1.1 inductive & deductive reasoning

use inductive reasoning to predict the next three numbers in the pattern. 1, 1/8, 1/5, 1/22, ___, ___, ___

1/29, 1/36, 1/43 see below how to solve: the difference between denominator is 7. Add 7 to get next number

use inductive reasoning to predict the next line in the pattern 100 = 10^2 1000 = 10^3 10,000 = 10^4 100,000 = 10^5

1000000 = 10^6

find a counterexample to show that the statement is incorrect. The product of any two counting numbers is divisible by 2 a) 3 x 4 = 12, which is not divisible by 2 b) 2 x3 = 6, which is not divisible by 2 c) 2 x 4 = 12, which is not divisisble by 2 d) 3 x 5 = 15, which is not divisble by 2

3 x 5 = 15, which is not divisble by 2

use inductive reasoning to predict the next three numbers in the pattern 4, -12, 36, -108, ___, ___, ___

324, -972, 2916 see below how to solve: multiple by 3 and alternate neg/positive

use inductive reasoning to predict the next three numbers in the pattern. 2, 3, 5, 8, 13, 21, __, __, __

34, 55, 89 see below how to solve: 13+ 8 = 21 21+ 13 = 34 34+ 21 = 55 55+ 34 = 89

An ancient culture labeled certain numbers as square numbers. The numbers 1, 4, 9, 16, 25, and so on are on the square numbers. Determine the next three squares

36, 49, 64 see below how to solve: 5^2 = 25 6^2 = 36 7^2 = 42 8^2 = 64

use inductive reasoning to predict the next line in the pattern 1 x 4 = 4 2 x 4 = 8 3 x 4 = 12 4 x 4 = 16

5 x 4 = 20

counting number

A whole number that can be used to count a set of objects. Counting numbers do not include 0. (Example: 1, 2, 3, 4...)

Counterexample

an example used to support a claim or statement that is the opposite of another claim or statement

the type of reasoning used to prove a conjucture is called

deductive reasoning

the process of reasoning to a general conclusion through observation of specific cases is called

inductive reasoning

identify a pattern in the sequence of figures. square, circle, triangle, square, circle, triangle, ____

square

determine a counterexample to show that the following statement is incorrect The sum of any three two-digit numbers is a three digit number

the numbers, 10,11, and 12 form a counterexample because their sum, 33 IS NOT a three digit number