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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.

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=

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Multiplying Two Numbers in the 90’s 97 x 94

Multiplying Two Numbers Near 100 109 x 106

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

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

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

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

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

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

Multiplying A 2-Digit # By 101 93 x 101

Multiplying A 3-Digit # By 101 934 x 101

Multiplying A 2-Digit # By 1001 87 x 1001

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

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

Fraction Foil (Type 1) 8 ½ x 6 ¼

Fraction Foil (Type 2) 7 ½ x 5 ½

Fraction Foil (Type 3) 7 ¼ x 7 ¾

Adding Reciprocals 7/8 + 8/7 5/6 + 6/5 11/13 + 13/11 7/2 + 2/7 7/10 + 10/7 11/15 +15/11

Percent Missing the Of 36 is 9% of __

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

Multiplying in Bases 4 x 536=___6

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

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

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

Base 2 to Base 8 Of 1110110102 =___8 1100012= _____8 1111002=_____8 421 Method 1100012= _____8 1111002=_____8 1010012=_____8 110112=_____8 10001102=_____8

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

Ft/sec to mph 44 ft/sec __mph

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}=

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

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

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

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

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

Pi To An Odd Power 13=____approximation

Pi To An Even Power 12=____approximation

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

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

Multiplying Two Numbers Near 1000 994 x 998

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

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

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

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=

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=

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=

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=

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

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

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

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

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

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

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

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

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

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

Estimation 999999 Rule 142857 x 26 = 142857 x 38 142857 x 54 142857 x 17 142857 x 31 142857 x 64

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

Estimation of a 3 x 3 Multiplication

Dividing by 11 and finding the remainder 7258 / 11=_____ Remainder 16235 / 11 326510 / 11 6152412 / 11 26543 / 11 123456 / 11

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

122 + 242= The Sum of Squares 142 + 282 172 + 342 112 + 222 252 + 502 (factor of 2) 122 + 242= 142 + 282 172 + 342 112 + 222 252 + 502 182 + 362

122 + 362= The Sum of Squares 142 + 422 172 + 512 112 + 332 252 + 752 (factor of 3) 122 + 362= 142 + 422 172 + 512 112 + 332 252 + 752 182 + 542

The Difference of Squares (Sum x the Difference) 322 - 302= 222 - 322 732 - 272 312 - 192 622 - 422 992 - 982

2989 + 456= Addition by Rounding 2994 + 658 3899 x 310 294 + 498 + 28 6499 + 621 2938 +64

123…x9 + A Constant (1111…Problem) 123 x 9 + 4 1234 x 9 + 5 12345 x 9 + 6 1234 x 9 + 7 123456 x 9 + 6 12 x 9 + 3

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

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

Larger or Smaller 55 52 5 13 4 11 +

Two Step Equations (Christmas Present Problem) 3 - = 11 1 2x -1 =8 x/3 - 4 =6 5x -12 = 33 x/2 + 5 =8 x/12 +5 = 3

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

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

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

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…

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,….

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