"If you can't do math "percentage", the junior high school entrance exam is difficult."
This is KO-HEI for junior high school entrance exams, mathematics, and online instruction.
On this page"How important is the idea of "percentage" when taking on the challenge of taking the junior high school entrance exam?"
In other words, "It is no exaggeration to say that if you can't get a 'percentage', the junior high school entrance exam will be difficult."
I will explain its meaning in detail, so if you are thinking of taking the junior high school entrance exam or are taking on the challenge, please refer to it.
What is the "percentage" of arithmetic in the first place?
It means "a number that expresses how much the amount to be compared when the original amount is 1".
This idea of "proportion" is the origin of arithmetic, or rather, mathematics, but it is not easy for children to learn this idea.
The reason is actually that there is a problem with this solution.
Many children are the first to fail at this "percentage" and become "math haters".
So why are you not good at "proportion"?
Let's explain in detail.
In cram school materials, as "the three formulas of proportion"
・Amount to be based × ratio = amount to be compared
・Amount to be compared ÷ amount based on = percentage
・Ratio ÷ amount to compare = amount to be based on
In the first place, children cannot imagine the amount to be compared to "the amount to be compared".
Originally, children asked, "Why is this happening?" and "Why?" I am interested in pursuing questions such as "It's strange".
However, even at the cram school, I did not mention the solution to that question.Learn only problem exercises using the "3 formulas of ratio"Let me.
The children feel confused and continue to learn without clarifying the meaning of "percentage".
"How much to base on?" "How much to compare?" I don't know what it means, and I think it's a natural result that I can never say that it is "interesting" to challenge problem exercises one after another.
Even if they know the answer, they don't understand "What does the answer mean?" and they don't like learning that is simply done by hand.
Look for insects in nature and observe them to have a simulated experience of "insects", and what is going on in the universe? I was impressed by researching videos and encyclopedias, and I felt like a doctor by researching the mechanism of trains and cars... Like games, I am not interested unless the content allows me to empathize with my emotions.
"Why? It is very understandable that children who are not interested in learning without understanding logic are less motivated to learn.
Children don't hear things that they are not interested in.
It is possible for adults to learn to some extent, "I can't help it to improve my grades!", but children are honest with themselves and don't feel like learning if they are not interested.
But in other words,What interests you immediately comes to mind.
In other words, the reason why I am not good at proportions is
This is because it is not interesting to learn to just "use the three formulas" without understanding the meaning and not having an image.
I don't want to learn because it's not fun!
I can't understand because I don't learn!
Furthermore, unfortunately, this idea of "proportion" is
・Consistency (concentration)
・Speed
・Profit and loss of trading (profit and loss calculation)
・Ratio (distribution, equivalent, work, etc.)
It will be necessary in all kinds of units, so in the end"I don't know the percentage" is linked to "I don't know math" and "I don't like math".
In other words, if you can think of "proportion", you will be able to do the above units! It can be said.
Extreme story,If you can do proportions, you can do math!It is.
So how can we start thinking about "proportion"?
In the first place, math is not a subject to memorize.
It is not about memorizing formulas and methods.
If you get into the habit of memorizing formulas, you will not be able to do math to the extreme.
It's not fun...
I'm not interested...
(1) Understand the meaning of proportion in the diagram
(2) Use line diagrams for proportions
Let's deepen our understanding.
(2) is explained in the teaching materials of the junior high school entrance examination cram school, and it is the content you learn at the cram school.The problem is that (1), which is the basis for this, is neglected in both teaching materials and cram schools.
And now
Let's explain "what is a percentage" in the following example!
"Mr. A used 3/8 of his money to buy a book for 750 yen.
In the cram school explanation
"This problem is a problem of finding the amount to be based on
Comparison amount ÷ percentage = amount to be based on
From the formula of
750÷3/8 = 2000 yen
The first money you have is 2,000 yen!"
It will be explained.
This will not allow the child to imagine anything. It seems like just a list of numbers.
Sometimes some students make a miscalculation and answer 200 yen without hesitation.
"Isn't it ridiculous that you buy a book for 750 yen and have 200 yen in your possession?" Even if you tell them, there are many students who have a stunned face.
What you meanI don't understand the meaning of this number, so I don't have any doubts about the number in the answer.It is.
Now, let's explain the "percentage" by comparing it to pizza.
"If you compare your money to one pizza, 3/8 of your money is 3 pizzas divided into 8 pieces.
As shown in the figure, 3 pizzas (1), (2), and (3) separated by black lines cost 750 yen.
So how much is one?"
When I asked the students
The student simply answers, "750÷3 = 250 yen".
One pizza divided into eight pieces costs 250 yen, so how about one pizza?"
The student immediately answers, "250×8 = 2000 yen".
"Yes! The money I had was 2,000 yen because it was one pizza!"
You can easily answer.
There is no need for the "3 formulas of proportions" at all,If you can write this pizza picture, any child can answerIt is.
What you meanIt makes math difficult by memorizing formulas that I don't understand.I think you will understand that.
Even if you change the content of this question as follows, the child will be asked from the picture of the pizza.
"How much is 750 yen out of 2000 yen?"
When a child has a problem like this,
2000÷ 750 or 750÷2000?
The meaning (phrasing) of words becomes ambiguous and unclear.
However, if one pizza costs 2,000 yen, you can imagine that 750 yen is at least one slice divided into several pieces.
2000÷750 = 2.6... This is more than one piece and it's strange! ! I understand.
I see~
750÷2000＝0.375（3/8）
3 pieces of pizza divided into 8 pieces~
It becomes fun to have an image.
Children with a strong inquisitive spirit
"I received 8,000 yen as a New Year's gift and spent 1,600 yen of it, but how much does that mean?"
"Wow~, I ate one of the five pizzas~"
Some children enjoy calculating the ratio on their own.
thusBy explaining with a design, the meaning of "proportion" becomes clear to the child and gives them an image.It will be.
If you can have an image, "It's interesting!"It is.
Mathematics is based on "percentage", and children who cannot think about proportions cannot take the junior high school entrance exam first.
In the fifth grade of elementary school, please be sure to be able to "percentage".
From here, it's a small talk,How important is it to learn to have an image for children!
The other day, a fifth-grade elementary school student asked me about the answer to a volume problem of 13 cubic centimeters.
Student: "How much is 13 cubic cm?"
Me: "It's about a dice about 2.5 cm on one side."
Student: "How many sips does that take?"
Me: "I think it's about 2~3 bites."
Student: "Hmm~"
I was thinking.
It is a moment when you are imagining it in your head, experiencing it yourself, and empathizing with it.
Looking at the dictionary that was nearby,
Student: "How many cubic centimeters is this?"
I was measuring it with a ruler.
Student: "13 cm× 20 cm× about 5 cm! 1300 cubic centimeters is 1.3 liters."
Me: "That's right~ This dictionary is bigger than a 1-liter plastic bottle!"
Student: "Eh~! The plastic bottle looks bigger, but it's not what it looks."
It was impressive that he was staring at the dictionary with interest.
Children love learning like this.
Also, how much is "13 cubic cm" and "1300 cubic cm" from such actual experience? You will understand the quantity, and it will be easier to imagine the numbers and units that are frequently used in arithmetic problems.
When you have an image, you will be interested in trying to solve the problem, and as a result, you will enjoy "arithmetic" and become good at it.
Again,
"Children say, "Why? Is that the case? "I am not interested unless I understand the logic and have an image."
No matter how much you study cram school materials, you won't learn what you are not interested in.
Please refer to it.
This page has been automatically translated. Please note that it may differ from the original content.
This is KO-HEI for junior high school entrance exams, mathematics, and online instruction.
On this page"How important is the idea of "percentage" when taking on the challenge of taking the junior high school entrance exam?"
In other words, "It is no exaggeration to say that if you can't get a 'percentage', the junior high school entrance exam will be difficult."
I will explain its meaning in detail, so if you are thinking of taking the junior high school entrance exam or are taking on the challenge, please refer to it.
What is the "percentage" of arithmetic in the first place?
It means "a number that expresses how much the amount to be compared when the original amount is 1".
This idea of "proportion" is the origin of arithmetic, or rather, mathematics, but it is not easy for children to learn this idea.
The reason is actually that there is a problem with this solution.
Many children are the first to fail at this "percentage" and become "math haters".
So why are you not good at "proportion"?
Let's explain in detail.
In cram school materials, as "the three formulas of proportion"
・Amount to be based × ratio = amount to be compared
・Amount to be compared ÷ amount based on = percentage
・Ratio ÷ amount to compare = amount to be based on
In the first place, children cannot imagine the amount to be compared to "the amount to be compared".
Originally, children asked, "Why is this happening?" and "Why?" I am interested in pursuing questions such as "It's strange".
However, even at the cram school, I did not mention the solution to that question.Learn only problem exercises using the "3 formulas of ratio"Let me.
The children feel confused and continue to learn without clarifying the meaning of "percentage".
"How much to base on?" "How much to compare?" I don't know what it means, and I think it's a natural result that I can never say that it is "interesting" to challenge problem exercises one after another.
Even if they know the answer, they don't understand "What does the answer mean?" and they don't like learning that is simply done by hand.
Look for insects in nature and observe them to have a simulated experience of "insects", and what is going on in the universe? I was impressed by researching videos and encyclopedias, and I felt like a doctor by researching the mechanism of trains and cars... Like games, I am not interested unless the content allows me to empathize with my emotions.
"Why? It is very understandable that children who are not interested in learning without understanding logic are less motivated to learn.
Children don't hear things that they are not interested in.
It is possible for adults to learn to some extent, "I can't help it to improve my grades!", but children are honest with themselves and don't feel like learning if they are not interested.
But in other words,What interests you immediately comes to mind.
In other words, the reason why I am not good at proportions is
This is because it is not interesting to learn to just "use the three formulas" without understanding the meaning and not having an image.
I don't want to learn because it's not fun!
I can't understand because I don't learn!
Furthermore, unfortunately, this idea of "proportion" is
・Consistency (concentration)
・Speed
・Profit and loss of trading (profit and loss calculation)
・Ratio (distribution, equivalent, work, etc.)
It will be necessary in all kinds of units, so in the end"I don't know the percentage" is linked to "I don't know math" and "I don't like math".
In other words, if you can think of "proportion", you will be able to do the above units! It can be said.
Extreme story,If you can do proportions, you can do math!It is.
So how can we start thinking about "proportion"?
In the first place, math is not a subject to memorize.
It is not about memorizing formulas and methods.
If you get into the habit of memorizing formulas, you will not be able to do math to the extreme.
It's not fun...
I'm not interested...
(1) Understand the meaning of proportion in the diagram
(2) Use line diagrams for proportions
Let's deepen our understanding.
(2) is explained in the teaching materials of the junior high school entrance examination cram school, and it is the content you learn at the cram school.The problem is that (1), which is the basis for this, is neglected in both teaching materials and cram schools.
And now
Let's explain "what is a percentage" in the following example!
"Mr. A used 3/8 of his money to buy a book for 750 yen.
In the cram school explanation
"This problem is a problem of finding the amount to be based on
Comparison amount ÷ percentage = amount to be based on
From the formula of
750÷3/8 = 2000 yen
The first money you have is 2,000 yen!"
It will be explained.
This will not allow the child to imagine anything. It seems like just a list of numbers.
Sometimes some students make a miscalculation and answer 200 yen without hesitation.
"Isn't it ridiculous that you buy a book for 750 yen and have 200 yen in your possession?" Even if you tell them, there are many students who have a stunned face.
What you meanI don't understand the meaning of this number, so I don't have any doubts about the number in the answer.It is.
Now, let's explain the "percentage" by comparing it to pizza.
"If you compare your money to one pizza, 3/8 of your money is 3 pizzas divided into 8 pieces.
As shown in the figure, 3 pizzas (1), (2), and (3) separated by black lines cost 750 yen.
So how much is one?"
When I asked the students
The student simply answers, "750÷3 = 250 yen".
One pizza divided into eight pieces costs 250 yen, so how about one pizza?"
The student immediately answers, "250×8 = 2000 yen".
"Yes! The money I had was 2,000 yen because it was one pizza!"
You can easily answer.
There is no need for the "3 formulas of proportions" at all,If you can write this pizza picture, any child can answerIt is.
What you meanIt makes math difficult by memorizing formulas that I don't understand.I think you will understand that.
Even if you change the content of this question as follows, the child will be asked from the picture of the pizza.
"How much is 750 yen out of 2000 yen?"
When a child has a problem like this,
2000÷ 750 or 750÷2000?
The meaning (phrasing) of words becomes ambiguous and unclear.
However, if one pizza costs 2,000 yen, you can imagine that 750 yen is at least one slice divided into several pieces.
2000÷750 = 2.6... This is more than one piece and it's strange! ! I understand.
I see~
750÷2000＝0.375（3/8）
3 pieces of pizza divided into 8 pieces~
It becomes fun to have an image.
Children with a strong inquisitive spirit
"I received 8,000 yen as a New Year's gift and spent 1,600 yen of it, but how much does that mean?"
"Wow~, I ate one of the five pizzas~"
Some children enjoy calculating the ratio on their own.
thusBy explaining with a design, the meaning of "proportion" becomes clear to the child and gives them an image.It will be.
If you can have an image, "It's interesting!"It is.
Mathematics is based on "percentage", and children who cannot think about proportions cannot take the junior high school entrance exam first.
In the fifth grade of elementary school, please be sure to be able to "percentage".
From here, it's a small talk,How important is it to learn to have an image for children!
The other day, a fifth-grade elementary school student asked me about the answer to a volume problem of 13 cubic centimeters.
Student: "How much is 13 cubic cm?"
Me: "It's about a dice about 2.5 cm on one side."
Student: "How many sips does that take?"
Me: "I think it's about 2~3 bites."
Student: "Hmm~"
I was thinking.
It is a moment when you are imagining it in your head, experiencing it yourself, and empathizing with it.
Looking at the dictionary that was nearby,
Student: "How many cubic centimeters is this?"
I was measuring it with a ruler.
Student: "13 cm× 20 cm× about 5 cm! 1300 cubic centimeters is 1.3 liters."
Me: "That's right~ This dictionary is bigger than a 1-liter plastic bottle!"
Student: "Eh~! The plastic bottle looks bigger, but it's not what it looks."
It was impressive that he was staring at the dictionary with interest.
Children love learning like this.
Also, how much is "13 cubic cm" and "1300 cubic cm" from such actual experience? You will understand the quantity, and it will be easier to imagine the numbers and units that are frequently used in arithmetic problems.
When you have an image, you will be interested in trying to solve the problem, and as a result, you will enjoy "arithmetic" and become good at it.
Again,
"Children say, "Why? Is that the case? "I am not interested unless I understand the logic and have an image."
No matter how much you study cram school materials, you won't learn what you are not interested in.
Please refer to it.
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