by Demi Lawrence 10 years ago
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Factoring/Multiples
Least Common Multiple
Greatest Common Factor
multiply by 1 "whole number as divisor"
one thousand threehundred forty-two and three thousand one hundred seventy six ten-thousandths
as division leads to decimals
any number that can be written in the form a/b where a,b E integers
contains all elements being considered in a given discussion
Contains no elements, cardinal number 0
exsist in a one-to-one correspondence between the sets
All elements that are in A are in B
for all sets A & B, B ps of A written B C A all elemnts that are in B are in A and there is atleast on elemnt of A that is not in B
Closure
Distributive
Zero
Identity
Associative
Communitive
characterized by finding all possible paring between two or more sets of objects
characterized by a product of two numbers representing the sides od a rectanglar region such that the product represents the number of unit sized squares with in the rectangular region
characterized by repeatedly adding a quanity of continuous quantities a specified number of times
Repeated Addition
Know: quantitu starting with & size of each group
Find: number of groups
characterized by using a given quantity to create groups (partitions) of a specifed size (amount) and determining the number of groups (partituns) that are formed
Know: quantity starting with & number of groups
Find: Size of each group
characterized by distributing a given quantity among a specified number of groups (partitun) and determing the size(amount) in each group or (partitun)
disadvantages to improper fractions
use mult/div within problem
more oppurtunity for mistake-converting between two forms
work with larger numbers
advantages to improper fractions
process is similar to mult/div of fractions
looks like part-whole context-not distracted
no regrouping needed of the fraction
any number that can be expressed as the quotient of two integers a/b
Proportional Reasoning
unitizing
compare appropriate units
Quantities and how they change
Relative Thinking
multiplictive thinking
Rational numbers
Ratio Sense
Proportion
as a analogy: a is to b as c is to d
a:b :: c:d
a:b = c:d
a:b as c:d
two ratios are equal
ratio
a quantitative relationship showing the number of times one vaule contains or is contained within another value
comaping two quantites regardless of whether the unit are the same
if units happen to be differnt this is typically referred to as a RATE
may look like a fraction
comparing two separate things
2/3 the ratio of boys to girls
copies of a unit fraction (accompaniement to part-whole)
2/3 is two copies of the unit fraction 1/3
division
repeated subtraction
find number of groups
know size of group
partitun (long divison)
find size of partitun
know number of groups/partitun
the fraction bar eventually becomes an alternate tool for indicating division
part-whole (most common)
2/3 represents 2 parts of a whole that was divided into 3 parts
Inverse of addition
Missing Addend
characterized by the need to determine what quanitity must be added to a specified number to reach some targeted amount
Comparison
characterized by a compaison of the relative sizes of two quantites and determing either how much larger or how much smaller one quanitity is than the other
Take-away
characterized by starting with some inital quantity and removing or taking away a specified amount
For any whole numbers a and b such that a>b, a-b is unique whole number c such that b+c+a
Table
diagonally numbers appear in bands all possible ways to add two numbers
Ways to Add
Any column first
Left-to-Right Method
Low Stress Method
Scratch Method
Lattice Method
Arithmetic Sequence with each successive term from the second on obtained from the previous term by the addition or subtraction of a fixed number, the differnce
let A & B be two disjoint finite sets. If n(A)=a and n(B)=b; then a+b=n(A U B)
