PROBLEM SOLVING AND REASONING

Question 1

is drawing a general conclusion from a repeated observation or limited sets of observations of specific examples.

Answer 1

Inductive Reasoning

Question 2

specific case to general case.

Answer 2

Inductive Reasoning

Question 3

Conjecture

Answer 3

is drawing conclusion using inductive reasoning.

Question 4

The conjecture may be true or false depending on the truthfulness of the argument.

Answer 4

True

Question 5

Is this example of conjecture or not?

1 is an odd number.
11 is an odd number.
21 is an odd number.

Thus, all number ending with 1 are odd numbers.

Answer 5

Conjecture

Question 6

is drawing general to specific examples or simply from
general case to specific case.

Answer 6

Conjecture

Question 7

Deductive starts with ?

Answer 7

a general statement (or hypothesis)

Question 8

Logical reasoning may be valid but nit necessarily true.

Answer 8

True

Question 9

Srinivasa Ramanujan wrote a letter to Godfrey Harold Hardy on

Answer 9

infinite sums, products, fractions, and roots.

Question 10

Intuitive can be found in mathematical literature and discovery.

Answer 10

True

Question 11

Ramanujan’s formulas prove there is

Answer 11

mathematical intuition,
though he didn’t prove them.

Question 12

made a sound judgment without directly proving the formulas of Ramanujan’s were correct.

Answer 12

Hardy

Question 13

a reliable mathematical belief without being
formalized and proven directly and serves as an essential part of mathematics.

Answer 13

Mathematical intuition

Question 14

carries a heavy load of mystery and ambiguity and it is not legitimate substitute for a formal proof.

Answer 14

intuition

Question 15

is being visual and is absent from the rigorous formal or abstract version.

Answer 15

Intuitive

Question 16

As a student, you can build and improve your intuition by doing the following :

Answer 16

i. Be observant and see things visually towards with your critical thinking.
ii. Make your own manipulation on the things that you have noticed and observed.
iii. Do the right thinking and make a connections with it before doing the solution.

Question 17

A __________ demonstrates that a certain statement is always true
in all possible cases.

Answer 17

mathematical proof

Question 18

is an essential defining attribute of mathematics and
mathematical knowledge.

Answer 18

Mathematical certainty

Question 19

By definition, a _________ is an inferential argument for a mathematical statement
while __________ are an example of mathematical logical certainty.

Answer 19

proof, proofs

Question 20

Let us say P and Q are two propositions. In an if-then statement, proposition P would be the ___________ while the proposition Q would be our
___________ denoted by: _____

Answer 20

hypothesis, conclusion, P → Q

Question 21

TWO WAYS ON HOW TO PRESENT THE PROOF

Answer 21

a. Outline Form
b. Paragraph Form

Question 22

Proposition: If P then Q.
1. Suppose/Assume P
2. Statement
3. Statement
.
.
. Statement
Therefore Q .

Answer 22

a. Outline Form

Question 23

Proposition: If P then Q.

Assume/Suppose P. ____________. ___________.

_____________________. ____________ . . . _____________. _______________.
Therefore Q.

Answer 23

b. Paragraph Form

Question 24

is a mathematical argument that uses rules of inference to derive the conclusion
from the premises.

Answer 24

direct proof

Question 25

The steps in taking a direct proof would be:

Answer 25

1. Assume P is true.
2. Conclusion is true.

Question 26

is a type of proof in which a statement to be proved is assumed false and if the assumption leads to an impossibility, then the statement assumed false has been proved to be true.

Answer 26

Indirect proof or contrapositive proof

Question 27

In an indirect proof, let us say we need to prove a given theorem in a form of P → Q. The steps or outline in taking an indirect proof would be:

Question 27

In an indirect proof, let us say we need to prove a given theorem in a form of P → Q. The steps or outline in taking an indirect proof would be:

Answer 27

Assume/Suppose ~Q is true.
.
.
.
Therefore ~P is true.

Question 28

There is a special
name for an example that disproves a statement

Answer 28

COUNTEREXAMPLE.

Question 29

This method works by assuming your implication is not true, then deriving a contradiction.

Answer 29

Proving by Contradiction

Question 30

Proof by contradiction is given by this way;

Answer 30

1. Assume p is true.
2. Suppose that ~q is also true.
3. Try to arrive at a contradiction.
4. Therefore q is true

Question 31

Proof by contradiction is given by this way; (give the four steps)

Answer 31

1. Assume p is true.
2. Suppose that ~q is also true.
3. Try to arrive at a contradiction.
4. Therefore q is true

Question 32

POLYA’S FOUR-STEPS IN PROBLEM SOLVING

Answer 32

Step 1: Understand the problem.

Step 2: Devise a plan.

Step 3: Carry out the plan.

Step 4: Look back.

Question 33

was a mathematics educator who
strongly believed that the skill of problem solving can be taught.

Answer 33

George Polya (1887-1985)

Question 34

was a mathematics educator who
strongly believed that the skill of problem solving can be taught.

Answer 34

George Polya (1887-1985)

Question 35

He developed a framework known as Polya’s Four-Steps in Problem Solving.

Answer 35

George Polya

Question 36

The process addressed the difficulty of students in problem
solving.

Answer 36

POLYA’S FOUR-STEPS IN PROBLEM SOLVING

Question 37

Mathematics is useful to predict.

Answer 37

True

Question 38

Number pattern

Answer 38

leads directly to the concept of functions in mathematics.

Question 39

is applied to problem-solving whether a pattern is present
and used to generalize a solution to a problem.

Answer 39

Number pattern

Question 40

can be in the form counting up or down and the missing number is
of the form of completing count up or down.

Answer 40

Pattern

Question 41

is a type of figurative number represented as dots or pebbles arranged in the shape of a regular polygon.

Answer 41

polygonal number

Question 42

Examples of polygonal number

Answer 42

Triangular number, Square number

Question 43

Alphametic

Answer 43

is a type of number puzzle containing sum (or other
arithmetic operation) in which digits (0 to 9) are replaced by
letters of the alphabet.

Question 44

One of the most famous alphametic puzzles is the one introduced by

Answer 44

Henry Dudeney in 1924.

Question 45

He was an English author and mathematician who specialized in
logic puzzles and mathematical games.

Answer 45

Henry Dudeney