“If you want your child to become familiar with math, you must become familiar with math first!”
The minimum knowledge I couldn't convey to my child because I didn't understand it

Have you ever gasped when your child asks you a math problem? Want to explain it to your child at their level, but feel bad because you can't quite remember what you learned in school? What if you've never been good with math, but you want your child to become familiar with it? If you've ever experienced anything like this, this book is a must-read for any mother.
It is absurd for a mother to expect her child to be a math expert if she is not familiar with math.


As a math teacher with 14 years of experience and a mother of elementary school twins, the author has counseled many struggling students and their parents. Through this experience, she has realized that a child's attitude toward math changes only when the mother takes the first step toward it.
If a mother's math self-esteem rises, her child will not be afraid of math.
So the author decided to write a simple and friendly math book that even mothers could understand.
This book explains the core concepts and principles of the middle school curriculum in a way that is accessible to mothers, and adds to the fun of reading with over 200 hand-drawn illustrations.
If you're worried about your child's math education, put aside the burden of having to teach them yourself and pick up this book instead.
A child will feel and learn a lot from seeing his mother reading a math book.

Understand concepts and background instead of memorizing
How do we understand the rules? The answer is simple.
I'm asking why this rule came into existence.
When you open a math book, you shouldn't just memorize the formulas, but listen to the stories of the mathematicians who created those formulas.
Before memorizing 'Pi is 3.1415926...', we should see the earnestness of Archimedes, who said 'don't destroy my circle' even at the moment he was killed by enemy soldiers.
Before memorizing the pun that 'an irrational number is a number that is not rational', we should sympathize with the injustice felt by Hippasus, who was murdered for discussing the possibility of irrational numbers.
No mathematical concept has existed since time immemorial.
These are things that have been defined or discovered by someone.
Shouldn't we ask them at least once why they made this rule?
--- pp.
25~26

Who said decimal was a given?
The Babylonians' sexagesimal system demonstrates its power in division.
For example, you can see this by comparing a box of apples containing 10 apples to a box of apples containing 60 apples.
If you open a box of apples and divide them among people, it is difficult to divide 10, but it is easy to divide 60.
For example, if you think about a situation where you are sharing something among 4 people, you would have to share a 10-package with 2.5 people each, but you can share a 60-package with 15 people each.
Of course, if you know the concept of fractions, you can cut up an apple and share it.
But in reality, fractions are not easy.
I know my limits, but I gave up on splitting the apple in half between my daughter and son.
No matter how you divide it, it's not fair.
--- pp.
38~39

Is there a material that can make numbers?
Anyone interested in food is bound to be curious about ingredients and recipes.
The same goes for mathematicians.
What I was curious about after the discovery of 'number' was the material.
What are numbers made of? If you break them down again and again, aren't there some materials that can't be broken down any further? The fundamental numbers of any number are the "prime numbers."
Since prime numbers are fundamental, they cannot be divided any further.
To express the expression 'indivisible' a little more mathematically, we say 'it is not divisible by anything except 1 and itself'.
For example, 2 is a prime number because it is only divisible by 1 and itself.
On the other hand, 4 is divisible by 1 and itself, but it is also divisible by 2, so it is not a prime number.
That is, if 2 is an ingredient in food, then 4 is like a dish made using 2 as an ingredient.
Ingredients are prime numbers, and dishes are composite numbers.

--- pp.
43~44

Letters replace unidentified numbers
There are 26 letters in the alphabet, so why did x become the symbol for unknown numbers? The first person to use x was René Descartes of France around 1600.
He is famous for his famous quote, 'I think, therefore I am.'
One day, Descartes went to the printer to submit his mathematical papers.
The printer who received the paper was puzzled to see a mathematical paper with more letters than numbers.
“It’s a math paper, but there are a lot of characters?”
“That’s because you’re writing an unknown number in letters.”
"okay.
“Then, can I change that letter to x?”
“Why are you like that?”
“I think the number of characters will be insufficient because the same characters are used over and over again.
“I have x left over at the printer right now. Is it okay to represent an unknown number as x?”
--- pp.
87~88

Equations have been boring for 3,800 years.
It has been said that more than half of math education is equations.
Because equations appear everywhere throughout the curriculum.
Even first graders learn equations.
Because problems like 'If I give two apples to my friend and he has three left, how many did he originally have?' are all equations. (Omitted)
It's surprising that equation problems from about 3,800 years ago were just as contrived as they are today.
I don't know what the purpose of the records on this clay tablet is.
It could have been a textbook at the time, or it could have been something the nobles made to show off in front of their slaves.
What is certain is that equations have seemed far-fetched and useless for a very long time.

--- pp.
115~119

A secret only you should know
Even if it's been a long time since you graduated, you probably remember the formula for the roots of a quadratic equation.
Because during my school days, I had to live by reciting it as if it were a poem.
It wasn't a poem with a particularly beautiful rhyme.
The formula for the roots of a quadratic equation has a fairly long history.
It is said that the solution to quadratic equations was discussed even in ancient Babylonia.
A quadratic equation is called a 'Quadratic Equation' in English, and if you look it up in the dictionary, 'quadratic' is a term related to squares.
As the name suggests, problems related to the area of ​​a rectangle are often expressed as quadratic equations.
When you think of area, what comes to mind first? Land.
From the agricultural society where land was valuable, the problem of calculating the area of ​​land became a major concern, and methods for solving quadratic equations naturally emerged.

--- pp.
131~132

Cutting the Puff with Thales' Theorem
Thales' theorem comes from the law that the central angle is half the central angle.
The central angle of a semicircle is 180°, so the circumferential angle of a semicircle is 90°.
This is Thales' theorem.
Thales' theorem is a great way to teach children how to cut round objects in half.
I'm talking about things like round popcorn.
If your child questions the half-puff, try holding up something with right-angled corners, like a notebook.
If the notebook touches the popcorn at three places: the two ends and the round part, the popcorn is cut exactly in half.
Otherwise, if one end of the popcorn doesn't touch the other end or the corner of the notebook doesn't touch the round part, it's not exactly half a popcorn.

--- p.
178

Embracing children with a heart that resembles a circle
Finding extraordinary value within an ordinary triangle is the essence of incenter and circumcenter.
Common acute and obtuse triangles were not easy to find features of, so they were outside the interest of mathematicians. However, when they met circles, they revealed a new value of their own that had not been seen before.
Who would have thought that we would find so many right triangles within an ordinary triangle?
It's almost like the process of raising our children.
Any parent would want their child to have special talents.
So it's true that I'm getting impatient.
If you don't show the talent you expect, you'll be disappointed.
But in such cases, all parents can do is to embrace their children with a warm heart and listen to what they have to say.
Then children will discover their own special value.
There is no child in this world who does not have something special.

--- pp.
187~188

The only tool in the geometric world
On the day of the geometry test, if you give a problem that requires finding the length of a shape, there will always be a student like this.
First, tear the end of the test paper lengthwise.
And on top of that, we draw with a pencil the most elaborate markings a human being can draw.
Then, place it on the test paper and measure the length directly.
These are truly creative students who can solve problems intuitively even without knowing the properties of triangles or circles.
More advanced students here can easily solve problems that ask about angles.
Fold the corner of the test paper to make a 'corner protractor'.
Students who applied the fact that the corners of the test paper are right angles and the similarity of shapes.
These students' strategies are somewhat effective.

--- pp.
261~262

Numbers that explain an uncertain world
The mean and variance can be interpreted differently as 'expectation' and 'uncertainty'.
Let's take the example of two restaurants again.
Both Store A and Store B had an average rating of 3 stars.
That means the food taste we expect from both stores is 3 stars.
However, store A, which has a large variance, has a wide distribution of variance, so the taste is also hit or miss.
You might expect a 3-star rating, but one day you might get a 5-star rating, and another day you might get a 1-star rating.
On the other hand, store B, which has a small variance, is unlikely to deviate significantly from the expected taste.
Variance can therefore be defined as the 'uncertainty' about the expected degree (mean).

--- p.
312