Problem Solving Flashcards
(22 cards)
Chaos
Used to describe something that appears to be random but is not actually random
Inductive reasoning
Inductive reasoning is the process of arriving at a general conclusion based on observations of specific examples.
Conjectures
Conclusions arrived at through inductive reasoning; also called hypotheses or educated guesses
Counterexample
A case for which a conjecture does not hold
Digits
The ten symbols we use to write out numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
Deductive reasoning
Deductive reasoning is the process of proving a specific conclusion from one or more general statements.
Theorem
A conclusion that is proved to be true by deductive reasoning
Variable
A letter used to represent any number in a collection of numbers
Estimation
Estimation is the process of arriving at an approximate answer to a question
Natural numbers
The numbers that we use for
counting (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, …)
Whole numbers
The natural numbers but counting zero (0, 1, 2, 3, …)
Symbol for “is approximately equal to”
≈
Circle graphs/pie charts
Show how a whole quantity is divided into parts
Sectors
Circle graphs/pie charts are divided into pieces, called sectors
Bar graphs
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
Line graphs
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
Formula
A formula is a statement of equality that uses letters to express a relationship between two or more variables
Mathematical modeling
The process of finding formulas to describe real-world phenomena
Mathematical models
Formulas with a meaning assigned to each variable, representing real world phenomena
Model breakdown
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
Polya’s four steps in problem solving
- Understand the problem
- Devise a plan
- Carry out the plan and solve the problem
- Look back and check the answer
Unit price
The total price divided by the total units