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Math part 1 up to Test 1


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What are the 4 steps of Polya's Problem solving Principle?
1) Understanding the problem - how else can you state the problem so it makes more sense?
2) Make a plan - choose one of the problem solving strategies
3) Carry out the plan - solce the problem following the plan you have chosen
4) Look Back - what did you learn? was there a pattern you discovered? Would a different strategy work better?
What is Guess and Check?
Make a guess, and see that it fits the constraints of the problem. If it doesn't, go up or down, and try again until it does.
What is Make A List?
when there are many possible answers, use a list (a variant is "make a table") to show all your possibilities so you don't skip any, or repeate any
What is Draw a Diagram?
Draw a diagram that represents the problem to help you better understand the problem, and to solve it.
What is Argue from a Special Case?
In a general case, pick a special case to work with to make the problem easier. Use the answer from the special case to argue that the general case works; use only the aspects of the special case that are typical of the general case.
What is Pascal's Triangle?
An order of numbers:
1 1
1 3 1
1 4 4 1
What is Work Backwards?
Start with the end result, and work backwards step by step until you reach the initial problem.
What is Eliminate the Possibilities?
Make a list of the possibilites, or use a logic chart, and use the clues to eliminate the possibilities.

At least one of the possibilities that aren't eliminated MUST be correct
What is the Pigeon Hole Principle?
When you have m pigeons placed into n pigeon holes where m > n, at least one pigeon hole will have 2 ore more pigeons.
What is the formula for the Extended Pigeon Hole Principle?
when you have n(K-1)+1 pigeons into n pigeon holes, at least one pigeon hole will have K pigeons
What is Inductive Reasoning?
It uses information from specific cases to make a general conclusion (generalization). The generalizatoin may be tru or false
What are the steps for Inductive Reasoning?
1) check several examples of a possible relationship
2) observe the relationship in all cases
3) conclude that the relationship is probably true for all such cases, so make a generalization about the relationship
What is a Counterexample?
an example, or case, that proves a generalization is false
What is representational reasoning?
Use an object (graph, drawing, chart, manipulatives, tables, conceptual models [variables, equations]) that shows the essence of a situation to help solve the problem
What is a Represntation?
the object used in representational reasoning
What is a mathematical statement?
A declarative statement that is either true or false, but NOT both
What is negation?
Transform a given statement, p, into ~p (not pe)
What is Conjunction
the use of and. denoted p^q

given two statements, p, q, conjunction is "p and q"

it is only true if both p AND q are true
What is Disjunction?
the use of or. denoted p V q

given two statements, p, q, disjunction is "p or q"

it is only false if both p AND q are false.
What is a Conditional Statement?
The use of "if, then". also known as a implication or a conditional statement. denoted p->q

given two statements, p, q, an implication is "if p then q"
"if" half is the hypothesis; "then" half is the conclusion.
sometimes stated "p implies q"

is only false if p is true and leads me to a falsity (q is false)
What is a truth table?
A table used to show the truth of various statements
Show me a truth table for p and ~p
p ~p
Show me a truth table for conjunction, disjunction, implication
p q p^q pVq p->q
What is the sum of the nth row in Pascal's Triangle?
2 to the power of n
What is the pattern for the "people in a canoe"?
You start with R then increas by one each move (so, LL then RRR then LLLL) until the number of like moves is equal to the number of pairs. Then you repeat that number of moves for the opposite direction, then back again to the first direction (so if there were 10 people it'd be R LL RRR LLLL RRRRR LLLLL RRRRR) then decrease by one until you reach LL and R.
What is the formula for the minimum number of moves to switch the "people in a canoe"
#people + #pairs squared


#pairs (#pairs +2)

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