Transcript Consecutive Decades 35 x 45

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.
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Copyright 2009: D.T. Simmons
The First Step
The first step in learning number sense should be to memorize
PERFECT SQUARES from 12 = 1 to 402 = 1600
PERFECT CUBES from 13 = 1 to 253 = 15625
These squares and cubes should be learned in both directions. ie.
172 = 289 and the
RAIDERMATH
Copyright 2009: D.T. Simmons
2 x 2 Foil (LIOF)
Working Backwards
 The last number is the units digit of
the product of the unit’s digits
 Multiply the outside, multiply the
23  12  276
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
RAIDERMATH
Copyright 2009: D.T. Simmons
2(1)  2
2(2)  3(1)  7
3(2)  6
 276
Squaring Numbers
Ending In 5
 First two digits = the ten’s digit
times one more than the ten’s
digit.
75  5625
 Last two digits are always 25
2
7  7  1  56
5  5  25
 5625
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Copyright 2009: D.T. Simmons
Ending In 5
Consecutive Decades
 First two digits = the small ten’s
digit times one more than the large
ten’s digit.
35  45  1575
 Last two digits are always 75
3  4  1  15
 75
 1575
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Copyright 2009: D.T. Simmons
Ending In 5
Ten’s Digits Both Even
 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
45  85  3825
4 8 
48
 38
2
5  5  25
 3825
RAIDERMATH
Copyright 2009: D.T. Simmons
Ten’s Digits Both Odd – Ending In 5
 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
35  75  2625
37
37 
 26
2
5  5  25
 2625
RAIDERMATH
Copyright 2009: D.T. Simmons
Ending in 5
Ten’s Digits Odd & Even
 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
35  85  2925
3 8 
38
 29
2
 75
 2975
RAIDERMATH
Copyright 2009: D.T. Simmons
Multiplying By 12 ½
(1/8 Rule)
 Divide the non-12 ½ number by 8.
 Add two zeroes.
1
32  12  400
2
32
4
8
 00
 400
RAIDERMATH
Copyright 2009: D.T. Simmons
Multiplying By 16 2/3
(1/6 Rule)
 Divide the non-16 2/3 number by
6.
 Add two zeroes.
2
42  16  700
3
42
7
6
 00
 700
RAIDERMATH
Copyright 2009: D.T. Simmons
Multiplying By 33 1/3
(1/3 Rule)
 Divide the non-33 1/3 number by
3.
 Add two zeroes.
1
24  33  800
3
24
8
3
 00
 800
RAIDERMATH
Copyright 2009: D.T. Simmons
Multiplying By 25
(1/4 Rule)
 Divide the non-25 number by 4.
 Add two zeroes.
32  25  800
32
8
4
00
8 00  800
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Copyright 2009: D.T. Simmons
Multiplying By 50
(1/2 Rule)
 Divide the non-50 number by 2.
 Add two zeroes.
32  50  1,600
32
 16
2
 00
 1600
RAIDERMATH
Copyright 2009: D.T. Simmons
Multiplying By 75
3/4 Rule
 Divide the non-75 number by 4.
 Multiply by 3.
 Add two zeroes.
32  75  2,400
32 3
  24
4 1
 00
 2400
RAIDERMATH
Copyright 2009: D.T. Simmons
Multiplying By 125
1/8 Rule
 Divide the non-125 number by 8.
 Add three zeroes.
32  125  4,000
32 3
 4
8 1
 000
 4000
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Copyright 2009: D.T. Simmons
Multiplying When Tens Digits Are Equal & The
Unit Digits Add To 10
 First two digits are the tens digit
times one more than the tens digit
 Last two digits are the product of
32  38  1,216
the units digits.
3(3  1)  12
2(8)  16
 1216
RAIDERMATH
Copyright 2009: D.T. Simmons
Multiplying When Tens Digits Add To 10
& The Units Digits Are Equal
 First two digits are the product of
the tens digit plus the units digit
 Last two digits are the product of
67  47  3,149
6(4)  7  31
7(7)  49
31 49  3149
the units digits.
RAIDERMATH
Copyright 2009: D.T. Simmons
Multiplying Two Numbers in the 90’s
 Find out how far each number is
from 100
 The 1st two numbers equal the
97  94  9,118
sum of the differences subtracted
from 100
 The last two numbers equal the
product of the differences
100  97  3
100  94  6
100  (3  6)  91
3(6)  18
 9118
RAIDERMATH
Copyright 2009: D.T. Simmons
Multiplying Two Numbers Near 100
 First Number is always 1
 The middle two numbers = the
sum on the units digits
109  106  11,554
 The last two digits = the product of
the units digits
1
9  6  15
9(6)  54
 11554
RAIDERMATH
Copyright 2009: D.T. Simmons
Multiplying Two Numbers With First Numbers
Equal & A Zero In The Middle
 The 1st two numbers = the product
of the hundreds digits
 The middle two numbers = the
109  106  11,554
sum of the units x the hundreds
digit
 The last two digits = the product of
the units digits
RAIDERMATH
Copyright 2009: D.T. Simmons
4(4)  16
4(2  5)  28
2(5)  10
 162810
Multiplying By 3367
(10101 Rule)
 Divide the non-3367 number by 3
 Multiply by 10101
18  3367  60606
18
6
3
6  10101  60606
RAIDERMATH
Copyright 2009: D.T. Simmons
Multiplying A 2-Digit Number By 11
(121 Pattern)
Work 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
92  11  1,012
carry
Last Digit = 2
9  2  11
9  1  10
10 1 2 1012
RAIDERMATH
Copyright 2009: D.T. Simmons
Multiplying A 3-Digit Number By 111
(1221 Pattern)
Work Right to Left
 Last digit is the units digit
 The next digit is the sum of the
tens and the units digits
192  11  2,112
 The next digit is the sum of the
tens and the hundreds digit + carry
 The first digit is the hundreds digit
+ any carry
Last Digit = 2
1  9  1  11
9  2  11
1 1  2
 2112
RAIDERMATH
Copyright 2009: D.T. Simmons
Multiplying A 3-Digit Number By 111
(12321 Pattern)
Work Right to Left
 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
192  11  2,112
 The next digit is the sum of the
units, tens and hundreds digits +
carry
 The next digit is the sum of the
tens and hundreds digits + carry
 The next digit is the hundreds digit
+ carry
RAIDERMATH
Copyright 2009: D.T. Simmons
Last Digit = 2
1  9  1  11
9  2  11
1 1  2
 2112
Multiplying A 3-Digit Number By 111
(12321 Pattern)
Work Right to Left
192  11  2,112
Last Digit = 2
1  9  1  11
9  2  11
1 1  2
2 1 1 2  2112
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Copyright 2009: D.T. Simmons
RAIDERMATH
Copyright 2009: D.T. Simmons