Math(equation) 참고 자료

글쓴이 한결맘

등록일 2004-06-20 23:03

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다음은 초등학교 1~2 학년 과정의 수학입니다.
수학을 접해 주신 분들은 아실 거고...접해 주지 못하신 분들을 위해 참고로 올립니다.
참고라는 것은 이 자료들이 주 자료가 아니라는 뜻입니다.
잘 하는 방법에는 여러가지 있을 거고 모두 많은 연구와 경험을 통해서 얻어낸 것이므로
그것이 맞다 하겠지만 자기만의 방법을 찾기란 쉬운 일이 아닙니다.

자료는 정말 많고 그것을 어떻게 활용하느냐에 따라 많은 차이가 있습니다.
적어도 여길 주로 다니시는 분들은 좋은 취미를 가졌다고 해야 하겠습니다. (저를 포함해서)
제가 발음, 읽기, 말하기 등을 빨리 끝내야 한다고 말씀 드렸는데요...
멜 보내시면 정말 황당하게 간단하면서도 효과가 큰 방법을 알려 드리겠습니다.
많은 자료에 대해서는 몇 가지 문제가 있으므로 차차 풀어나가도록 하겠습니다.

What is it?
(Writing and Solving One-Step Linear Equations in One Variable)

Equations statements that say that two quantities are equal.
Numerical equations, such as 7 + 9 = 16, include only numbers.
Algebraic equations, such as 12 ? y = 2, include at least one variable.
Solving an algebraic equation is like solving a mystery.
You are seeking the value of the variable that will make the equation a true statement.
For example, in the equation x + 2 = 7, the value x = 5 makes the equation 5 + 2 = 7
a true statement.
Notice that the variable x in the equation is raised only to the first power.
When the variable in an equation is raised to the first power, the equation is called linear.
When the variable in an equation is raised to a power greater than one,
the equation is not linear.
For example, the equation 9 - S(3승) = 1 is not linear because the variable S is raised to
the third power.

When solving a linear equation, students should keep in mind three important ideas.
The first is that they are trying to get the variable onto one side of the equation, by itself.
To do this, they employ the second idea, that is,
use the inverse operation to undo what was done to the variable.
Look at the examples below.

Type of Equation Example Operation to Use
Addition Equation x + 3 = 5 Subtract 3
Subtraction Equation y - 4 = 3 Add 4
Multiplication Equation 2x = 12 Divide by 2
Division Equation x / 3 = 5 Multiply by 3

(위의 것은 표입니다. 줄이 그어진 것으로 보세요. 나누기는 따로 칠 수 없어서 컴의 기호로...)

The third idea to keep in mind is that an equation is similar to a balance scale.
You are given two quantities that are in balance.
In order to solve the equation, you need to keep the equation balanced by doing the exact same thing to both sides of the equation.
Therefore, if you add four to one side of the equation, you must add four to the other side of the equation to keep in balance.

Let's apply these three ideas to some specific equations.
Given the equation 3x = 12, you want to isolate the variable x.
In order to do this, you must undo what was done to the variable x.
Sice x was multiplied by 3, use the inverse operation of multiplication and divide x by 3.
To keep the equation in balance, you will then need to divide the other side by 3.
Dividing both sides of the equation by 3 gives a value of x = 4.

Applying these same ideas to the equation x - 7 = 13, you begin by getting x by itself.
To do this, undo the operation of subtracting 7 by adding 7 to the variable.
Then add 7 to the other side of the equation to keep the equation balanced.
The solution is x = 20.

Writing an algebraic equation often involves translating a written statement into algebraic form.
The variable in the equation represents the number you need to find.

It is very helpful to make use of the four-step process of problem solving when writing an equation: (1) understand, (2) plan, (3) solve, and (4) look back.
This process is described in the problem-solving lessons.
Let's apply this four-step process to the following problem.
Have students try to visualize what is happening as you read the problem.

......

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