Problem Solving

Question 1

Chaos

Answer 1

Used to describe something that appears to be random but is not actually random

Question 2

Inductive reasoning

Answer 2

Inductive reasoning is the process of arriving at a general conclusion based on observations of specific examples.

Question 3

Conjectures

Answer 3

Conclusions arrived at through inductive reasoning; also called hypotheses or educated guesses

Question 4

Counterexample

Answer 4

A case for which a conjecture does not hold

Question 5

Digits

Answer 5

The ten symbols we use to write out numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

Question 6

Deductive reasoning

Answer 6

Deductive reasoning is the process of proving a specific conclusion from one or more general statements.

Question 7

Theorem

Answer 7

A conclusion that is proved to be true by deductive reasoning

Question 8

Variable

Answer 8

A letter used to represent any number in a collection of numbers

Question 9

Estimation

Answer 9

Estimation is the process of arriving at an approximate answer to a question

Question 10

Natural numbers

Answer 10

The numbers that we use for

counting (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, …)

Question 11

Whole numbers

Answer 11

The natural numbers but counting zero (0, 1, 2, 3, …)

Question 12

Symbol for “is approximately equal to”

Answer 12

≈

Question 13

Circle graphs/pie charts

Answer 13

Show how a whole quantity is divided into parts

Question 14

Sectors

Answer 14

Circle graphs/pie charts are divided into pieces, called sectors

Question 15

Bar graphs

Answer 15

Graphs that are convenient for comparing some measurable attribute of various items; the bars’ heights or lengths are used to
show the amounts of different items

Question 16

Line graphs

Answer 16

Line graphs are often used to illustrate trends over time; some measure of time frequently appears on the horizontal axis, and amounts on the vertical axis; points are drawn to represent the given information; the graph is formed by connecting the points with line segments

Question 17

Formula

Answer 17

A formula is a statement of equality that uses letters to express a relationship between two or more variables

Question 18

Mathematical modeling

Answer 18

The process of finding formulas to describe real-world phenomena

Question 19

Mathematical models

Answer 19

Formulas with a meaning assigned to each variable, representing real world phenomena

Question 20

Model breakdown

Answer 20

Occurs when a model becomes ineffective or wrong

Can happen when a model gives an estimate that is not a good approximation or is extended to include values that do not make sense; models that accurately describe data for the past 10 years may not serve as reliable predictions for what can reasonably be expected to occur in the future; can occur when formulas are extended too far in the future

Question 21

Polya’s four steps in problem solving

Answer 21

1. Understand the problem
2. Devise a plan
3. Carry out the plan and solve the problem
4. Look back and check the answer

Question 22

Unit price

Answer 22

The total price divided by the total units