Objective
- Overcome fear of numbers.
- Solve large arithmetic problems quickly and accurately
- (수학 자신감을 심어줄 수 있다?)
Contents
- + , - , / , x
2-Digit Addition (Left to Right)
Extraction Questions
- Why would we add from left to right. What are the benefits?
There are many good reasons why adding left to right is a superior method for mental calculation. For one thing, you do not have to reverse the numbers (as you do when adding right to left). And if you want to estimate your answer, then adding only the leading digits will get you pretty close.
Add from left to right
Practice Exercises PG4
Practice Exercises PG4 Solution
3-Digit Addition (Left to Right)
Extract Q:
- What is the main goal of solving more come complex addition problems.
- What's a great way to keep track of the numbers mentally?
Add from left to right
Goal is to keep simplifying the problem until you are left adding a 1-digit number. Simplify and the problem gets easier!
- Try to HEAR the numbers mentally.
Number Hearing Example
I hear the problem 623 + 159 as six hundred twenty-three plus one hundred fifty-nine; by emphasizing the word "hundred" to myself, I know where to begin adding.
When first doing these problems, practice them out loud.
Reinforcing yourself verbally will help you learn the mental method much more quickly.
This reinforces the number so that you remember.
There is an alternate method for roughly close to hundred numbers.
And you can also switch which number to break up as long as it is consistent.
Practice Exercises
Practice Exercises Solution
Story of Gauss and Mathematical Thinking.
What is the sum of numbers from 1 to 100? While his
fellow students were frantically calculating with paper and pencil, Gauss
immediately envisioned that if he spread out the numbers 1 through 50
from left to right, and the numbers 51 through 100 from right to left directly
below the 1-50 numbers, each combination would add to 101 (1 + 100; 2
- 99; 3 + 98 ... ). Since there were 50 combinations, the answer would
be 101 x 50 = 5050.
3-Digit Subtraction (Left to Right)
Basic
If the subtraction of two numbers requires you to borrow a
number, round up the second number to a multiple of ten
and add back the difference.
Using Complements
Use when upper number is lower than bottom number.
Practice Exercises
2-Digit Multiplication
Rounding Up
The subtraction method works especially well for numbers just
one or two digits away from a multiple of 10. I
Practice Exercises
3-Digit Multiplication
There is no magic secret to remembering that first number, but
with practice I guarantee you will improve your concentration so that
holding on to numbers while performing other functions will get
easier.
When you are first tackling these problems, repeat the answers to
each part out loud as you compute the rest.
I can assure you from
experience that doing mental calculations is just like riding a bicycle
or typing. It might seem impossible at first, but once you've mastered
it, you will never forget how to do it.
Practice Exercises
