1st Grade Math Dictionary

Exponentiation | Isn't it 300 since it is 3 multiplied 100 times?
Prime and composite numbers | Aren't numbers like 0.1 or 0.37 prime? Are 2 and 3 also prime?
Determining Prime Numbers | Is there a quick way to determine whether a large number like 101 is prime or composite?
Factorization | If you factorize 30, isn't it 2×15?
Finding Divisors | Why factorize when finding divisors? Just divide.
Greatest Common Divisor and Least Common Multiple | How can the least common multiple be greater than the greatest common divisor?
Integers and Rational Numbers | How is it a rational number? Isn't it a fraction?
Absolute Value and Magnitude | Doesn't the larger of two numbers also have a larger absolute value?
Addition and Subtraction of Rational Numbers | Why do we find the difference when finding the sum of two numbers with different signs?
Commutative and Associative Laws | The commutative law holds, so why is 3-5=-2 and 5-3=2?
Multiplication and Division of Rational Numbers | If the signs are different in multiplication, the result is negative?
Distributive law | If so, is it?
The calculation order of mixed calculations | It's confusing even if only +, -, ×, ÷ are mixed, so how do I solve it when there are also parentheses and exponentiation?
Omission of multiplication and division symbols | If 3×a can be simply expressed as 3a, is 3×5 simply 35?
Coefficients and Degrees | Is the coefficient of x in 3-2x 2?
Addition and subtraction of linear equations | Isn't 5x-3x=2?
Equations and identities | If an equation contains x, like 5x=2x+3x, isn't it an equation?
Solving a linear equation | When you divide by 4x=8, the sign changes, so it becomes , right?
Ordered Pairs and Coordinates | Who on Earth Does "Third Line, Fourth" Refer to?
Interpreting a Graph | Why does the graph look different when it's the same 5cm tall?
Proportionality and Inverse Proportion | A proportional graph goes up from the origin to the right, and an inverse graph goes down, right?
Vertical angles | Are all angles vertical if they are the same size?
Corresponding and alternate angles on parallel lines | Aren't corresponding and alternate angles always the same?
Positional Relationships of Points, Lines, and Planes | Two lines neither intersect nor are parallel?
Drawing | They ask me to bring an unmarked ruler for drawing, but don't all rulers have marks?
Construction of a triangle | To draw a triangle, you need to know 3 sides and 3 angles, a total of 6, so why are you only giving me 3 and asking me to draw it?
Conditions for Congruence of Triangles | Can You Tell if a Triangle is Congruent Without Overlaying It?
Number of Diagonals | It's hard to draw an icosahedron, so how do you find the number of diagonals?
The sum of the interior angles of a polygon | Since a hexagon is divided into 6 triangles, the sum of the interior angles is 1080°, right?
The sum of the exterior angles of a polygon | The size of the interior angles increases by 180°, but how much does the size of the exterior angle increase?
Pi | As the circle gets bigger, doesn't pi also get bigger?
Arc length and area of ​​a sector | Can you find the area of ​​a sector without knowing the size of the central angle?
Polyhedron and regular polyhedron | All faces are regular polygons, but it's not a regular polyhedron?
Properties of a solid of revolution | A truncated cone is a truncated cone, so why is it called a solid of revolution made by rotating a trapezoid?
Surface area and volume of a column | I need to find the base area, but I can't see the base.
Surface area and volume of a cone | If you cut a cylinder, it seems like you'll get two cones, one on top and one on the bottom. Why is the volume of the cone the same as that of the cylinder?
Surface Area and Volume of a Sphere | A sphere is round, so how do you find its surface area and volume?
Representative value | The mean is sufficient, so why do we also calculate the median and mode?
Stem and leaf diagram | Isn't the stem supposed to be the first position?
Frequency Table | Why create a frequency table when a stem-and-leaf plot is better?
Histograms and Frequency Polygons | Why is the number of points in a frequency polygon different from the number of classes?
Relative Frequency | If the frequencies of two groups are the same, why do they differ when compared relatively?

2nd grade math dictionary

Fractions that can be expressed as finite decimals | I said that if the denominator has a prime factor other than 2 or 5, it becomes an infinite decimal, right?
Fractions that can be expressed as repeating decimals | 1÷23 doesn't repeat even if you divide it 10 times, so it's not a repeating decimal, right?
Recurring decimals to fractions | When converting a recurring decimal to a fraction, how do you know whether to multiply by 10 or 100?
Law of Exponents | How many times is 4.5 billion 45 million?
Multiplication and Division of Polynomials | When dividing an expression, wouldn't it be easier to multiply the reciprocal of the divisor?
Linear equation with two unknowns | Doesn't a linear equation have only one solution?
Simultaneous Equations | How do I find a solution that satisfies both linear equations simultaneously?
Solving the first-order inequality | If you move the binomial, the sign changes, right?
Definition of a function | If the webtoon ( x ) changes, the author ( y ) also changes, so why is it not a function?
Graph of a linear function | I wrote the linear function as y=ax+b. Why is it wrong?
Slope and Intercept | Why is a slightly inclined line said to have a large slope?
Linear function equation | To find the equation of the linear function y=ax+b, don't you need to know the slope and y-intercept?
Properties of the graph of a linear function | If the slope of the graph of a linear function is positive, it is increasing?
Linear functions and linear equations | A linear equation has only one solution, so how does its graph become a straight line?
Equation of a straight line parallel to an axis | x=2 Since the value of x is 2 and the value of y is non-existent, can we represent it as the point (2, 0) on the axis?
Intersection of Two Lines and Simultaneous Equations | Why Solve Simultaneous Equations to Find the Intersection of Two Linear Function Graphs?
Properties of an isosceles triangle | Aren't the two base angles of an isosceles triangle the same size?
Congruence of right triangles | SAS Congruence means that two sides and their included angles must be equal, right?
Incenter and Circumcenter of a Triangle | Isn't the incenter of a triangle the center inside the triangle, and the circumcenter the center outside the triangle?
Parallelogram | The properties of a parallelogram are too numerous and complex.
Please tidy up a bit.
Various quadrilaterals | Is a square a trapezoid?
Parallel Lines and Area-Equivalent Transformations | The long triangle has the largest area, right?
Similarity of Shapes | Circles and regular polyhedra are all similar, right? Are all rectangular solids similar, too?
Similarity of Triangles | Why Does AA Similarity Have Two Conditions?
Ratio of lengths between parallel lines | Are similarity always the same ratio?
Centroid of a triangle | Is there a guarantee that the three medians of a triangle meet at exactly one point?
Area and volume ratios of similar figures | The volume ratio is very different from what I expected.
Pythagorean theorem | If the ratio of the side lengths is 3:4:5, isn't it a right triangle?
Number of events and cases | Isn't it multiplying when they happen 'simultaneously'?
When adding and multiplying | Doesn't simultaneous mean that they happen at exactly the same time?
Definition and Properties of Probability | The probability of winning any lottery is , so why do I never win?
Calculating Probability | When calculating the probability of event A or event B occurring, you add the two probabilities, right?

3rd Grade Math Dictionary

Square root | What is the difference between 'square root of a' and 'square root a'?
Properties of square roots | When , why is it ? I heard that only positive numbers appear in the root?
Definition of an irrational number | The circumference of a circle is 3.14, so how is π considered an irrational number?
Real Number System | How can we be sure that all non-rational numbers are irrational?
The relationship between the magnitude of errors | Which value is greater?
Multiplication and division of expressions involving radicals | Moving numbers in and out of radicals is difficult!
Addition and subtraction of expressions including radicals | Is that right?
Rationalization of the denominator | Is it necessary to rationalize when the denominator is an irrational number?
Multiplication Formulas | There are five multiplication formulas. Do I really have to memorize them all?
Factoring | No matter how you factor, the result of factoring is always the same, right?
Factoring Formula | How to think about addition and multiplication at the same time?
Quadratic Equations and Factoring | How do you determine which method to use when looking at a quadratic equation?
The root formula | Perfect square! It's so complicated.
Is there no other way?
Quadratic function | Do I need to find multiple ordered pairs to draw the graph of a quadratic function each time?
Parallel translation of the graph of a quadratic function | I translated +3 in the direction of the x-axis, but why does the equation change to x -3?
Graph of a Quadratic Function | Can't you draw the graph of a quadratic function by just plotting a few points?
Maximum and minimum of a quadratic function | How can we say that a quadratic function has a maximum (minimum) value when we cannot find all the values ​​of the quadratic function?
Trigonometric functions | In a triangle, this is cosine, right?
Applications of Trigonometry | How do I find the area of ​​a triangle without knowing its height?
Properties of Circles and Chords | How can we be sure that the perpendicular bisector of a chord passes through the center of the circle?
Properties of Tangents to a Circle | Are the lengths of two tangents drawn to a circle from a point outside the circle always equal?
Properties of Central Angles | There are dozens of central angles for a single arc, so how come they are all the same size?
Circle through four points | I'm having trouble drawing a circle through four points. Can you tell me the secret?
Scatterplot | Isn't it enough to look at the data and find the mean and other representative values ​​within it?
Boxplot | Isn't the center line of the boxplot the mean?
Scatterplots and Correlation | Why are two variables correlated if they don't increase together?

Elementary, middle, and high school math concept connection map
Middle School Math Concept Connection Map
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『Concept Connection Middle School Mathematics Dictionary』 is recommended for the following students.

1.
Middle school students worried that they will become math dropouts because math suddenly became more difficult.
2.
Prospective middle school students who want to preview the connections between middle school math concepts rather than prior learning.
3.
A prospective high school student who wants to quickly review the concepts of three years of middle school math.
4.
A high school student who has struggled with math and needs the courage to start studying again.
5.
All students who want to study real math without giving up until the college entrance exam.
For middle school students, it can immediately solve their current math problems, for high school students, it can provide customized review of their weaknesses, and even encourage students who have struggled to start math again.
For prospective middle school students, it provides a big picture of the math they will learn in the future, helping them to engage in healthy previewing rather than indiscriminate pre-study.