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This is a new powerpoint. If you find any errors please let
me know at [email protected]
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=
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=
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=
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=
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
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
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
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,….