DUE 6-13: Facilitators Guide Template - CC 6-12
... • We can use arrows on a number line to show the sum, p + q, on a number line. The sum is the distance|q|from p to the right of p if p is positive, and to the left of p if p is negative. • Subtracting a number is the same as adding its opposite. • The properties of operations justify the rules for m ...
... • We can use arrows on a number line to show the sum, p + q, on a number line. The sum is the distance|q|from p to the right of p if p is positive, and to the left of p if p is negative. • Subtracting a number is the same as adding its opposite. • The properties of operations justify the rules for m ...
Deductive Reasoning
... A Venn Diagram consists of circles that represent sets and shows every logical relationship between these sets. Ex. 1 Use deductive reasoning to make a conclusion from these statements: “All koalas are marsupials. All marsupials are mammals.” “All mammals are warm-blooded. Keith is a koala.” Steps: ...
... A Venn Diagram consists of circles that represent sets and shows every logical relationship between these sets. Ex. 1 Use deductive reasoning to make a conclusion from these statements: “All koalas are marsupials. All marsupials are mammals.” “All mammals are warm-blooded. Keith is a koala.” Steps: ...
Section 11.5 - Probability with the Fundamental Counting Principle
... For each case, the total number of possible outcomes is the same. Because the order of the 5 numbers does not matter, the total possible outcomes involves counting combinations, and equals: ...
... For each case, the total number of possible outcomes is the same. Because the order of the 5 numbers does not matter, the total possible outcomes involves counting combinations, and equals: ...
Imaginary Numbers and The Fundamental Theorem of Agebra
... • Multiplying complex numbers works the same as for real numbers ...
... • Multiplying complex numbers works the same as for real numbers ...
PROOFS Math 174 May 2017 I. Introduction. In the natural sciences
... I. Introduction. In the natural sciences, we cannot prove anything to be true. We can only support hypotheses with data and make decisions based on the most strongly-supported hypotheses, but the fact remains that fringe philosophical problems still apply (can we trust our senses? Are we living in a ...
... I. Introduction. In the natural sciences, we cannot prove anything to be true. We can only support hypotheses with data and make decisions based on the most strongly-supported hypotheses, but the fact remains that fringe philosophical problems still apply (can we trust our senses? Are we living in a ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.