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# MTTC - Elementary Ed

### History of Math/Basic Math Concepts

Question | Answer |
---|---|

1650BCE shows how ancient Egyptians worked out arithmetic and geometry in the 1st math book | Rhind Papyrus |

_____________ were the first to create a character for the number 0. | Babylonians |

developed his theory about right triangles ~530BCE | Pythagoreas |

__________ developed a number system that correlated with predicting astronomy-related events. | Mayans |

this person used a 192-sided polygon to calculate the value of pi to 5 decimal places (~263CE) | Liu Hui |

this math strategy was the 1st one created in China to help servants calculate taxes, wages, and engineering solutions | abacus |

_________ were the 1st to 0 as a number rather than just a placeholder | Indians |

_________ developed trigonometry concepts (i.e. sin, cos, tan) to calculate distance | Indians |

_________ developed the early foundations of calculus in the 12th century. | Indians |

_________ developed the numbers 0-9 | Hindu |

this person developed many algebraic techniques (~900CE) | Al-Khwarizmi |

The __________ brought about algebraic geometry. | Persians |

this person wrote the 1st computer program in the early 1800s | Ada Lovelace |

a set of axioms used to derive theorems has 3 properties: consistent, independent, and complete | Axiomatic System |

a statement that is considered true and doesn't require proof | axioms |

an axiomatic system property where it isnt able to prove both a statement and its negation; it won't contradict itself; this is the only requirement | consistent |

an axiomatic system property where an axiom cannot be derived or proved from the other axioms in the system | independent |

an axiomatic system property where the system can prove or disprove any statement | complete |

says that straight lines can be drawn from any point to any other point, can go on infinitely; a circle has a center and a radius;a line that intersects 2 lines forms interior angles less than 90 will also intersect on the sides less than 90degrees | Euclidian Geometry |

lines that bend | Non-Euclidian Geometry |

representation of a real world scenario in formula form not perfectly accurate; representations of a perfect scenario | Mathematical Model |

what are the 5 principles of problem-solving? | 1. The Always Principle 2. Counterexample Principle 3. The Order Principle 4. The Splitting Hairs Principle 5. The Analogy Principle |

the problem-solving principle that says that something is true, 100% of the time, no exceptions ex: the sun always rises in the East | The Always Principle |

the problem-solving principle that says any example that disproves a theory or statement ex: "all prime numbers are odd"; 2 is a prime number even though it's an even number | Counterexample Principle |

the problem-solving principle that says that order usually does matter ex: PEMDAS | The Order Principle |

the problem-solving principle that says that things that seem to be the same, but aren't truly identical ex: "equal" and "equivalent" | The Splitting Hairs Principle |

the problem-solving principle that says that comparisons and relationships to illustrate unknown concepts | The Analogy Principle |

any real object that you can use as a visual aid and tangible item to help you solve math | math manipulatives |

Real numbers abide by 3 rules...they have to be ________, _________, and _____________. | measurable, concrete value, and manipulated |

all real numbers are ____________, meaning they can be mapped on a number line | measurable |

all real numbers are ___________, meaning they all can be rewritten as a decimal | manipulated |

positive numbers that aren't fractions or decimals | whole numbers |

whole numbers and their opposites | integers |

counting numbers | natural numbers |

fractions that, when written as a decimal, either have an end point or repeat | rational numbers |

fractions that, when written as a decimal, have no end point | irrational numbers |

a system that lets us express numbers in writing | number system |

the standard number system | base-ten |

a base-two system (computers use this) | binary system |

numbers that can be written as the division of 2 integers | rational numbers |

a number greater than 1 that can be divided by a number other than 1 and itself | composite numbers |