by Isabella DiFatta 2 years ago
114
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8 = dividend
_________ 2 = divisor
2 l 8 the answer = qoutient
8 / 2 = 4 R0
Division Algorithms
*** Refer to notebook on how to do these.
Multiplication Algorithms
*** Refer to notebook on how to do these.
7 minuend
-3 subtrahend
----
4 difference
Subtraction Algorithms
*** Refer to notebook on how to do these.
Multiplication (aka groups of things)
Arrays
---------} #2
________________
l 0 0 0 0 0 0 0 l l
l 0 0 0 0 0 0 0 l l
l 0 0 0 0 0 0 0 l l #1 3 x 7 = 0
l 0 0 0 0 0 0 0 l l
l 0 0 0 0 0 0 0. l l
l 0 0 0 0 0 0 0 l V
________________
Subtraction
Subtraction Algorithms
Addition (aka putting things together)
Addition Algorithms
BASE-5 SYSTEM
Australians use the Base-5 System because there are 5 fingers on a hand
The place values differ from Base-10
Digits used: 0,1, 2, 3, 4, 10(base 5), 11(base 5), 12(base 5), 13(base 5), 14(base 5), 20(base 5)
How to convert Base-5 to Base-10:
232 (base 5) = (2x25)+(3x5)+(2x1)
232 (base 5) = (2x5^2)+(3x5^1)+(2x5^0)
232 (base 5) = 50 + 15 + 2
232 (base 5) = 67
The video shows a much faster, straight forward way to convert without showing as much work. But, it shows what the thinking process should be while converting
Expanded Notation
the simple definition is to break down or expand numbers.
For example in Base-10:
375 = 300 + 70 + 5
375 = (3x100)+(7x10)+(5x1)
375 = (3x10^2)+(7x10^1)+(5x10^0)
BASE-10 SYSTEM
In the US, we use the Base-10 system (also referred to as a decimal or positional system)
Numbers always relate to each other on a 1-10 relationship
The spot where a number is placed indicates the number's value
When you move to the left, the number gets bigger by 10 times
When you move to the right, the number gets smaller by 10 times
For example:
375
The same applies for different units such as decimals, money, miles, etc.
POLYA'S RULES
Step 1: Understand the problem.
Step 2: Devise a plan (translate).
Step 3: Carry out the plan (solve).
Step 4: Look back (check and interpret).
This week we solved more problems while applying this method. The biggest thing I took away from this week is that MULTIPLICATION tables are the key to solving a lot of problems!
Our professor had us start off as doing problems the "hard" way, then at the end of class revealed the "easy" way. It was very helpful to start our problem solving without having the easier method so that we could understand how things are broken down and how different students could interpret problems differently.
POLYA'S RULES
Step 1: Understand the problem.
Step 2: Devise a plan (translate).
Step 3: Carry out the plan (solve).
Step 4: Look back (check and interpret).
We solved a few problems in class using these steps. Multiple students would go up to the board and write out how they solved problems to show different ways of interpreting the problems.
INTRODUCTION
The syllabus includes just about all the information for this course that I could ever need. It includes contact information, policies, assignments, and information about the course itself.
The syllabus can be found on canvas.
+3 x -2 = -6 (-)(-)(-)(-)(-)(-) **3 groups of -2
+6 / 2 = +3 (+)(+)(+)(+)(+)(+) ** 3 groups of 2 in 6
+5 - -1 = +4 (+)(+)(+)(+)(+) - (+) = (+)(+)(+)(+)
-5 - +1 = -6 (-)(-)(-)(-)(-) - (+)(-) = (-)(-)(-)(-)(-)(-) **cross out (+)
-5 + -1 = -6 (-)(-)(-)(-)(-) + (-) = (-)(-)(-)(-)(-)
-5 + +1 = -4 (-)(-)(-)(-)(-) + (+) = (-)(-)(-)(-) **cross out (+) & one (-) because it is a zero pair
Integers are positive and negative numbers.
-------l--------l------l-------l-------l-------l-------l-------l-------l-----
-4 -3 -2 -1 0 1 2 3 4
Example:
+5 + +1 = +6 (+)(+)(+)(+)(+) + (+) = (+)(+)(+)(+)(+)(+)
Pay attention to the wording of a problem - it will tell you what you need to solve for.
25n/25 = 100 x 9/25
n = 100 x 9 / 25
36% of students voted for Marina
3 7 5 . 3 2
100's 10's ones 1/10 1/100
3/10 is 3 dimes
3/10 = 0.3 = 0.30
0.8 = 8/10 "eight tenths"
0.123 = "123 thousandths"
0.003 = three thousandths
72/100 = 0.72
31/1000 = 0.031
0.83 = 83/100
5/6 = 5 divided by 6 (do long division) = 0.83 (3 repeating)
In order to successfully teach children how to problem solve with fractions, you HAVE to draw pictures!
Each fraction of a whole is equal in value.
Example:
If **** represents 2/7 of the whole, draw what the whole looks like.
** = 1/7
**** = 2/7
****** = 3/7
******** = 4/7
********** = 5/7
************ = 6/7
************** = 7/7
Multiplying fractions
EX: 1/3 X 1/8 = 1/24
Dividing fractions
EX: 2/3 divided by 4/5
2/3 X 5/4 = 10/12
Adding fractions with common denominators:
1/4 + 2/4 = 3/4
2/5 +2/5 = 4/5
3/8 + 4/8 = 7/8
** add the numerators, don't change denominator.
Subtracting fractions with common denominators:
5/7 - 2/7 = 3/7
9/10 - 1/10 = 8/10
** subtract the numerators, don't change denominator.
If the denominators aren't the same?
EX:
1/4 + 1/6
ANSWER: 3/12 + 2/12 = 5/12
Fractional parts are equivalent parts.
To simplify fractions, you need to:
** The bigger the common factor, the less steps you will have to simplify a fraction
EX:
25/100
ANSWER: 1/4
Models:
Fraction:
All prime numbers 1-60:
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59
Best ways to factor:
Use the factorization tree OR list method to find the Greatest Common Factor (GCF) and Least Common Multiple (LCM)
24: 1,2,3,4,6,8,12,24
42: 1,2,3,6,7,14,21,42
39: 1,3,13,39
136: 1,2,4,8,17,34,68,136
91: 1,7,13,91
60: 1,2,3,4,5,6,12,15,30
Prime numbers: #'s that have only 2 factors - 1 and itself
Composite numbers: #'s that have more than 2 factors
A is divisible by B if there's a number C that meets this requirement.
c x b = a
ex: 10 is divisible by 5 2x5=10
Divisibility Rules
Ending:
a # is divisible by 2 if it ends with..... 0,2,4,6,8
a # is divisible by 5 if it ends with..... 0,5
a # is divisible by 10 if it ends with..... 0
Sum of digits:
Last digits:
By 7:
By 11:
---> if you double, you subtract
---> if you chop off, you add
