put 421 over each number
• Figure out how each base number
  can be written with a 4, 2 and 1
• Write the three digit number down

421
421
421
7
3
2
111
011
010
87
Base 8 to Base 27328 ____2
421 Method

1. 3548 _____2
2. 3258_____2
3. 1568_____2
4. 3548_____2
5. 5748_____2

88
Base 2 to Base 8 Of1110110102 ___8
421 Method

1. Separate the number into groups
   of 3 from the right.
2. Mentally put 421 over each group
3. Add the digits together and write the sum

421
421
421
011
010
111
7
3
2
89
Base 2 to Base 8 Of1110110102 ___8
421 Method

1. 1100012 _____8
2. 1111002_____8
3. 1010012_____8
4. 110112_____8
5. 10001102_____8

90
Cubic Feet to Cubic Yards3ft x 6ft x 12ft__yds3

• Try to eliminate three 3s by division
• Multiply out the remaining numbers
• Place them over any remaining 3s

3
12
6
3
3
3
1 x 2 x 4 8
Cubic yards
91
Cubic Feet to Cubic Yards3ft x 6ft x 12ft__yds3

1. 6ft x 3ft x 2ft
2. 9ft x 2ft x 11ft
3. 2ft x 5ft x 7ft
4. 27ft x 2ft x5ft
5. 10ft x 12ft x 3ft

92
Ft/sec to MPH44 ft/sec __mph

• Use 15 mph 22 ft/sec
• Find the correct multiple
• Multiply the other number

22x244
15x230 mph
93
Ft/sec to mph44 ft/sec __mph

1. 88 ft/sec_____mph
2. 120 mph_____ft/sec
3. 90 mph ______ft/sec
4. 132 ft/sec _____mph
5. 45 mph ____ft/sec

94
Subset ProblemsF,R,O,N,T______
SUBSETS

• Subsets2n
• Improper subsets always 1
• Proper subsets 2n - 1
• Power sets subsets

95
Subset ProblemsF,R,O,N,T______
SUBSETS

1. A,B,C
2. D,G,H,J,U,N
3. !!, , ,
4. AB, FC,GH,DE,BM
5. M,A,T,H

96
Repeating Decimals to Fractions.18___fraction
___

• The numerator is the number
• Read the number backwards. If a number has a
  line over it then there is a 9 in the denominator
• Write the fraction and reduce

18
2

99
11
97
Repeating Decimals to Fractions.18___fraction
___

1. .25
2. .123
3. .74
4. .031
5. .8

98
Repeating Decimals to Fractions.18___fraction
_

• The numerator is the number minus
  the part that does not repeat
• For the denominator read the number backwards.
  If it has a line over it,
  it is a 9. if not it is a o.

18-1
17

90
90
99
Repeating Decimals to Fractions.18___fraction
_

1. .16
2. .583
3. .123
4. .45
5. .92

100
Gallons Cubic Inches2 gallons__in3
(Factors of 231 are 3, 7, 11)

• Use the fact 1 gal 231 in3
• Find the multiple or the factor and adjust the
  other number. (This is a direct variation)

2(231) 462 in3
101
Gallons Cubic Inches2 gallons__in3

1. 3 gallons _____in3
2. ½ gallon ______in3
3. 77 in3_______gallons
4. 33 in3_______gallons
5. 1/5 gallon______in3

102
Finding Pentagonal Numbers5th Pentagonal __

• Use the house method)
• Find the square , find the triangular ,
  then add them together

1234 10
251035
25
5
5
103
Finding Pentagonal Numbers5th Pentagonal __

1. 3rd pentagonal number
2. 6th pentagonal number
3. 10th pentagonal number
4. 4th pentagonal number
5. 6th pentagonal number

104
Finding Triangular Numbers6th Triangular __

• Use the n(n1)/2 method
• Take the number of the term that you are looking
  for and multiply it by one more than that term.
• Divide by 2 (Divide before multiplying)

6(61)42
42/221
105
Finding Triangular Numbers6th Triangular __

1. 3rd triangular number
2. 10th triangular number
3. 5th triangular number
4. 8th triangular number
5. 40th triangular number

106
Pi To An Odd Power13____approximation

• Pi to the 1st 3 (approx) Write a 3
• Add a zero for each odd power
  of Pi after the first

3000000
107
Pi To An Odd Power13____approximation

1. Pi11
2. Pi7
3. Pi9
4. Pi5
5. Pi3

108
Pi To An Even Power12____approximation

• Pi to the 2nd 95 (approx) Write a 95
• Add a zero for each even power
  of Pi after the 4th

950000
109
Pi To An Even Power12____approximation

1. Pi10
2. Pi8
3. Pi6
4. Pi14
5. Pi16

110
The More Problem17/15 x 17

1. The answer has to be more than the whole number.
2. The denominator remains the same.
3. The numerator is the difference in the two
   numbers squared.
4. The whole number is the original whole number
   plus the difference

(17-15)2
172
15
19 4/15
111
The More Problem17/15 x 17

1. 19/17 x 19
2. 15/13 x 15
3. 21/17 x 21
4. 15/12 x 15
5. 31/27 x 31

112
The Less Problem15/17 x 15

1. The answer has to be less than the whole number.
2. The denominator remains the same.
3. The numerator is the difference in the two
   numbers squared.
4. The whole number is the original whole number
   minus the difference

(17-15)2
15-2
17
13 4/17
113
The Less Problem15/17 x 15

1. 13/17 x 13
2. 21/23 x 21
3. 5/7 x 5
4. 4/7 x4
5. 49/53 x49

114
Multiplying Two Numbers Near 1000994 x 998

• Find out how far each number is from 1000
• The 1st two numbers equal the sum of the
  differences subtracted from 1000
• The last two numbers equal the product of the
  differences written as a 3-digit number

1000-(62)
6(2)
992 012
115
Multiplying Two Numbers Near 1000994 x 998

1. 996 x 991
2. 993 x 997
3. 995 x 989
4. 997 x 992
5. 985 x 994

116
The (Reciprocal) Work Problem1/6 1/5 1/X
Two Things Helping

1. Use the formula ab/ab.
2. The numerator is the product of the two numbers.
3. The deniminator is the sum of the two numbers.
4. Reduce if necessary

6(5)
65
30/11
117
The (Reciprocal) Work Problem1/6 1/5 1/X
Two Things Helping

1. 1/3 1/5 1/x
2. 1/2 1/6 1/x
3. 1/4 1/7 1/x
4. 1/8 1/6 1/x
5. 1/10 1/4 1/x

118
The (Reciprocal) Work Problem1/6 - 1/8 1/X
Two Things working Against Each Other

1. Use the formula ab/b-a.
2. The numerator is the product of the two numbers.
3. The denominator is the difference of the two
   numbers from
   right to left.
4. Reduce if necessary

6(8)
8-6
24
119
The (Reciprocal) Work Problem1/6 - 1/8 1/X
Two Things working Against Each Other

1. 1/8 1/5 1/x
2. 1/11 1/3 1/x
3. 1/8 1/10 1/x
4. 1/7 1/8 1/x
5. 1/30 1/12 1/x

120
The Inverse Variation Problem30 of 12 20
of ___

• Compare the similar terms as a reduced ratio
• Multiply the other term by the reduced ratio.
• Write the answer

121
The Inverse Variation Problem30 of 12 20
of ___

1. 27 of 50 54 of _____
2. 15 of 24 20 of _____
3. 90 of 70 30 of _____
4. 75 of 48 50 of _____
5. 14 of 27 21 of _____
6. 26 of 39 78 of _____

122
Sum of Consecutive Integers123..20

• Use formula n(n1)/2
• Divide even number by 2
• Multiply by the other number

(20)(21)/2
10(21) 210
123
Sum of Consecutive Integers123..20

1. 123.30
2. 123.16
3. 123.19
4. 12349
5. 123.100

124
Sum of Consecutive Even Integers246..20

• Use formula n(n2)/4
• Divide the multiple of 4 by 4
• Multiply by the other number

(20)(22)/4
5(22) 110
125
Sum of Consecutive Even Integers246..20

1. 246.16
2. 246.40
3. 246.28
4. 246.48
5. 246.398

126
Sum of Consecutive Odd Integers135..19

• Use formula ((n1)/2)2
• Add the last number and the first number
• Divide by 2
• Square the result

(191)/2
102 100
127
Sum of Consecutive Odd Integers135..19

1. 135.33
2. 135.49
3. 135.67
4. 135.27
5. 135.47

128
Finding Hexagonal NumbersFind the 5th
Hexagonal Number

1. Use formula 2n2-n
2. Square the number and multiply by2
3. Subtract the number wanted from the previous
   answer

2(5)2 50
50-5
45
129
Finding Hexagonal NumbersFind the 5th
Hexagonal Number

1. Find the 3rd hexagonal number
2. Find the 10th hexagonal number
3. Find the 4th hexagonal number
4. Find the 2nd hexagonal number
5. Find the 6th hexagonal number

130
Cube PropertiesFind the Surface Area of a Cube
Given the Space Diagonal 12

1. Use formula Area 2D2
2. Square the diagonal
3. Multiply the product by 2

2(12)(12)
2(144)
288
131
Cube PropertiesFind the Surface Area of a Cube
Given the Space Diagonal of 12

1. Space diagonal 24
2. Space diagonal 10
3. Space diagonal 50
4. Space diagonal 21
5. Space diagonal 8

132
Cube Properties
Find S, Then Use It To Find Volume or Surface
Area
133
Cube Properties
Find S, Then Use It To Find Volume or Surface
Area
134
Finding Slope From An Equation3X2Y10

• Solve the equation for Y
• The number in front of X is the Slope

3X2Y10

Slope -3/2
135
Finding Slope From An Equation3X2Y10

1. Y 2X 8
2. Y -7X 6
3. 2Y 8X - 12
4. 2X 3Y 12
5. 10X 4Y 13

136
Hidden Pythagorean Theorem Find The Distance
Between These Points(6,2) and (9,6)

• Find the distance between the Xs
• Find the distance between the Ys
• Look for a Pythagorean triple
• If not there, use the Pythagorean Theorem

9-63
6-24
3 4 5

5 12 13
3
4
5
7 24 25
8 15 17
The distance is 5
Common Pythagorean triples
137
Hidden Pythagorean Theorem Find The Distance
Between These Points(6,2) and (9,6)

1. (4,3) and (7,7)
2. (8,3) and (13,15)
3. (1,2) and (3,4)
4. (12,29) and (5,5)
5. (3,4) and (2,4)

138
Finding Diagonals Find The Number Of
Diagonals In An Octagon

• Use the formula n(n-3)/2
• N is the number of vertices in the polygon

8(8-3)/2

20
139
Finding Diagonals Find The Number Of
Diagonals In An Octagon

1. of diagonals in a pentagon
2. of diagonals of a hexagon
3. of diagonals of a decagon
4. of diagonals of a dodecagon
5. of diagonals of a heptagon

140
Finding the total number of factors 24 ________

• Put the number into prime factorization
• Add 1 to each exponent
• Multiply the numbers together

31 x 23

112 314
2x48
141
Finding the total number of factors 24 ________

1. 12
2. 30
3. 120
4. 50
5. 36

142
Estimating a 4-digit square root
7549 _______

• The answer is between 802 and 902
• Find 852
• The answer is between 85 and 90
• Guess any number in that range

8026400

8527225
87
9028100
143
Estimating a 4-digit square root
7549 _______
3165
1.
6189
2.
3.
1796

9268
4.
5.
5396
144
Estimating a 5-digit square root
37485 _______

• Use only the first three numbers
• Find perfect squares on either side
• Add a zero to each number
• Guess any number in that range

192361

190-200
195
202400
145
Estimating a 5-digit square root
37485 _______
31651
1.
61893
2.
3.
17964

92682
4.
5.
53966
146
C F
55C _______F

1. Use the formula F 9/5 C 32
2. Plug in the F number
3. Solve for the answer

9/5(55) 32

9932
131
147
C F
59C _______F

1. 4500C______F
2. 400C _____F
3. 650C _____F
4. 250C_____F
5. 900C_____F

148
C F
50F _______C

1. Use the formula C 5/9 (F-32)
2. Plug in the C number
3. Solve for the answer

5/9(50-32)

5/9(18)
10
149
C F
50F _______C

1. 680F
2. 590F
3. 1130F
4. 410F
5. 950F

150
Finding The Product of the Roots
4X2 5X 6
a
b
c

1. Use the formula c/a
2. Substitute in the coefficients
3. Find answer

6 / 4 3/2

151
Finding The Product of the Roots
4X2 5X 6
a
b
c

1. 5x2 6x 2
2. 2x2 -7x 1
3. 3x2 4x -1
4. -3x2 2x -4
5. -8x2 -6x 1

152
Finding The Sum of the Roots
4X2 5X 6
a
b
c

1. Use the formula -b/a
2. Substitute in the coefficients
3. Find answer

-5 / 4

153
Finding The Sum of the Roots
4X2 5X 6
a
b
c

1. 5x2 6x 2
2. 2x2 -7x 1
3. 3x2 4x -1
4. -3x2 2x -4
5. -8x2 -6x 1

154
Estimation
999999 Rule
142857 x 26

1. Divide 26 by 7 to get the first digit
2. Take the remainder and add a zero
3. Divide by 7 again to get the next number
4. Find the number in 142857 and copy in a circle

26/7 3r5

5050/77
3 714285
155
Estimation
999999 Rule
142857 x 26

1. 142857 x 38
2. 142857 x 54
3. 142857 x 17
4. 142857 x 31
5. 142857 x 64

156
Area of a Square Given the Diagonal
Find the area of a square with a diagonal of 12

1. Use the formula Area ½ D1D2
2. Since both diagonals are equal
3. Area ½ 12 x 12
4. Find answer

½ D1 D2

½ x 12 x 12
72
157
Area of a Square Given the Diagonal
Find the area of a square with a diagonal of 12

1. Diagonal 14
2. Diagonal 8
3. Diagonal 20
4. Diagonal 26
5. Diagonal 17

158
Estimation of a 3 x 3 Multiplication
346 x 291

1. Take off the last digit for each number
2. Round to multiply easier
3. Add two zeroes
4. Write answer

35 x 30

1050 00
105000
159
Estimation of a 3 x 3 Multiplication
346 x 291

1. 316 x 935
2. 248 x 603
3. 132 x 129
4. 531 x 528
5. 248 x 439

160
Dividing by 11 and finding the remainder
7258 / 11_____

Remainder

1. Start with the units digit and add up every other
   number
2. Do the same with the other numbers
3. Subtract the two numbers
4. If the answer is a negative or a number greater
   than 11 add or subtract 11 until you get a number
   from 0-10

8210 75 12
10-12 -2 11 9
161
Dividing by 11 and finding the remainder
7258 / 11_____

Remainder

1. 16235 / 11
2. 326510 / 11
3. 6152412 / 11
4. 26543 / 11
5. 123456 / 11

162
Multiply By Rounding
2994 x 6

• Round 2994 up to 3000
• Think 3000 x 6
• Write 179. then find the last two numbers by
  multiplying what you added by 6 and subtracting
  it from 100.

3000(6)179_ _

6(6)36 100-3664
17964
163
Multiply By Rounding
2994 x 6

1. 3994 x 7
2. 5991 x 6
3. 4997 x 8
4. 6994 x 4
5. 1998 x 6

164
The Sum of Squares
(factor of 2)
122 242

• Since 12 goes into 24 twice
• Square 12 and multiply by 10
• Divide by 2

122144
144x10

1440/2
720
165
The Sum of Squares
(factor of 2)
122 242

1. 142 282
2. 172 342
3. 112 222
4. 252 502
5. 182 362

166
The Sum of Squares
(factor of 3)
122 362

• Since 12 goes into 36 three times
• Square 12 and multiply by 10

122144
144x10

1440
167
The Sum of Squares
(factor of 3)
122 362

1. 142 422
2. 172 512
3. 112 332
4. 252 752
5. 182 542

168
The Difference of Squares
(Sum x the Difference)
322 - 302

• Find the sum of the bases
• Find the difference of the bases
• Multiply them together

323062

32-302
62 x 2 124
169
The Difference of Squares
(Sum x the Difference)
322 - 302

1. 222 - 322
2. 732 - 272
3. 312 - 192
4. 622 - 422
5. 992 - 982

170
Addition by Rounding
2989 456

• Round 2989 to 3000
• Subtract the same amount to 456, 456-11 445
• Add them together

298911 3000

456-11445
30004453445
171
Addition by Rounding
2989 456

1. 2994 658
2. 3899 310
3. 294 498 28
4. 6499 621
5. 2938 64

172
123x9 A Constant
(1111Problem)
123 x 9 4

• The answer should be all 1s. There should be 1
  more 1 than the length of the 123 pattern.
• You must check the last number. Multiply the last
  number in the 123 pattern and add the constant.
  

3x9 4 31

1111
173
123x9 A Constant
(1111Problem)
123 x 9 4

1. 1234 x 9 5
2. 12345 x 9 6
3. 1234 x 9 7
4. 123456 x 9 6
5. 12 x 9 3

174
Supplement and Complement

Find The Difference Of The Supplement And The
Complement Of An Angle Of 40.

• The answer is always 90

90
175
Supplement and Complement

Find The Difference Of The Supplement And The
Complement Of An Angle Of 40.

1. angle of 70
2. angle of 30
3. angle of 13.8
4. angle of 63
5. angle of 71 ½

176
Supplement and Complement

Find The Sum Of The Supplement And The Complement
Of An Angle Of 40.

• Use the formula 270-twice the angle
• Multiple the angle by 2
• Subtract from 270

270-80
190
177
Supplement and Complement

Find The Sum Of The Supplement And The Complement
Of An Angle Of 40.

1. angle of 70
2. angle of 30
3. angle of 13.8
4. angle of 63
5. angle of 71 ½

178
Larger or Smaller
55
52

• Find the cross products
• The larger fraction is below the larger number
• The smaller number is below the smaller number

Larger 5/4

Smaller 13/11
179
Larger or Smaller
55
52

180
Two Step Equations(Christmas Present Problem)

• Start with the answer and undo the
  operations using reverse order of operations

11112

12 x3 36
181
Two Step Equations(Christmas Present Problem)

1. 2x -1 8
2. x/3 - 4 6
3. 5x -12 33
4. x/2 5 8
5. x/12 5 3

182
Relatively Prime(No common Factors Problem)
One is relatively prime to all numbers

How Many s less than 20 are relatively prime to
20?

• Put the number into prime factorization
• Subtract 1 from each exponent and multiply
  out all parts separately
• Subtract 1 from each base
• Multiply all parts together

2 x 1 x 1 x 4 8
183
Relatively Prime(No common Factors Problem)
One is relatively prime to all numbers

How Many s less than 20 are relatively prime to
20?

1. less than 18
2. less than 50
3. less than 12
4. less than 22
5. less than 100

184
Product of LCM and GCF

Find the Product of the GCF and the LCM of 6 and
15

• Multiple the two numbers together

6 x 15 90

185
Product of LCM and GCF

Find the Product of the GCF and the LCM of 6 and
15

1. 21 and 40
2. 38 and 50
3. 25 and 44
4. 12 and 48
5. 29 and 31

186
Estimation

15 x 17 x 19

• Take the number in the middle and cube it

1734913

187
Estimation

15 x 17 x 19

1. 7 x 8 x 9
2. 11 x 13 x 15
3. 19 x 20 x 21
4. 38 x 40 x 42
5. 9 x 11 x 13

188
Sequences-Finding the Pattern

7, 2, 5, 8, 3, 14
Find the next number in this pattern

• If the pattern is not obvious try looking at
  every other number. There may be two patterns
  put together

7, 2, 5, 8, 3, 14

1
189
Sequences-Finding the Pattern

7, 2, 5, 8, 3, 14
Find the next number in this pattern

1. 5,10,15,20,25..
2. 11, 12, 14, 17,..
3. 8,9,7,8,6
4. 7,13,14,10,21,7..
5. 2,8,5,4,6,10,6,4,15

190
Sequences-Finding the Pattern

1, 4, 5, 9, 14, 23
Find the next number in this pattern

• If nothing else works look for a Fibonacci
  Sequence where the next term is the sum of the
  previous two

1, 4, 5, 9, 14, 23

142337
191
Sequences-Finding the Pattern

1, 4, 5, 9, 14, 23
Find the next number in this pattern

1. 1,4,5,9,14,23
2. 2,3,5,10,18,33,
3. 1,4,9,16,25.
4. 8, 27,64,125.
5. 10,8,6,4,.

192
Degrees Radians

900 _____
Radians

• If you want radians use p X/180
• If you want degrees use 180 x/ p

90(p)/180

p/2
193
Degrees Radians

900 _____
Radians

1. 1800
2. 450
3. 2700
4. 1800
5. 1350