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# MTTC - Elementary Ed

### History of Math/Basic Math Concepts

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
Created by: jmeeker
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