number sense book part 1 dts

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.


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.


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


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


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


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


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


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


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


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


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


Multiplying By 25(1/4 Rule)

Divide the non-25 number by 4.

Add two zeroes. 32 25 800

328

400

8 00 800


Multiplying By 50(1/2 Rule)


Add two zeroes. 32 50 1,600 32

162

00

1600


Multiplying By 753/4 Rule


Multiply by 3.

Add two zeroes. 32 75 2,400

32 324

4 100

2400


Multiplying By 1251/8 Rule


Add three zeroes. 32 125 4,000 32 3

48 1

000

4000


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


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


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


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


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


Multiplying By 3367(10101 Rule)

Divide the non-3367 number by 3

Multiply by 10101 18 3367 60606 18

310101 606 6

6

60


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



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




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




192 11 2,112

1

Last Digit = 2

1 9 1 1

9 2 1

1 2

2 1 1 2

1

1

2112


number sense book part 1 dts

Education

units digits

digit number

hundreds digits

tens digits odd

unit digits

large tens digit

middle digit

leftlast digit