Download worksheet reasoning

0
1
Exercise 2.1
1. The form of the equation given. Find the equation Next, using inductive reasoning,
and check the accuracy of the answers provided by the method of
calculation
1) (1 × 9) + 2 = 11
(12 × 9) + 3 = 111
(123 × 9) + 4 = 1,111
……………………………………………………………………………………………………………………………….
2)
1=1
1+2=3
1+2+3=6
1 + 2 + 3 + 4 = 10
……………………………………………………………………………………………………………………………….
3)
1=1
1+3=4
1+3+5=9
……………………………………………………………………………………………………………………………….
4)
1 + 10 = 11
1 + 10 + 100 = 111
1 + 10 + 100 = 1111
2
……………………………………………………………………………………………………………………………….
5)
11 × 11 = 121
111 × 111 = 12321
1,111 × 1,111 = 1,234,321
……………………………………………………………………………………………………………………………….
6) 9 × 9 = 81
99 × 9 = 891
999 × 9 = 8,991
……………………………………………………………………………………………………………………………….
7)
9 × 9 = 81
909 × 9 = 8,181
90,909 × 9 = 818,181
……………………………………………………………………………………………………………………………….
8)
(1 × 8) + 1 = 9
(12 × 8) + 2 = 98
(123 × 8) + 3 = 987
……………………………………………………………………………………………………………………………….
9)
(9 × 1) − 1 = 8
(9 × 21) − 1 = 188
(9 × 321) − 1 = 2,888
……………………………………………………………………………………………………………………………….
3
10)
1,089 × 1 = 1,089
1,089 × 2 = 2,178
1,089 × 3 = 3,267
1,089 × 4 = ⋯ … … … ..
1,089 × 5 = ⋯ … … … ….
1,089 × 6 = ⋯ … … … ….
1,089 × 7 = ⋯ … … … ….
1,089 × 8 = ⋯ … … … ….
1,089 × 9 = ⋯ … … … ….
1.By using the inductive reasoning find the next sequence
1. 12,22,32,42, …………….
6. -15,-5,15, …………….
2. 12,10,8,6, …………….
7. 1,-1,-3,-5, …………….
3. 5, 3,-1,-3, …………….
8.-5,-3,-1,1, …………….
4. 1,-1,1,-1,,1, …………….
9. 1,6,11,16,25, …………….
5. 1,4,9,16,25, …………….
10. 8 ,14 ,20,26 , …………….
4
2. The multiplier effect of the following. It has been noted on the multiplier and the multiplier
effect. And can provide conclusive or not
1×9=9
6 × 9 = 54
11 × 9 = 99
× 9 = 18
7 × 9 = 63
12 × 9 = 108
3 × 9 = 27
8 × 9 = 72
13 × 9 = 117
4 × 9 = 36
5 × 9 = 45
9 × 9 = 81
10 × 9 = 90
14 × 9 = 126
15 × 9 = 135
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
……………………………………………………………………………………………….
3. The multiplier effect of the following numbers
142,857 x 1 = 142,857
142,857 x 2 = 285,714
142,857 x 3 = 428,571
142,857 x 4 = 571,428
1. A note about the numbers instead of the multiplier effect, however
……………………………………………………………………………………………..
……………………………………………………………………………………………..
……………………………………………………………………………………………..
……………………………………………………………………………………………..
5
2. 142 857 with a multiple of 5 and 6 have the same format as above
……………………………………………………………………………………………..
……………………………………………………………………………………………..
……………………………………………………………………………………………..
……………………………………………………………………………………………..
3. The product obtained by multiplying 142,857 by the seventh and eighth on the
conclusion of the above is true or not.
……………………………………………………………………………………………..
……………………………………………………………………………………………..
……………………………………………………………………………………………..
……………………………………………………………………………………………..
……………………………………………………………………………………………..
……………………………………………………………………………………………..
6
4. Consider the following multiples
37 × 3 = 111
37 × 6 = 222
37 × 9 = 333
37 × 12 = 444
1) It should be noted, however, about the multiplier and the multiplier effect of the
above.
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
2) use inductive reasoning to find the multipliers that have a multiplier effect. 555 ,
666, 777, 888 ,999
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
7
5) The form of the equation given. Find the equation Next, using inductive reasoning, and
check the accuracy of the answers provided by the method of calculation
1)
(9 × 9) + 7 = 88
(98 × 9) + 6 = 888
(987 × 9) + 5 = 8888
(9,876 × 9) + 4 = 88,888
…………………………………………………….
2)
34 × 34 = 1,156
334 × 334 = 111,556
3, 334 × 3,334 = ⋯ … … … … … …
…………………………………………………….
3)
2 =4−2
2+4 =8−2
2 + 4 + 8 = 16 − 2
2 + 4 + 8 + 16 = 32 − 2
…………………………………………………….
8
4)
3 =
3(2)
2
3+6 =
3+6+9 =
6(3)
2
9(4)
3 + 6 + 9 + 12 =
2
12(5)
2
…………………………………………………….
5)
5(6) = 6(6 − 1)
5(6) + 5(36) = 6(36 − 1)
5(6) + 5(36) + 5(216) = 6(216 − 1)
…………………………………………………….
6) By using the inductive reasoning find the value of the following
1) 1 + 2 + 3 + … + 150
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
9
2) 1 + 2 + 3 + … + 300
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
3) 1 + 2 + 3 + … + 500
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
4) 1 + 2 + 3 + … + 1,000
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
10
7) By using the inductive reasoning find the value of the following
1) 2 + 4 + 6 + … + 100
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
2) 1 + 2 + 3 + … + 125
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
3) 1 + 2 + 3 + ... + n, where n is the number of counts is odd.
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
11
8. The ancient Greeks wrote of 1,3,6,10,15,21 Please use the following symbol
Based on the Triangle Write the triangle next two numbers .
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………………
3)
Considering that the number 72 is a triangle or not .
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
12
9) Use inductive reasoning to determine the following conclusions .
(ใช้การให้เหตุผลแบบอุปนัยในการตรวจสอบข้อสรุ ปต่อไปนี้ )
1 ) The product of two numbers , any number divided by two is always perfect
ผลคูณของจานวนนับสองจานวนใด ๆ จะหารด้วย 2 ลงตัวเสมอ
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
2) Count any more than four will be written as the sum of the numbers on a
combination of two or more than double the number at any time
(จานวนนับใด ๆ ที่มากกว่า 4
จะเขียนในรู ปการบวกของจานวนนับที่เรี ยบติดกันสองจานวนหรื อมากกว่าสองจานว
นได้เสมอ เช่น 5 = 2 + 3
6=1+2+3
14 = 2 + 3 + 4 + 5)
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
13
3) Two counts of any kind will always be an even number .
(กาลังสองของจานวนนับใด ๆ จะเป็ นจานวนคู่เสมอ)
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
10). .Photos from the patterns Write the Next Picture
14
Exercises 2.2
Determine whether reasonable or not
จงตรวจสอบว่ าผลสรุปต่ อไปนีส้ มเหตุสมผลหรื อไม่ โดยใช้ แผนภาพ
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
15
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
16
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
17
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
18
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
19
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
20
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
21
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
22
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
23
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
………………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
24