af Lauren Bennett 7 år siden
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Includes how integers are added, subtracted, multiplied, and divided with dependence on their charge (positive or negative).
These operations can easily be shown on a number line to first demonstrate the concept of negative numbers.
Integer: "properties including opposites, positive, negative, number line, and signs"
* Positive Integers are greater than 0
* Negative Integers are less than 0
* Integers are opposite of each other if they have opposite signs and are the same distance from 0 on the number line
Absolute Value: the value of a number regardless of its sign
* How far a number is away from zero
* Designated by |x|
Multiplying Positive and Negative Integers
How I learned to tell what sign the product of two Integers would be:
https://goo.gl/images/dDeZtT
Number theory includes concepts such as prime numbers and congruence congruence.
Prime Number-
"A prime number is a whole number greater than 1, whose only two whole-number factors are 1 and itself."
Strategies
Decomposition
Addition and Subtraction
https://www.google.com/amp/s/www.whatihavelearnedteaching.com/composing-and-decomposing-numbers-for/amp/
Algorithms for Addition/Subtraction
Traditional Method
48 48
+ 33 - 33
_____ _____
81 15
Partial Sums Method
48 1: Add/Subtract the 4 and 3 as they are in their tens place.
+ 33 (Ex. 40+30=70)
_____ Step 2: Add/Subtract the 8 and 3 as they are.
70
+ 11
_____ Step 3: Combine your two sums or find the difference.
81 (Ex. 70+11=81)
Expanded Notation
40 + 8 Step 1: Write each addend in expanded form.
+ 30 + 3 Step 2: Add or subtract by place value.
____________
70 + 11=81
Algorithms for Multiplication
Traditional Method
43
12 x
____
86
430 +
____
516
Partial Products
43
12 x
____
80------> 2x40
6--------> 2x3
40------> 1x4
3--------> 1x3
Addition Problem Types
Subtraction Problem Types
Multiplication Problem Types
Division Problem Types
Properties of Addition
Properties of Subtraction
Properties of Multiplication
When using base 10 block to add, subtract, multiply or divide decimals, flats represent 1 whole, flat are equal to a tenth, units are hundredths.
Method such as 10 block grid papers can also be used for these operations.
Remember: The ones place before the decimal can be seen as a a number of tenths. Ex: 2.0 = 20 tenths
Place Value when working with decimals is slightly shifted to the left when looking at the numbers behind a decimal. The decimal is used as a ones place. For example, the first number after the decimal is in the tens place.
How to Pronounce Decimals:
http://www.themathpage.com/arith/decimals-2.htm
Improper Fractions/Mixed Numbers
Ex: 1 and 1/2
Equivalent Fractions
Ex: 1/2 = 2/4
Adding Fractions
•Area Model
•Numberline Model
•Unit Square
How to use a Unit Square:
https://education.ti.com/~/media/682BA8BCC0FD491298991D9F0189A85C
Subtracting Fractions
•Area Model
•Numberline Model
•Unit Square
How to use a Unit Square:
http://mps.milwaukee.k12.wi.us/MPS-English/CAO/Documents/RtI-Academics/math-intervention-4NF3b_Decomposing_Fractions.pdf
Fraction Models
•Area Model
•Set Model
•Linear Model (a row or number line)
*these are used to demonstrate the different concepts involving fractions
Equivalent Fractions- fractions that don't necessarily have the same denominator, but equal the same percentage of their whole
Ex: 1/4=2/8, these can be equivalent because they are the same ratio
Definitions
Counting Numbers- positive integers, not including fractions or decimals and 0
Digits- counting numbers, single symbols
Types of Number Systems
Different areas of the world may have ways of symbolizing numbers and counting. For example, America, and many other countries use Hindu-Arabic symbols under a base 10 counting system.
Base 12 System
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, x, y
Ex: 1, 2, 3, 4, 5, 6, 7, 8, 9, x, y, 10. . .1x, 1y
Base 10 System
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Ex: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Base 5 System *
0, 1, 2, 3, 4
Ex: 1, 2, 3, 4, 10, 11, 12
Base 2 System
0, 1
Ex: 1, 10, 11, 100, 101, 110, 111, 1000
* "10" is 1 and 0, NOT "ten"
-----------------------------------------------------------------Single, Small Cubes = Ones = Units
Rectangular Block of 10 units = Tens = Long
Square of 10 Longs = Hundreds = Flat
Cube of 10 Flats = Thousands = Cube
Our numerical system is the Hindu Arabic System. Other places and points in time may have other systems such as:
