This is a new powerpoint. If you find any errors please let me know at kenneth.lee2@fortbend.k12.tx.us. NUMBER SENSE AT A FLIP. NUMBER SENSE AT A FLIP. Number Sense.
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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 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 me know at
Work Backwards
2x2 Foil (LIOF)23 x 12Used when you forget a rule about 2x2 multiplication
The last number is the units digit of the product of the unit’s digits
Multiply the outside, multiply the inside
Add the outside and the inside together plus any carry and write down the units digit
Multiply the first digits together and add and carry. Write down the number
2(1)
2(2)+3(1)
3(2)
2
7
6
276
First two digits = the ten’s digit times one more than the ten’s digit.
Last two digits are always 25
7(7+1)25
=5625
First two digits = the small ten’s digit times one more than the large ten’s digit.
Last two digits are always 75
3(4+1)75
=1575
First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digits.
Last two digits are always 25
4(8) + ½ (4+8)25
=3825
First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digits.
Last two digits are always 25
3(7) + ½ (3+7)25
=2625
First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digits. Always drop the remainder.
Last two digits are always 75
3(8) + ½ (3+8)75
=2975
(1/8 rule) me know at
Multiplying By 12 ½ 32 x 12 ½32
Divide the non12 ½ number by 8.
Add two zeroes.
4+00
=
8
=400
(1/6 rule) me know at
Multiplying By 16 2/3 42 x 16 2/342
Divide the non16 2/3 number by 6.
Add two zeroes.
7+00
=
6
=700
(1/3 rule) me know at
Multiplying By 33 1/3 24 x 33 1/324
8+00
=
3
=800
(1/4 rule) me know at
Multiplying By 2532 x 2532
Divide the non25 number by 4.
Add two zeroes.
8
+00
=
4
=800
(1/2 rule) me know at
Multiplying By 5032 x 5032
Divide the non50 number by 2.
Add two zeroes.
16
=
+00
2
=1600
(3/4 rule) me know at
Multiplying By 7532 x 75Divide the non75 number by 4.
Multiply by 3.
Add two zeroes.
32
=
8x3=24+00
4
=2400
(1/8 rule) me know at
Multiplying By 12532 x 125Divide the non125 number by 8.
Add three zeroes.
32
4+000
=
8
=4000
First two digits are the tens digit times one more than the tens digit
Last two digits are the product of the units digits.
3(3+1)
2(8)
=1216
First two digits are the product of the tens digit plus the units digit
Last two digits are the product of the units digits.
6(4)+7
7(7)
=3149
Find out how far each number is from 100
The 1st two numbers equal the sum of the differences subtracted from 100
The last two numbers equal the product of the differences
100(3+6)
3(6)
=9118
First Number is always 1
The middle two numbers = the sum on the units digits
The last two digits = the product of the units digits
1
9+6
9(6)
= 11554
The 1st two numbers = the product of the hundreds digits
The middle two numbers = the sum of the units x the hundreds digit
The last two digits = the product of the units digits
4(4)
4(2+5)
2(5)
= 162810
10101 Rule Digits Are Equal
Multiplying By 336718 x 3367Divide the non3367 # by 3
Multiply by 10101
18/3 = 6 x 10101=
= 60606
121 Pattern Digits Are Equal
Multiplying A 2Digit # By 1192 x 11(ALWAYS WORK FROM RIGHT TO LEFT)
Last digit is the units digit
The middle digit is the sum of the tens and the units digits
The first digit is the tens digit + any carry
9+1
9+2
2
= 1012
1221 Pattern Digits Are Equal
Multiplying A 3Digit # By 11192 x 11(ALWAYS WORK FROM RIGHT TO LEFT)
Last digit is the units digit
The next digit is the sum of the tens and the units digits
The next digit is the sum of the tens and the hundreds digit + carry
The first digit is the hundreds digit + any carry
1+1
1+9+1
9+2
2
=2112
12321 Pattern Digits Are Equal
Multiplying A 3Digit # By 111192 x 111(ALWAYS WORK FROM RIGHT TO LEFT)
Last digit is the units digit
The next digit is the sum of the tens and the units digits
The next digit is the sum of the units, tens and the hundreds digit + carry
The next digit is the sum of the tens and hundreds digits + carry
The next digit is the hundreds digit + carry
1+1
1+9+1
1+9+2+1
9+2
2
= 21312
1221 Pattern Digits Are Equal
Multiplying A 2Digit # By 11141 x 111(ALWAYS WORK FROM RIGHT TO LEFT)
Last digit is the units digit
The next digit is the sum of the tens and the units digits
The next digit is the sum of the tens and the units digits + carry
The next digit is the tens digit + carry
4
4+1
4+1
1
= 4551
The first two digits are the 2digit number x1
The last two digits are the 2digit number x1
93(1)
93(1)
= 9393
The last two digits are the last two digits of the 3digit number
The first three numbers are the 3digit number plus the hundreds digit
934+9
34
= 94334
The first 2 digits are the 2digit number x 1
The middle digit is always 0
The last two digits are the 2digit number x 1
87(1)
0
87(1)
= 87087
Take half of one number
Double the other number
Multiply together
52/2
13(2)
= 26(26)= 676
Find how far each number is from 100
The last two numbers are the product of the differences subtracted from 100
The first numbers = the small number difference from 100 increased by 1 and subtracted from the larger number
108(5+1)
100(5x8)
= 10260
Multiply the fractions together
Multiply the outside two number
Multiply the inside two numbers
Add the results and then add to the product of the whole numbers
(8)(6)+1/2(6)+1/4(8)
(1/2x1/4)
= 531/8
Multiply the fractions together
Add the whole numbers and divide by the denominator
Multiply the whole numbers and add to previous step
(7x5)+6
(1/2x1/2)
= 411/4
Multiply the fractions together
Multiply the whole number by one more than the whole number
(7)(7+1)
(1/4x3/4)
= 563/16
(87) Digits Are Equal2
2
7x8
=21/56
Adding Reciprocals7/8 + 8/7Keep the denominator
The numerator is the difference of the two numbers squared
The whole number is always two plus any carry from the fraction.
Divide the first number by the percent number
Add 2 zeros or move the decimal two places to the right
36/9
00
= 400
Multiply the left digit times the base
Add the number in the units column
4(6)+2
= 2610
Multiply the units digit by the multiplier
If number cannot be written in base n subtract base n until the digit can be written
Continue until you have the answer
= 4x3=12subtract 12Write 0
= 4x5=20+2=22subtract 18Write 4
= Write 3
= 3406
Mentally take off the zero
Divide the numerator by the denominator and write down the digit
Put the remainder over the 4 and write the decimal without the decimal point
Put the decimal point in front of the numbers
.
5
25
21/4
1/4
Add the digits until you get a single digit
Write the remainder
8+6+7=21=2+1=3
= 3
421 Method Digits Are Equal
Base 8 to Base 27328 =____2Mentally put 421 over each number
Figure out how each base number can be written with a 4, 2 and 1
Write the three digit number down
421
421
421
7
3
2
111
011
010
421 Method Digits Are Equal
Base 2 to Base 8 Of1110110102 =___8Separate the number into groups of 3 from the right.
Mentally put 421 over each group
Add the digits together and write the sum
421
421
421
011
010
111
7
3
2
Try to eliminate three 3s by division
Multiply out the remaining numbers
Place them over any remaining 3s
3
6
12
3
3
3
1 x 2 x 4 = 8
Cubic yards
Use 15 mph = 22 ft/sec
Find the correct multiple
Multiply the other number
22x2=44
15x2=30 mph
2 Digits Are Equal5=32
subsets
Subset Problems{F,R,O,N,T}=______SUBSETS
Subsets=2n
Improper subsets always = 1
Proper subsets = 2n  1
Power sets = subsets
___ Digits Are Equal
Repeating Decimals to Fractions.18=___fractionThe numerator is the number
Read the number backwards. If a number has a line over it then there is a 9 in the denominator
Write the fraction and reduce
18
2
=
99
11
_ Digits Are Equal
Repeating Decimals to Fractions.18=___fractionThe numerator is the number minus the part that does not repeat
For the denominator read the number backwards. If it has a line over it, it is a 9. if not it is a o.
181
17
=
90
90
(Factors of 231 are 3, 7, 11)
Use the fact: 1 gal= 231 in3
Find the multiple or the factor and adjust the other number. (This is a direct variation)
2(231)= 462 in3
Use the house method)
Find the square #, find the triangular #, then add them together
1+2+3+4= 10
25+10=35
25
5
5
Use the n(n+1)/2 method
Take the number of the term that you are looking for and multiply it by one more than that term.
Divide by 2 (Divide before multiplying)
6(6+1)=42
42/2=21
Pi to the 1st = 3 (approx) Write a 3
Add a zero for each odd power of Pi after the first
3000000
Pi to the 4th = 95 (approx) Write a 95
Add a zero for each even power of Pi after the 4th
950000
The answer has to be more than the whole number.
The denominator remains the same.
The numerator is the difference in the two numbers squared.
The whole number is the original whole number plus the difference
(1715)2
17+2
15
=194/15
The answer has to be less than the whole number.
The denominator remains the same.
The numerator is the difference in the two numbers squared.
The whole number is the original whole number minus the difference
(1715)2
152
17
=134/17
Find out how far each number is from 1000
The 1st two numbers equal the sum of the differences subtracted from 1000
The last two numbers equal the product of the differences written as a 3digit number
1000(6+2)
6(2)
=992012
Two Things Helping Digits Are Equal
The (Reciprocal) Work Problem1/6 + 1/5 = 1/X=6(5)
Use the formula ab/a+b.
The numerator is the product of the two numbers.
The deniminator is the sum of the two numbers.
Reduce if necessary
=6+5
=30/11
Two Things working Against Each Other Digits Are Equal
The (Reciprocal) Work Problem1/6  1/8 = 1/XUse the formula ab/ba.
The numerator is the product of the two numbers.
The denominator is the difference of the two numbers from right to left.
Reduce if necessary
=6(8)
=86
=24
30/20=3/2 Digits Are Equal
3/2(12)=18
=18
The Inverse Variation % Problem30% of 12 = 20% of ___Compare the similar terms as a reduced ratio
Multiple the other term by the reduced ratio.
Write the answer
(20)(21)/2
Use formula n(n+1)/2
Divide even number by 2
Multiply by the other number
10(21)= 210
(20)(22)/4
Use formula n(n+2)/4
Divide the multiple of 4 by 4
Multiply by the other number
5(22)= 110
Use formula ((n+1)/2)2
Add the last number and the first number
Divide by 2
Square the result
(19+1)/2=
102 = 100
Use formula 2n2n
Square the number and multiply by2
Subtract the number wanted from the previous answer
2(5)2= 50
505=
45
Use formula Area = 2D2
Square the diagonal
Multiply the product by 2
2(12)(12)
2(144)=
288
Y =  Digits Are Equal3X +5
2
Finding Slope From An Equation3X+2Y=103X+2Y=10
Solve the equation for Y
The number in fron of X is the Slope
Slope = 3/2
Find the distance between the X’s
Find the distance between the Y’s
Look for a Pythagorean triple
If not there, use the Pythagorean Theorem
96=3
62=4
3 4 5
5 12 13
3
4
5
7 24 25
8 15 17
The distance is 5
Common Pythagorean triples
Use the formula n(n3)/2
N is the number of vertices in the polygon
8(83)/2=
20
Put the number into prime factorization
Add 1 to each exponent
Multiply the numbers together
31 x 23=
1+1=2 3+1=4
2x4=8
7549 = _______ Digits Are Equal
Estimating a 4digit square root802=6400
852=7225
87
902=8100
374 Digits Are Equal85 = _______
Estimating a 5digit square root192=361
190200
195
202=400
55C = _______F Digits Are Equal
C F9/5(55) + 32
99+32
= 131
50F = _______C Digits Are Equal
C F5/9(5032)
5/9(18)
= 10
4X Digits Are Equal2 + 5X + 6
a
b
c
Finding The Product of the Roots6 / 4 = 3/2
4X Digits Are Equal2 + 5X + 6
a
b
c
Finding The Sum of the Roots5 / 4
999999 Rule Digits Are Equal
142857 x 26 =
Estimation26/7 =3r5
5+0=50/7=7
3 714285
Find the area of a square with a diagonal of 12 Digits Are Equal
Area of a Square Given the Diagonal½ D1 D2
½ x 12 x 12
72
346 x 291 = Digits Are Equal
Estimation of a 3 x 3 Multiplication35 x 30
1050 + 00
105000
7258 / 11=_____ Digits Are Equal
Dividing by 11 and finding the remainderRemainder
8+2=10 7+5= 12
1012= 2 +11= 9
2994 x 6 = Digits Are Equal
Multiply By Rounding3000(6)=179_ _
6(6)=36 10036=64
=17964
(factor of 2) Digits Are Equal
122 + 242=
The Sum of Squares122=144
144x10=
=1440/2
=720
(factor of 3) Digits Are Equal
122 + 362=
The Sum of Squares122=144
144x10=
=1440
(Sum x the Difference) Digits Are Equal
322  302=
The Difference of Squares32+30=62
3230=2
62 x 2 =124
(Sum x the Difference) Digits Are Equal
2989 + 456=
Addition by Rounding2989+11= 3000
45611=445
3000+445=3445
(1111…Problem) Digits Are Equal
123 x 9 + 4
123…x9 + A Constant3x9 + 4 =31
1111
Find The Difference Of The Supplement And The Complement Of An Angle Of 40.
Supplement and Complement=90
Find The Sum Of The Supplement And The Complement Of An Angle Of 40.
Supplement and Complement27080=
=190
5 Angle Of 40. 13
+
4 11
55
52
Larger or SmallerLarger = 5/4
Smaller = 13/11
A Angle Of 40.

1
= 11
3
Two Step Equations(Christmas Present Problem)11+1=12
12 x3 = 36
2 Angle Of 40. 2 x 51
=21 x 50
=2 x 1
How Many #s less than 20 are relatively prime to 20?
Relatively Prime(No common Factors Problem)* One is relatively prime to all numbers2 x 1 x 1 x 4 = 8
Find the Product of the GCF and the LCM of 6 and 15 Angle Of 40.
Product of LCM and GCF6 x 15 = 90
7, 2, 5, 8, 3, 14 Angle Of 40.
SequencesFinding the PatternFind the next number in this pattern
7, 2, 5, 8, 3, 14
1
1, 4, 5, 9, 14, 23 Angle Of 40.
SequencesFinding the PatternFind the next number in this pattern
1, 4, 5, 9, 14, 23
14+23=37
90 Angle Of 40. 0= _____
Degrees RadiansRadians
90(Pi)/180
=Pi/2