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NUMBER SENSE AT A FLIPNUMBER SENSE AT A FLIP

NUMBER SENSE AT A FLIPNUMBER 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 StepThe 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.

2x2 Foil (LIOF)

23 x 1223 x 12Work Backwards

The Rainbow Method

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 4535 x 451.45 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 8545 x 851.45 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 7535 x 751.35 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 8535 x 851.45 x 75=

2.35 x 65=

3.65 x 15=

4.15 x 85=

5.55 x 85=

Squaring Numbers Ending In 5

757522

1.45 x 45=

2.952=

3.652=

4.352=

5.15 x 15=

Multiplying By 12 ½

32 x 12 ½32 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=

Multiplying By 16 2/3

42 x 16 2/342 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=

Multiplying By 33 1/3

24 x 33 1/324 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=

Multiplying By 25

32 x 2532 x 25

(1/4 rule)

1. 24 x 44=

2. 444 x 25=

3. 25 x 88=

4. 25 x 36=

5. 25 x 12=

Multiplying By 50

32 x 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=

Multiplying By 75

32 x 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=

Multiplying By 125

32 x 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=

Multiplying When Tens Digits Are Equal And The Unit Digits Add To 10

32 x 3832 x 381. 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 4767 x 471. 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 9497 x 941. 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 106109 x 1061. 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 405402 x 4051. 405 x 405=

2. 205 x 206=

3. 703 x 706=

4. 603 x 607=

5. 801 x 805=

Multiplying By 3367

18 x 336718 x 3367

10101 Rule

1. 3367 x 33=

2. 3367 x123=

3. 3367 x 66=

4. 3367 x 93=

5. 3367 x 24=

Multiplying A 2-Digit # By 11

92 x 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=

Multiplying A 3-Digit # By 11

192 x 11192 x 11

1221 Pattern

(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=

Multiplying A 3-Digit # By 111

192 x 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=

Multiplying A 2-Digit # By 111

41 x 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 1111=

Multiplying A 2-Digit # By 101

93 x 10193 x 1011. 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 101934 x 1011. 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 100187 x 10011. 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 1352 x 131. 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 10895 x 1081. 105 x 96=

2. 98 x 104=

3. 109 x 97=

4. 98 x 105=

5. 97 x 107=

Fraction Foil (Type 1)

8 ½ x 6 ¼ 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

Fraction Foil (Type 2)

7 ½ x 5 ½ 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

Fraction Foil (Type 3)

7 ¼ x 7 ¾ 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

Adding Reciprocals

7/8 + 8/77/8 + 8/71. 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 __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

424266 =____ =____1010

1. 546=_____10

2. 347=_____7

3. 769=_____9

4. 1245=_____5

5. 2346=_____6

Multiplying in Bases

4 x 534 x 5366=___=___66

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___21/40___decimaldecimal

1. 31/40=

2. 27/40=

3. 51/40=

4. 3/40=

5. 129/40=

Remainder When Dividing By 9

867867//9=___9=___remainderremainder

1. 3251/9=

2. 264/9=

3. 6235/9=

4. 456/9=

5. 6935/9=

Base 8 to Base 2

73273288 =____ =____22

421 Method

1. 3548= _____2

2. 3258=_____2

3. 1568=_____2

4. 3548=_____2

5. 5748=_____2

Base 2 to Base 8 Of

11101101011101101022 =___ =___88

421 Method

1. 1100012= _____8

2. 1111002=_____8

3. 1010012=_____8

4. 110112=_____8

5. 10001102=_____8

Cubic Feet to Cubic Yards

33ftft xx 6 6ftft x x 1212ftft=__yds=__yds33

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=

Ft/sec to mph

44 44 ft/sec ft/sec ____mphmph

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}{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}=

Repeating Decimals to Fractions

.18=___.18=___fractionfraction

______

1. .25

2. .123

3. .74

4. .031

5. .8

Repeating Decimals to Fractions

.18=___.18=___fractionfraction

__

1. .16

2. .583

3. .123

4. .55

5. .92

Gallons Cubic Inches

2 gallons=__in2 gallons=__in33

1. 3 gallons =_____in3

2. ½ gallon =______in3

3. 77 in3=_______gallons

4. 33 in3=_______gallons

5. 1/5 gallon=______in

Finding Pentagonal Numbers

55thth Pentagonal Pentagonal # =# =____1. 3rd pentagonal number=

2. 6th pentagonal number=

3. 10th pentagonal number=

4. 4th pentagonal number=

5. 6th pentagonal number=

Finding Triangular Numbers

66thth Triangular 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

1313=____=____approximationapproximation

1. Pi11

2. Pi7

3. Pi9

4. Pi5

5. Pi3

Pi To An Even Power

1212=____=____approximationapproximation

1. Pi10

2. Pi8

3. Pi6

4. Pi14

5. Pi16

The More Problem

17/15 x 1717/15 x 171. 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 1515/17 x 151. 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 998994 x 9981. 998 x 993=

2. 993 x 991=

3. 994 x 996=

4. 997 x 995=

5. 992 x 996=

The (Reciprocal) Work Problem

1/6 + 1/5 = 1/X1/6 + 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

The (Reciprocal) Work Problem

1/6 - 1/8 = 1/X1/6 - 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

The Inverse Variation % Problem

30% of 12 = 20% of ___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+…..+201+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+…..+202+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+…..+191+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

Find the 5Find the 5thth Hexagonal NumberHexagonal 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 Find the Surface Area of a Cube Given the Space Diagonal of 12Given 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

2

S

3S

S

Find S, Then Use It To Find Find S, Then Use It To Find Volume or Surface AreaVolume or Surface Area

Finding Slope From An Equation

3X+2Y=103X+2Y=101. 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 PointsFind The Distance Between These Points

(6,2) (6,2) andand (9,6) (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)

Finding Diagonals

Find The Number Of Find The Number Of Diagonals In An OctagonDiagonals 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= ________24= ________

1. 12=

2. 30=

3. 120=

4. 50=

5. 36=

Estimating a 4-digit square root 7549 = _______7549 = _______

3165

6189

1796

9268

5396

1.

2.

3.

4.

5.

Estimating a 5-digit square root 37437485 = _______85 = _______

31651

61893

17964

92682

53966

1.

2.

3.

4.

5.

C F 59C = _______F59C = _______F1. 4500C=______F

2. 410C =_____F

3. 630C =_____F

4. 680C=_____F

5. 860C=_____F

C F 50F = _______C50F = _______C1. 650F=

2. 350F=

3. 750F=

4. 800F=

5. 450F=

Finding The Product of the Roots 4X4X22 + 5X + 6 + 5X + 6a 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 4X4X22 + 5X + 6 + 5X + 6a b c

1. 5x2 + 6x + 2

2. 2x2 + -7x +1

3. 3x2 + 4x -1

4. -3x2 +2x -4

5. -8x2 -6x +1

Estimation 142857 x 26 = 142857 x 26 = 999999 Rule

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 Find the area of a square with a diagonal of 12 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 = 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=_____7258 / 11=_____ RemainderRemainder

1. 16235 / 11

2. 326510 / 11

3. 6152412 / 11

4. 26543 / 11

5. 123456 / 11

Multiply By Rounding 2994 x 6 = 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 121222 + 24 + 2422= = (factor of 2)

1. 142 + 282

2. 172 + 342

3. 112 + 222

4. 252 + 502

5. 182 + 362

The Sum of Squares 121222 + 36 + 3622= = (factor of 3)

1. 142 + 422

2. 172 + 512

3. 112 + 332

4. 252 + 752

5. 182 + 542

The Difference of Squares 323222 - 30 - 3022= = (Sum x the Difference)

1. 222 - 322

2. 732 - 272

3. 312 - 192

4. 622 - 422

5. 992 - 982

Addition by Rounding 2989 + 456= 2989 + 456= 1. 2994 + 658

2. 3899 x 310

3. 294 + 498 + 28

4. 6499 + 621

5. 2938 +64

123…x9 + A Constant 123 x 9 + 4 123 x 9 + 4 (1111…Problem)

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 Find The Difference Of The Supplement And The Supplement And The

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

Complement Of An Angle Of 40. 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 13134 114 11++

55 52

Two Step Equations(Christmas Present Problem) AA33

-- = 11= 11111. 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 How Many #s less than 20 are relatively prime to 20?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 Find the Product of the GCF and the LCM of 6 and 15and 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 1915 x 17 x 191. 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, 147, 2, 5, 8, 3, 14Find the next number in this patternFind 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, 231, 4, 5, 9, 14, 23Find the next number in this patternFind 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 Radians

909000= _____= _____RadiansRadians

1. 1800=

2. 450=

3. 2700=

4. 1800=

5. 1350=