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A process standard, an essential component in every classroom.
Problem Solving Steps:
1. Understand/Communicate
2. Devise a Plan/Strategize
3. Implement Plan
4. Look Back/Check your answer.
Is this reasonable?
Invented by George Polya (Einstein's Son's advisor)
A numeration system is a system for representing quantity of a number in a consistent manner
There are 10 digits (numerals): 0,1,2,3,4,5,6,7,8,9
Using the ten digits every number can be written.
Base 10 means using the ten different digits to write numbers. Digits (numerals): 0,1,2,3,4,5,6,7,8,9.
Base 10 = Decimal System
Decimal System is positional which means that the placement of digits (or numerals) in the number specifies the value of the number.
Base-5 (Quinary /ˈkwaɪnəri/ or pental) is a numeral system with five as the base.
5^0 = Ones = five to the 0
5^1 = Fives = five to the one
5^2 = 25's = five to the two
5^3 = 125's = five to the 3
Digits used in numeration system:
In Base 10 - 0,1,2,3,4,5,6,7,8,9
In Base 2 - 0,1
In Base 3 - 0,1,2
In Base 4 - 0,1,3
In Base 5 - 0,1,2,3,4
Expanded Notation:
Example:
723 = 700+20+3
723 = (7x100) + (2x10) + (3x1)
723 = (7x10^2) + (2x10^1) + (3x10^0)
IMPORTANT: Exponent operations do not have a commutative property. AND, the ^ symbol is used to represent an exponent.
Raising fractions to higher terms is the opposite of reducing a fraction to lowest terms. Steps follow:
Step 1: Divide the old bottom number into the new one (the number you want to raise to). Keep the bottom number as the number you want to raise to ( the new one).
Step 2: Multiply the answer by the old top number. Place it on the top.
Check: Reduce the new fraction to see if you get the original fraction.
Changing improper fraction to whole or mixed numbers.
An improper fraction is a fraction with the top number that is big or bigger than the bottom number. An improper fraction is equal to or larger than one whole.
Change an improper fraction by dividing the bottom number into the top number and writing the remainder. Steps follow:
Step 1: Divide the bottom into the top
Step 2: Write the remainder as a fraction over the original bottom.
Step 3: Reduce the remaining fraction.
Changing mixed numbers to improper fractions. Steps follow:
Step 1: Multipy the bottom number by the whole number.
Step 2: Add the result to the top number.
Step 3: Place the total over the bottom number.
PROPERTIES:
Properties of Multiplication:
Division does not have properties. Division, in a sense is the opposite of multiplication.
Properties of Addition:
Subtraction does not have properties. Subtraction in a sense is the opposite of addition.
EXAMPLE of Addition Expanded Notation:
478 + 394 =
Solve using expanded notation:
400 + 70 + 8 =478
300 + 90 + 4 = 394
800 + 70 + 2 = 872
EXAMPLE of Subtraction Expanded Notation:
645 - 279 = 366
Solve using Expanded Notation of Subtraction:
_ 600 + 40 + 5 =
200 + 70 + 9 =
300 + 60 + 6 = 366
Type in the name of your subject.
Fractions:
A fraction is a part of something.
A penny is a fraction of a dollar.
The two numbers in a fraction are called the numerator and denominator.
Numerator is over the denominator:
Numerator - which tells how many parts you have
Denominator - which tells how many parts in the whole
Forms of Fractions:
Proper fraction The top number is less than the bottom number.
Improper fraction The top number is equal to or larger than the bottom number.
Mixed number A whole number is written next to a proper fraction
Reducing a fraction means writing it an easier way - with smaller numbers. When you reduce a fraction the value does not change. A reduced fraction is equal to the original fraction. When you have reduced a fraction as much as possible, the fraction is then in lowest terms.
Reduce: 20
30
In multiplication, when both the top and bottom numbers end with 0's, cross out the 0's. Then check to see if you can continue to reduce.
Algorithm is a process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer.
Addition Algorithms:
Subtraction Algorithms:
Multiplication Algorithms:
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