Algebra Practice for Your Child 适合您孩子的代数练习

The relationship between algebra in schools and real-life experience is never clear to our children. We, adults, know that algebra helps us to think logically for a solution to the many X-s and Y-s in our lives. Just as a simple example, if 3 apples and 4 oranges cost $13.00, and an apple costs $3.00, what is the cost of an orange? To solve this, we need to read the example in algebraic terms like 3a + 4o = 13 and a = 3. That being so, 3a = 9. Using the usual child’s conception that the equal sign is a bridge, and every time a number crosses the bridge, the sign (+ or -) changes, we have:

3a + 4o = 13; if a = 3, then (3 x 3) + 4o = 13; or, 9 + 4o = 13; 4o = 13 - 9; or 4o = 4; and so ‘o’, representing the price of orange is equal to $1.00

We can read the thirteen everyday examples of the use of algebra in real life with this link: https://studiousguy.com/examples-of-algebra-in-everyday-life/

Right from the time a person wakes up in the morning, algebra comes into play. Take, for example, a person has a meeting in the morning, what is that person likely to do? He/she will set up an alarm for waking up in the morning to get ready and assemble all the essential documents. What actually is happening here? The person knowingly or unknowingly makes use of algebra to calculate the time required to bathe, have breakfast or collect coffee, gather all important paperwork, and reach the office on time.

Algebra is as crucial in business as in other fields. A business owner makes use of algebraic operations to calculate the profits or losses incurred.

Before we go into the worksheet for your child to do, let us consider two further examples.

Example # 1: (2 + 6y)(-6) = 0

-12 + 36y = 0

36y = +12

y = 12 divided by 36 or 12/36

y = 1/3. one-third.

Example # 2: 5(x - 2) = 2(x +1)

5x - 10 = 2x + 2

5x - 2x = 2 + 10

3x = 12

x = 12/3

x = 4

It is important to emphasize to your child that showing the step-by-step approach, as illustrated above, in a solution is important for school works. The teacher usually gives more marks for the logical steps than for the right answer.

Here below is the worksheet for your child. Ask your child to record the time he/she starts working the answers and the time he/she stops. As he/she progresses through the worksheets given in http://www.mathscentre.co.nz/Homework-Sheets/ you can see that your child’s time taken for perfect answers getting shorter.

Worksheet for your child today:

# 1. -2(7 - 3y) = 4

# 2. (2 + 4z)2 = 20

# 3. 5(x + 3) = 25

# 4. 5x - 1 = 2(x + 4)

# 5. 4(x + 2) = - 8

# 6. 3(x – 4) = 2(–2x + 1)

# 7. 9 = v + 4 / v + 12

# 8. (–8 – 3k) / 2 = 11

# 9. –15b + 21 + 5b = –19

# 10. 14 + 13y = 20y – 21

我们的孩子永远都不清楚学校中的代数与现实生活之间的关系。我们成年人，都知道代数可以帮助我们逻辑思考，以解决生活中许多X和Y的问题。

举一个简单的例子，如果3个苹果和4个橙子的价格为$ 13.00，而一个苹果的成本为$ 3.00，一个橙子的价格是多少？
为了解决这个问题，我们需要以代数形式阅读示例，例如3a + 4o = 13和a =3。也就是说，3a = 9。使用通常的儿童的概念，即等号是一座桥梁，每当一个数字越过这座桥梁时，符号（+或-）都会发生变化，我们有：3a + 4o = 13;如果a = 3，则（3 x 3）+ 4o = 13;或9 + 4o = 13; 4o = 13-9;或4o = 4;所以’o’，代表橙色的价格等于$ 1.00.

通过以下链接，我们可以阅读13个日常使用代数在现实生活中的示例：https://studiousguy.com/examples-of-algebra-in-everyday-life/

一个16周的婴儿可以评估物体接近的方向，甚至可以确定物体降落的位置。这是一门实用的代数课程，无需教授。

从一个人早上醒来的那一刻起，代数就开始发挥作用。以一个人早上开会为例，这个人可能会做什么？他/她将在早晨醒来时设置一个警报，以准备并收集所有基本文件。这里实际上发生了什么？人们有意或无意地利用代数计算洗澡，吃早餐或收集咖啡，收集所有重要文书工作以及准时到达办公室所需的时间。

代数在商业中和其他领域一样重要。企业主利用代数运算来计算所产生的损益。

代数在烹饪和食谱中也很有用。
在为您的孩子准备工作表之前，让我们考虑另外两个示例。
示例问题 1：(2 + 6y)(-6) = 0
-12 + 36y = 0
36y = + 12
y = 12 / 36
y = 1/3 三分几一

示例问题 2：  5(x - 2) = 2(x + 1)
5x - 10 = 2x + 2
5x - 2x = 2 + 10
3x = 12
x = 12/3
x = 4
必须向您的孩子强调，在解决方案中展示如上所述的分步教学方法对于学校作业很重要。与正确答案相比，教师通常在逻辑步骤上给出更多的分数。以下是您孩子的工作表。要求您的孩子记录他/她开始使用答案的时间和他/她停止的时间。随着他/她逐步浏览http://www.mathscentre.co.nz/Homework-Sheets/ 中给出的工作表，您可以看到您的孩子花费完美答案的时间越来越短。
今天为您的孩子准备的工作表：

# 1. -2(7 - 3y) = 4

# 2. (2 + 4z)2 = 20

# 3. 5(x + 3) = 25

# 4. 5x - 1 = 2(x + 4)

# 5. 4(x + 2) = - 8.

# 6. 3(x – 4) = 2(–2x + 1)

# 7. 9 = v + 4 / v + 12

# 8. (–8 – 3k) / 2 = 11

# 9. –15b + 21 + 5b = –19

# 10. 14 + 13y = 20y – 21

More difficult questions below. Write to us if you wish to have answers to the questions shown here quoting the question #.

# 11. (6 - 4A) = (7A - 8)(-2)

# 12. (-5A + 8) 4 = 9(8 + 6A)

# 13. -8(2 + 9A) = -1(-5 - 3A)

# 14. -3(3 - 8A) = -9(8 - 2A)

# 15. - 4(9A + 9) = 2(-5 - 7A)

# 16. (- 5A + 1) (-2) = (3A - 2) (-3)

# 17. - 9(A - 4) = 2 (3A - 8)

# 18. 4(-6A + 4) = (2 - 5A)(-5)

# 19. -4(-4A - 5) = - 8(6A + 3)

# 20. - 6(8A + 3) = 2(4 + 9A)