Content Knowledge Praxis II: MATHEMATICS- NUMBER SENSE AND NUMERATION

-ability to understand numbers and thier relationships -skill develops over time by experiencing numbers in a variety of contexts, exploring numbers, and relating numbers -should encompass all types of numbers -capability to progress beyond basic numeration concepts and reading and writing of numerals -should include....relative magnitude, real world connections, approximations and rounding

-size relationship between numbers *is the number.... smaller, larger, close to, or the same

-how do #'s affect our lives -where do we use #'s -what do you do with #'s

-estimation skills important for... mental computations, verification of solutions

-NATURAL #'s=counting #'s 1,2,3,4,5,6,7,,,, -WHOLE #'s=all natural #'s and 0 -INTEGERS=natural, whole #'s and negatives of natural #'s -RATIONAL #'s=all integers, fractional #'s/fractions, any interger over an interger -PRIME #'s=intergers other than 0 and 1 that only has 2 factors, itself and 1; # that can only be divisable by itself=3,5,7,11,13,17 -EVEN #'s=interger divisible by 2= 2n -ODD #'s=integer not divisible by 2= 2n-1 -COMPLEX #'s=#'s w/ 'i' in them: 6-2i

-counting tells how many items/objects in a group/set -#'s related to one another through a multitude of # relationships -#concepts are interwined and essential to the world around as they help us make sense of the world

-learn to recognize sets of items in patterns and w/out counting to tell how many items are present

-begin w/the one and two more or the one and two less

-useful relationships to know as 10 plays a lg. role in numeration system

-learn to recognize that a # is made up of 2 more parts, as this will help students construct and deconstruct process #'s

-ADDITION=carrying regrouping -SUBTRACTION=borrowing regrouping -MULTIPLICATION=based on 3 concepts-place value system, memorization of multiplication, ditributive property of multiplication over addition -DIVISION=involves quotient,(answer) remainder, divisor(how many times to divide), and dividend(number being divided) division requires strong grasp of multiplication facts,subtraction, and place value