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NUMBER SENSE AT A FLIP
NUMBER SENSE AT A FLIP
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.
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.
The Rainbow Method
2x2 Foil (LIOF)
Work Backwards
23 x 12
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=
Consecutive Decades
35 x 45
1. 45 x 55=
2. 65 x 55=
3. 25 x 35=
4. 95 x 85=
5. 85 x754=
Ending in 5…Ten’s Digits Both Even
45 x 85
1. 45 x 65=
2. 65 x 25=
3. 85 x 65=
4. 85 x 25=
5. 65 x65=
Ending in 5…Ten’s Digits Both Odd
35 x 75
1. 35 x 75=
2. 55 x 15=
3. 15 x 95=
4. 95 x 55=
5. 35 x 95=
Ending in 5…Ten’s Digits Odd&Even
35 x 85
1. 45 x 75=
2. 35 x 65=
3. 65 x 15=
4. 15 x 85=
5. 55 x 85=
Squaring Numbers Ending In 5
2
75
1. 45 x 45=
2. 952=
3. 652=
4. 352=
5. 15 x 15=
(1/8 rule)
Multiplying By 12 ½
32 x 12 ½
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=
(1/6 rule)
Multiplying By 16 2/3
42 x 16 2/3
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=
(1/3 rule)
Multiplying By 33 1/3
24 x 33 1/3
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=
(1/4 rule)
Multiplying By 25
32 x 25
1. 24 x 44=
2. 444 x 25=
3. 25 x 88=
4. 25 x 36=
5. 25 x 12=
(1/2 rule)
Multiplying By 50
32 x 50
1. 50 x 44=
2. 50 x 126=
3. 50 x 424=
4. 50 x 78=
5. 50 x 14=
(3/4 rule)
Multiplying By 75
32 x 75
1. 75 x 44=
2. 75 x 120=
3. 75 x 24=
4. 48 x 75=
5. 84 x 75=
(1/8 rule)
Multiplying By 125
32 x 125
1. 125 x 48=
2. 125 x 88=
3. 125 x 408=
4. 125 x 24=
5. 125 x 160=
Multiplying When Tens Digits Are
Equal And The Unit Digits Add To 10
32 x 38
1. 34 x 36=
2. 73 x 77=
3. 28 x 22=
4. 47 x 43=
5. 83 x 87=
Multiplying When Tens Digits Add To 10
And The Units Digits Are Equal
67 x 47
1. 45 x 65=
2. 38 x 78=
3. 51 x 51=
4. 93 x 13=
5. 24 x 84=
Multiplying Two Numbers in the 90’s
97 x 94
1. 98 x 93=
2. 92 x 94=
3. 91 x 96=
4. 96 x 99=
5. 98 x 98=
Multiplying Two Numbers Near 100
109 x 106
1. 106 x109=
2. 103 x 105=
3. 108 x 101=
4. 107 x 106=
5. 108 x 109=
Multiplying Two Numbers With 1st
Numbers = And A “0” In The Middle
402 x 405
1. 405 x 405=
2. 205 x 206=
3. 703 x 706=
4. 603 x 607=
5. 801 x 805=
10101 Rule
Multiplying By 3367
18 x 3367
1. 3367 x 33=
2. 3367 x123=
3. 3367 x 66=
4. 3367 x 93=
5. 3367 x 24=
121 Pattern
Multiplying A 2-Digit # By 11
92 x 11
(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=
1221 Pattern
Multiplying A 3-Digit # By 11
192 x 11
(ALWAYS WORK FROM RIGHT TO LEFT)
1. 11 x 231=
2. 11 x 687=
3. 265 x 112=
4. 879x 11=
5. 11 x 912=
12321 Pattern
Multiplying A 3-Digit # By 111
192 x 111
(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=
1221 Pattern
Multiplying A 2-Digit # By 111
41 x 111
(ALWAYS WORK FROM RIGHT TO LEFT)
1. 45 x 111=
2. 111 x 57=
3. 111 x93=
4. 78 x 111=
5. 83 x 1111=
Multiplying A 2-Digit # By 101
93 x 101
1. 45 x 101=
2. 62 x 101=
3. 101 x 72=
4. 101 x 69=
5. 101 x 94=
Multiplying A 3-Digit # By 101
934 x 101
1. 101 x 658=
2. 963 x 101=
3. 101 x 584=
4. 381 x 101=
5. 101 x 369=
Multiplying A 2-Digit # By 1001
87 x 1001
1. 1001 x 66=
2. 91 x 1001=
3. 1001 x 53=
4. 1001 x 76=
5. 5.2 x 1001=
Halving And Doubling
52 x 13
1. 14 x 56=
2. 16 x 64=
3. 8 x 32=
4. 17 x 68=
5. 19 x 76=
One Number in the Hundreds
And One Number In The 90’s
95 x 108
1. 105 x 96=
2. 98 x 104=
3. 109 x 97=
4. 98 x 105=
5. 97 x 107=
Fraction Foil (Type 1)
8½ x6¼
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
Fraction Foil (Type 2)
7½ x5½
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
Fraction Foil (Type 3)
7¼ x7¾
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
Adding Reciprocals
7/8 + 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
Percent Missing the Of
36 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 _____=
Base N to Base 10 Of
426 =____10
1. 546=_____10
2. 347=_____7
3. 769=_____9
4. 1245=_____5
5. 2346=_____6
Multiplying in Bases
4 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
N/40 to a % or Decimal
21/40___decimal
1. 31/40=
2. 27/40=
3. 51/40=
4. 3/40=
5. 129/40=
Remainder When Dividing By 9
867/9=___
1. 3251/9=
2. 264/9=
3. 6235/9=
4. 456/9=
5. 6935/9=
remainder
421 Method
Base 8 to Base 2
7328 =____2
1. 3548= _____2
2. 3258=_____2
3. 1568=_____2
4. 3548=_____2
5. 5748=_____2
421 Method
Base 2 to Base 8 Of
1110110102 =___8
1. 1100012= _____8
2. 1111002=_____8
3. 1010012=_____8
4. 110112=_____8
5. 10001102=_____8
Cubic Feet to Cubic Yards
3ft x 6ft x 12ft
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=
3
=__yds
Ft/sec to mph
44 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
Subset Problems
{F,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}=
___
.18=___
Repeating Decimals to Fractions
1. .25
2. .123
3. .74
4. .031
5. .8
fraction
_
.18=___
Repeating Decimals to Fractions
1. .16
2. .583
3. .123
4. .55
5. .92
fraction
Gallons
2
Cubic Inches
3
gallons=__in
1. 3 gallons =_____in3
2. ½ gallon =______in3
3. 77 in3=_______gallons
4. 33 in3=_______gallons
5. 1/5 gallon=______in
Finding Pentagonal Numbers
th
5
Pentagonal # =__
1. 3rd pentagonal number=
2. 6th pentagonal number=
3. 10th pentagonal number=
4. 4th pentagonal number=
5. 6th pentagonal number=
Finding Triangular Numbers
th
6
Triangular # =__
1. 3rd triangular number=
2. 10th triangular number=
3. 5th triangular number=
4. 8th triangular number=
5. 40th triangular number=
Pi To An Odd Power
13=____
1. Pi11
2. Pi7
3. Pi9
4. Pi5
5. Pi3
approximation
Pi To An Even Power
12=____
1. Pi10
2. Pi8
3. Pi6
4. Pi14
5. Pi16
approximation
The More Problem
17/15 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=
The Less Problem
15/17 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=
Multiplying Two Numbers Near 1000
994 x 998
1. 998 x 993=
2. 993 x 991=
3. 994 x 996=
4. 997 x 995=
5. 992 x 996=
Two Things Helping
The (Reciprocal) Work Problem
1/6 + 1/5 = 1/X
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
Two Things working Against Each Other
The (Reciprocal) Work Problem
1/6 - 1/8 = 1/X
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
The Inverse Variation % Problem
30% 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 _____
Sum of Consecutive Integers
1+2+3+…..+20
1. 1+2+3+….+30=
2. 1+2+3+….+16=
3. 1+2+3+….+19=
4. 1+2+3+…+49=
5. 1+2+3+….100=
Sum of Consecutive Even Integers
2+4+6+…..+20
1. 2+4+6+….+16=
2. 2+4+6+….+40=
3. 2+4+6+….+28=
4. 2+4+6+….+48=
5. 2+4+6+….+398=
Sum of Consecutive Odd Integers
1+3+5+…..+19
1. 1+3+5+….+33=
2. 1+3+5+….+49=
3. 1+3+5+….+67=
4. 1+3+5+….+27=
5. 1+3+5+….+47=
Finding Hexagonal Numbers
th
Find the 5
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=
Cube Properties
Find 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
Cube Properties
Find S, Then Use It To Find
Volume or Surface Area
S
3
S
S
2
Finding Slope From An Equation
3X+2Y=10
1. Y = 2X + 8
2. Y = -7X + 6
3. 2Y = 8X - 12
4. 2X + 3Y = 12
5. 10X – 4Y = 13
Hidden Pythagorean Theorem
Find The Distance Between These Points
(6,2)
and
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)
(9,6)
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 diagonal of a heptagon
Finding the total number of factors
24= ________
1. 12=
2. 30=
3. 120=
4. 50=
5. 36=
Estimating a 4-digit square root
7549 = _______
1.
3165
2.
6189
3.
1796
4.
9268
5.
5396
Estimating a 5-digit square root
37485 = _______
1.
31651
2.
61893
3.
17964
4.
92682
5.
53966
C
F
59C = _______F
1. 4500C=______F
2. 410C =_____F
3. 630C =_____F
4. 680C=_____F
5. 860C=_____F
C
F
50F = _______C
1. 650F=
2. 350F=
3. 750F=
4. 800F=
5. 450F=
Finding The Product of the Roots
2
4X
a
+ 5X
+
6
b
c
1. 5x2 + 6x + 2
2. 2x2 + -7x +1
3. 3x2 + 4x -1
4. -3x2 +2x -4
5. -8x2 -6x +1
Finding The Sum of the Roots
2
4X
a
+ 5X
+
6
b
c
1. 5x2 + 6x + 2
2. 2x2 + -7x +1
3. 3x2 + 4x -1
4. -3x2 +2x -4
5. -8x2 -6x +1
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
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
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
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
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
The Sum of Squares
(factor of 2)
2
12
1. 142 + 282
2. 172 + 342
3. 112 + 222
4. 252 + 502
5. 182 + 362
+
2
24 =
The Sum of Squares
(factor of 3)
2
12
1. 142 + 422
2. 172 + 512
3. 112 + 332
4. 252 + 752
5. 182 + 542
+
2
36 =
The Difference of Squares
(Sum x the Difference)
2
32
1. 222 - 322
2. 732 - 272
3. 312 - 192
4. 622 - 422
5. 992 - 982
-
2
30 =
Addition by Rounding
2989 + 456=
1. 2994 + 658
2. 3899 x 310
3. 294 + 498 + 28
4. 6499 + 621
5. 2938 +64
123…x9 + A Constant
(1111…Problem)
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
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
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
Larger or Smaller
55
52
5 13
+
4 11
Two Step Equations
(Christmas Present Problem)
1.
A - 1 = 11
3
2x -1 =8
2. x/3 - 4 =6
3. 5x -12 = 33
4. x/2 + 5 =8
5. x/12 +5 = 3
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
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
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
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…
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,….
Degrees
0
90 =
Radians
_____
Radians
1. 1800=
2. 450=
3. 2700=
4. 1800=
5. 1350=