Number Sense Book

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 1 2 = 1 to 40 2 = 1600 and the PERFECT CUBES from 1 3 = 1 to 25 3 = 15625. These squares and cubes should be learned in both directions. ie. 17 2 = 289 and the 289 is 17.

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

Squaring Numbers Ending In 5 75 2 ,[object Object],[object Object],[object Object],[object Object]

Consecutive Decades 35 x 45 ,[object Object],[object Object],[object Object],[object Object]

Ending in 5…Ten’s Digits Both Even 45 x 85 ,[object Object],[object Object],[object Object],[object Object]

Ending in 5…Ten’s Digits Both Odd 35 x 75 ,[object Object],[object Object],[object Object],[object Object]

Ending in 5…Ten’s Digits Odd&Even 35 x 85 ,[object Object],[object Object],[object Object],[object Object]

Multiplying By 12 ½ 32 x 12 ½ ,[object Object],[object Object],[object Object],8 = 4+00 = 4 00 (1/8 rule) 32

Multiplying By 16 2/3 42 x 16 2/3 ,[object Object],[object Object],[object Object],6 = 7+00 = 7 00 (1/6 rule) 42

Multiplying By 33 1/3 24 x 33 1/3 24 3 = 8+00 = 8 00 (1/3 rule) ,[object Object],[object Object],[object Object]

Multiplying By 25 32 x 25 ,[object Object],[object Object],4 = 8 +00 = 8 00 (1/4 rule) 32

Multiplying By 50 32 x 50 ,[object Object],[object Object],[object Object],2 = 16 +00 = 16 00 (1/2 rule) 32

Multiplying By 75 32 x 75 ,[object Object],[object Object],[object Object],4 = 8x3=24+00 = 24 00 (3/4 rule) 32

Multiplying By 125 32 x 125 ,[object Object],[object Object],[object Object],8 = 4+000 = 4 000 (1/8 rule)

Multiplying When Tens Digits Are Equal And The Unit Digits Add To 10 32 x 38 ,[object Object],[object Object],3(3+1) = 12 16 2(8)

Multiplying When Tens Digits Add To 10 And The Units Digits Are Equal 67 x 47 ,[object Object],[object Object],6(4)+7 = 31 49 7(7)

Multiplying Two Numbers in the 90’s 97 x 94 ,[object Object],[object Object],[object Object],100-(3+6) = 91 18 3(6)

Multiplying Two Numbers Near 100 109 x 106 ,[object Object],[object Object],[object Object],1 = 1 15 54 9+6 9(6)

Multiplying Two Numbers With 1 st Numbers = And A 0 In The Middle 402 x 405 ,[object Object],[object Object],[object Object],4(4) = 16 28 10 4(2+5) 2(5)

Multiplying By 3367 18 x 3367 ,[object Object],[object Object],18/3 = 6 x 10101= = 60606 10101 Rule

Multiplying A 2-Digit # By 11 92 x 11 ,[object Object],[object Object],[object Object],9+ 1 = 10 1 2 9+2 2 121 Pattern (ALWAYS WORK FROM RIGHT TO LEFT)

Multiplying A 3-Digit # By 11 192 x 11 ,[object Object],[object Object],[object Object],[object Object],1+9+ 1 = 2 1 1 2 9+2 2 1221 Pattern (ALWAYS WORK FROM RIGHT TO LEFT) 1+ 1

Multiplying A 3-Digit # By 111 192 x 111 ,[object Object],[object Object],[object Object],[object Object],[object Object],1+9+ 1 = 2 1 3 1 2 9+2 2 12321 Pattern (ALWAYS WORK FROM RIGHT TO LEFT) 1+ 1 1+9+2+ 1

Multiplying A 2-Digit # By 111 41 x 111 ,[object Object],[object Object],[object Object],[object Object],4 = 4 5 5 1 4+1 1 1221 Pattern (ALWAYS WORK FROM RIGHT TO LEFT) 4+1

Multiplying A 2-Digit # By 101 93 x 101 ,[object Object],[object Object],= 93 93 93(1) 93(1)

Multiplying A 3-Digit # By 101 934 x 101 ,[object Object],[object Object],= 943 34 934+9 34

Multiplying A 2-Digit # By 1001 87 x 1001 ,[object Object],[object Object],[object Object],= 87 0 87 87(1) 0 87(1)

Halving And Doubling 52 x 13 ,[object Object],[object Object],[object Object],= 26(26)= 676 52/2 13(2)

One Number in the Hundreds And One Number In The 90’s 95 x 108 ,[object Object],[object Object],[object Object],= 102 60 108-(5+1) 100-(5x8)

Fraction Foil (Type 1) 8 ½ x 6 ¼ ,[object Object],[object Object],[object Object],[object Object],= 53 1/8 (8)(6)+1/2(6)+1/4(8) (1/2x1/4)

Fraction Foil (Type 2) 7 ½ x 5 ½ ,[object Object],[object Object],[object Object],= 41 1/4 (7x5)+6 (1/2x1/2)

Fraction Foil (Type 3) 7 ¼ x 7 ¾ ,[object Object],[object Object],= 56 3/16 (7)(7+1) (1/4x3/4)

Adding Reciprocals 7/8 + 8/7 ,[object Object],[object Object],[object Object],2 = 2 1/56 (8-7) 2 7x8

Percent Missing the Of 36 is 9% of __ ,[object Object],[object Object],36/9 = 400 00

Base N to Base 10 42 6 =____ 10 ,[object Object],[object Object],4(6)+2 = 26 10

Multiplying in Bases 4 x 53 6 =___ 6 ,[object Object],[object Object],[object Object],= 340 6 = 4x3=12 subtract 12 Write 0 = 4x5=20+2=22 subtract 18 Write 4 = Write 3

N/40 to a % or Decimal 21/40___ decimal ,[object Object],[object Object],[object Object],[object Object],5 25 . 21/4 1/4

Remainder When Dividing By 9 867 / 9=___ remainder ,[object Object],[object Object],8+6+7=21=2+1=3 = 3

Base 8 to Base 2 732 8 =____ 2 ,[object Object],[object Object],[object Object],7 421 Method 3 2 421 421 421 111 011 010

Base 2 to Base 8 Of 111011010 2 =___ 8 ,[object Object],[object Object],[object Object],7 421 Method 3 2 421 421 421 111 011 010

Cubic Feet to Cubic Yards 3 ft x 6 ft x 12 ft =__yds 3 ,[object Object],[object Object],[object Object],3 12 6 3 3 3 1 x 2 x 4 = 8 Cubic yards

Cubic Feet to Cubic Yards 44 ft/sec __ mph ,[object Object],[object Object],[object Object],22x2=44 15x2=30 mph Cubic yards

Subset Problems {F,R,O,N,T} =______ ,[object Object],[object Object],[object Object],[object Object],SUBSETS 2 5 =32 subsets

Repeating Decimals to Fractions .18=___ fraction ,[object Object],[object Object],[object Object],18 99 = 2 11 ___

Repeating Decimals to Fractions .18=___ fraction ,[object Object],[object Object],18-1 90 = 17 90 _

Gallons Cubic Inches 2 gallons=__in 3 ,[object Object],[object Object],2(231)= 462 in 3 (Factors of 231 are 3, 7, 11)

Finding Pentagonal Numbers 5 th Pentagonal # = __ ,[object Object],[object Object],25+10=35 5 5 25 1+2+3+4= 10

Finding Triangular Numbers 6 th Triangular # = __ ,[object Object],[object Object],[object Object],6(6+1)=42 42/2=21

Pi To An Odd Power 13 =____ approximation ,[object Object],[object Object],3000000

Pi To An Even Power 12 =____ approximation ,[object Object],[object Object],950000

The “More” Problem 17/15 x 17 ,[object Object],[object Object],[object Object],[object Object],= 19 4/15 (17-15) 2 15 17+2

The “Less” Problem 15/17 x 15 ,[object Object],[object Object],[object Object],[object Object],= 13 4/15 (17-15) 2 17 15-2

Multiplying Two Numbers Near 1000 994 x 998 ,[object Object],[object Object],[object Object],1000-(6+2) = 992 012 6(2)

The (Reciprocal) Work Problem 1/6 + 1/5 = 1/X ,[object Object],[object Object],[object Object],[object Object],= 30/11 = 6(5) =6+5 Two Things Helping

The (Reciprocal) Work Problem 1/6 - 1/8 = 1/X ,[object Object],[object Object],[object Object],[object Object],= 24 = 6(8) =8-6 Two Things working Against Each Other

The Inverse Variation % Problem 30% of 12 = 20% of ___ ,[object Object],[object Object],[object Object],30/20=3/2 = 18 3/2(12)=18

Sum of Consecutive Integers 1+2+3+…..+20 ,[object Object],[object Object],[object Object],10(21)= 210 (20)(21)/2

Sum of Consecutive Even Integers 2+4+6+…..+20 ,[object Object],[object Object],[object Object],5(22)= 110 (20)(22)/4

Sum of Consecutive Odd Integers 1+3+5+…..+19 ,[object Object],[object Object],[object Object],[object Object],10 2 = 100 (19+1)/2=

Finding Hexagonal Numbers Find the 5 th Hexagonal Number ,[object Object],[object Object],[object Object],50-5= 2(5) 2 = 50 45

Cube Properties Find the Surface Area of a Cube Given the Space Diagonal of 12 ,[object Object],[object Object],[object Object],2(144)= 2(12)(12) 288

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

Finding Slope From An Equation 3X+2Y=10 ,[object Object],[object Object],3X+2Y=10 Slope = -3/2 Y = - 3 X +5 2

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

Finding Diagonals Find The Number Of Diagonals In An Octagon ,[object Object],[object Object],8(8-3)/2= 20

Finding the total number of factors 24= ________ ,[object Object],[object Object],[object Object],3 1 x 2 3 = 1+1=2 3+1=4 2x4=8

Estimating a 4-digit square root 80 2 =6400 7549 = _______ ,[object Object],[object Object],[object Object],[object Object],90 2 =8100 85 2 =7225 87

Estimating a 5-digit square root 19 2 =361 374 85 = _______ ,[object Object],[object Object],[object Object],[object Object],20 2 =400 195 190-200

C F 9/5(55) + 32 55C = _______F ,[object Object],[object Object],[object Object],= 131 99+32

C F 5/9(50-32) 50F = _______C ,[object Object],[object Object],[object Object],= 10 5/9(18)

Finding The Product of the Roots 6 / 4 = 3/2 4X 2 + 5X + 6 ,[object Object],[object Object],[object Object],a b c

Finding The Sum of the Roots -5 / 4 4X 2 + 5X + 6 ,[object Object],[object Object],[object Object],a b c

Estimation 26/7 = 3 r5 142857 x 26 = ,[object Object],[object Object],[object Object],[object Object],999999 Rule 5+0=50/7=7 3 714282

Area of a Square Given the Diagonal ½ D 1 D 2 Find the area of a square with a diagonal of 12 ,[object Object],[object Object],[object Object],[object Object],72 ½ x 12 x 12

Estimation of a 3 x 3 Multiplication 35 x 30 346 x 291 = ,[object Object],[object Object],[object Object],[object Object],105000 1050 + 00

Dividing by 11 and finding the remainder 7258 / 11=_____ ,[object Object],[object Object],[object Object],[object Object],10-12= -2 +11= 9 8+2=10 7+5= 12 Remainder

Multiply By Rounding 2994 x 6 = ,[object Object],[object Object],[object Object],6(6)=36 100-36=64 3000(6)=179_ _ =17964

The Sum of Squares 12 2 + 24 2 = ,[object Object],[object Object],[object Object],144x10/2= 12 2 =144 =720 (factor of 2)

The Sum of Squares 12 2 + 36 2 = ,[object Object],[object Object],144x10= 12 2 =144 =1440 (factor of 3)

The Difference of Squares 32 2 - 30 2 = ,[object Object],[object Object],[object Object],32+30=62 32-30=2 (Sum x the Difference) 62 x 2 =124

Addition by Rounding 2989 + 456= ,[object Object],[object Object],[object Object],2989+11= 3000 456-11=445 (Sum x the Difference) 3000+445=3445

123…x9 + A Constant 123 x 9 + 4 ,[object Object],[object Object],3x9 + 4 =3 1 1111 (1111…Problem)

Supplement and Complement ,[object Object],=90 Find The Difference Of The Supplement And The Complement Of An Angle Of 40.

Supplement and Complement ,[object Object],[object Object],[object Object],270-80= Find The Sum Of The Supplement And The Complement Of An Angle Of 40. =190

Larger or Smaller ,[object Object],[object Object],[object Object],Larger = 5/4 55 52 Smaller = 13/11 5 13 4 11 +

Two Step Equations (Christmas Present Problem) ,[object Object],11+1=12 12 x3 = 36 A 3 - = 11 1

Relatively Prime (No common Factors Problem) * One is relatively prime to all numbers ,[object Object],[object Object],[object Object],[object Object],How Many #s less than 20 are relatively prime to 20? 2 x 1 x 1 x 4 = 8 2 2 x 5 1 =2 1 x 5 0 =2 x 1

Product of LCM and GCF ,[object Object],Find the Product of the GCF and the LCM of 6 and 15 6 x 15 = 90

Estimation ,[object Object],15 x 17 x 19 17 3 =4913

Subtracting Reverses ,[object Object],[object Object],[object Object],[object Object],64 - 46 ,[object Object],[object Object],[object Object]

Subtracting Reverses 2 ,[object Object],[object Object],[object Object],[object Object],634 - 436 ,[object Object],[object Object],[object Object]

Subtracting Reverses 3 ,[object Object],[object Object],[object Object],[object Object],2821 - 1282 ,[object Object],[object Object],[object Object]

Sequences-Finding the Pattern ,[object Object],7, 2, 5, 8, 3, 14 7 , 2, 5 , 8, 3 , 14 Find the next number in this pattern 1

Sequences-Finding the Pattern ,[object Object],1, 4, 5, 9, 14, 23 1, 4, 5, 9, 14, 23 Find the next number in this pattern 14+23=37

Degrees Radians ,[object Object],[object Object],90 0 = _____ 90(Pi)/180 Radians =Pi/2

Number Sense Book

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Number Sense Book