number sense book part 1 dts
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Number Sense LessonsTRANSCRIPT
RAIDERMATHCopyright 2009: D.T. Simmons
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.
RAIDERMATHCopyright 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 289 17.
RAIDERMATHCopyright 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 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
3(2) 6
2(2) 3(1) 7
2(1) 2
276
23 12 276
RAIDERMATHCopyright 2009: D.T. Simmons
Squaring NumbersEnding In 5
First two digits = the ten’s digit times one more than the ten’s digit.
Last two digits are always 25
7 7 1 56
5 5 25
5625
275 5625
RAIDERMATHCopyright 2009: D.T. Simmons
Ending In 5Consecutive Decades
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 15
75
1575
35 45 1575
RAIDERMATHCopyright 2009: D.T. Simmons
Ending In 5Ten’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
4 84 8 38
25 5 25
3825
45 85 3825
RAIDERMATHCopyright 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 3 7
3 7 262
5 5 25
2625
35 75 2625
RAIDERMATHCopyright 2009: D.T. Simmons
Ending in 5Ten’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 3 83 8 29
275
2975
35 85 2975
RAIDERMATHCopyright 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 4002
324
800
400
RAIDERMATHCopyright 2009: D.T. Simmons
Multiplying By 16 2/3 (1/6 Rule)
Divide the non-16 2/3 number by 6.
Add two zeroes.
242 16 700
3
427
600
700
RAIDERMATHCopyright 2009: D.T. Simmons
Multiplying By 33 1/3(1/3 Rule)
Divide the non-33 1/3 number by 3.
Add two zeroes.
124 33 800
3
248
300
800
RAIDERMATHCopyright 2009: D.T. Simmons
Multiplying By 25(1/4 Rule)
Divide the non-25 number by 4.
Add two zeroes. 32 25 800
328
400
8 00 800
RAIDERMATHCopyright 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
162
00
1600
RAIDERMATHCopyright 2009: D.T. Simmons
Multiplying By 753/4 Rule
Divide the non-75 number by 4.
Multiply by 3.
Add two zeroes. 32 75 2,400
32 324
4 100
2400
RAIDERMATHCopyright 2009: D.T. Simmons
Multiplying By 1251/8 Rule
Divide the non-125 number by 8.
Add three zeroes. 32 125 4,000 32 3
48 1
000
4000
RAIDERMATHCopyright 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 the units digits.
32 38 1,216 3(3 1) 12
2(8) 16
1216
RAIDERMATHCopyright 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 the units digits.
67 47 3,149 6(4) 7 31
7(7) 49
31 49 3149
RAIDERMATHCopyright 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 sum of the differences subtracted from 100
The last two numbers equal the product of the differences
97 94 9,118 100 97
100 94
100 ( ) 91
3
6
3 6
3( )6 18
9118
RAIDERMATHCopyright 2009: D.T. Simmons
Multiplying Two Numbers Near 100
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
109 106 11,554 1
9 6 15
9(6) 54
11554
RAIDERMATHCopyright 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 sum of the units x the hundreds digit
The last two digits = the product of the units digits
109 106 11,554 4(4) 16
4(2 5) 28
2(5) 10
162810
RAIDERMATHCopyright 2009: D.T. Simmons
Multiplying By 3367(10101 Rule)
Divide the non-3367 number by 3
Multiply by 10101 18 3367 60606 18
310101 606 6
6
60
RAIDERMATHCopyright 2009: D.T. Simmons
Multiplying A 2-Digit Number By 11(121 Pattern)
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
92 11 1,012 Last Digit = 2
9 2 1
9 10
10 1 2 1 1
1
2
1
0
Work Right to LeftWork Right to LeftWork Right to LeftWork Right to LeftWork Right to Left
RAIDERMATHCopyright 2009: D.T. Simmons
Multiplying A 3-Digit Number By 111(1221 Pattern)
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
192 11 2,112 Last Digit = 2
1 9 1 1
9 2 1
1 2
211
1
1
1
2
Work Right to LeftWork Right to LeftWork Right to LeftWork Right to LeftWork Right to Left
RAIDERMATHCopyright 2009: D.T. Simmons
Multiplying A 3-Digit Number By 111(12321 Pattern)
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 hundreds digits + carry
The next digit is the sum of the tens and hundreds digits + carry
The next digit is the hundreds digit + carry
192 11 2,112 Last Digit = 2
1 9 1 1
9 2 1
1 2
211
1
1
1
2
Work Right to LeftWork Right to LeftWork Right to LeftWork Right to LeftWork Right to Left
RAIDERMATHCopyright 2009: D.T. Simmons
Multiplying A 3-Digit Number By 111(12321 Pattern)
192 11 2,112
1
Last Digit = 2
1 9 1 1
9 2 1
1 2
2 1 1 2
1
1
2112
Work Right to LeftWork Right to LeftWork Right to LeftWork Right to LeftWork Right to Left
RAIDERMATHCopyright 2009: D.T. Simmons