Mathematics 1-9 grade knowledge explain

From First to Ninth grade math. What are the subjects and materials Kids need to know?

First grade math

What the student should know in light of the curriculum 
A. The natural numbers in the 100 range
    Count to 100
    Counting in whole tens
    Countdown and countdown
    Share up to 30
    Reading and writing numbers up to 100
    equal, greater, less (between given numbers)
    Completing missing numbers in a series of numbers
    Knowing the terms: units, tens
B. account operations
    Knowing addition and subtraction facts by heart up to 10
    Knowing the terms: addition, subtraction and the signs of the operations
    Simple verbal questions
    Writing addition and subtraction exercises up to 20 and solving them with the help of illustrations
C. Measurements
    Comparing lengths of segments, sides or non-straight lines
    Using arbitrary units of measure to measure length
    Expression of a certain length in different units
    Knowing the terms: length, unit of measure, circumference
    Using cm to measure length
d. Geometry
    Construction of polygons using different means of illustration
    Sorting polygons according to the number of sides and their order
    Recognition and identification of polygons in a plane in different situations
    Identification of polygons, similarity and difference between polygons
    Knowing the terms: polygon, triangle, square, pentagon, side, vertex

 

Second grade math

What the student should know in light of the curriculum
A. The natural numbers in the 1,000 range

Share and count in units and tens
Order two-digit numbers
Reading and writing numbers up to 100
Knowing the terms: units, tens, hundreds, digit, number, one-digit number, two-digit number, three-digit number, even number, odd number, previous number, next number

B. Account operations in the 100 or more field

Addition and subtraction in the field of 100- horizontally and vertically
Oral knowledge of addition (and subtraction) facts up to 20
One-step addition and subtraction questions and two-step addition-type questions that have more than one addition or subtraction operation
Performing research tasks related to numbers up to 100 and applying addition and subtraction operations up to 100
Ability to illustrate multiplication and division exercises
Multiples of 1, 2, 3, 4, 5, 10
Exploration of the multiplication table
Division by 2
Knowing the terms: factors, product
One-step multiplication questions

third. Expanding the field of numbers

Straight out the numbers
Knowing the fractions half and quarter

d. data exploration

Collection, organization and direct representation of data in different ways
Bar diagrams drawn on the positive side of the axes

God. Measurements

Comparing areas, measuring areas by covering or disassembling
Using arbitrary units to measure area
Finding the perimeter of shapes by counting units of length
Intuitive distinction between area and perimeter and between area units and length units
Knowing the terms: area, perimeter, area unit

and. Geometry

Construction and disassembly of simple bodies using different means of illustration
Informal classifications of bodies
Analyzing the components of bodies and knowing the terms vertex, edge, face
Knowing the terms (in addition to those from grade 1): solids, shapes, cube, box, cylinder, pyramid, cone
Matching bodies to their drawings or photographs (in simple cases)
Distinguishing similarities and differences between bodies and their informal description

G. mirroring or sliding

The mirroring properties
Symmetry (relative to the line)
The sliding properties

Third grade math

What the student should know in light of the curriculum
A. The natural numbers are up to ten

Reading and writing numbers up to 1,000
Sort numbers up to 1,000
Completing assignments that show understanding of the decimal structure
Knowing the terms: units, tens, hundreds, thousands, one-digit, two-digit, three-digit number

B. Straight out the numbers

Placement of numbers in the multiplication field on the number line
Comparing fractions
Uses of negative numbers

third. Account operations in the field of rabba

Oral knowledge of addition and subtraction facts up to 20
Simple addition and subtraction exercises in the 1,000 range orally or in writing in balance
Addition and subtraction in the 1,000 field vertically
Estimation: Estimating the results of various actions in numbers
Use of parentheses and rules of operations
Verbal questions
Knowing the multiplication table up to 10 X 10 and multiplying by whole tens
Division in the domain of the multiplication table
Knowing the terms: factors, multiplier, double, half, quarter, third, eighth, whole
Verbal questions in multiplication

d. A fundamental fracture

Knowing elementary fractions (fractions whose octets are equal to 1) with the use of tangible means, such as circles, rectangles, etc.
The fragment as part of a unit
Comparing fractions
Part of the quantity expressed as a fraction

God. data exploration

Collection, organization and direct representation of data in different ways, discussion of data
Bar charts drawn on the positive side of the axes

and. Geometry

Recognizing polygons and investigating their properties
Comparing angles to a right angle
sorting triangles by sides; Sorting triangles by angles (each sorting separately)
Knowing the terms: polygon, triangle, square, pentagon, hexagon, angle, angle vertex, angle bisectors, acute angle, obtuse angle, right angle, right triangle, obtuse triangle, equiangular triangle, isosceles triangle, isosceles triangle, Equilateral triangle, square, rectangle, parallelogram, Dalton
parallel sides, perpendicular sides

G. Measurements

Measuring length in arbitrary units
Length measurement in standard units: centimeter, meter
Length estimates
Comparing volumes in different ways

Fourth grade math

What the student should know in light of the curriculum
A. Simple fractions and decimal fractions

Arrange fractions (including fractions greater than 1 and mixed numbers) by size
Comparing fractions
expansion and contraction
Adding and subtracting fractions
Fraction addition and subtraction questions
Research tasks in the field of addition and subtraction of fractions
Knowing the terms: simple fraction, mixed number, common denominator
Reading and using different representations of a decimal number (area, number line, simple fraction)
Comparing decimal numbers
Simple addition and subtraction exercises
Knowing the terms: decimal number, basic series: 1/100, 1/10, 1, 10, 100
Questions with decimal numbers

B. Arithmetic operations with natural numbers

Operations with natural numbers including the use of the order of operations, use of parentheses
Multi-step verbal questions

third. Data exploration, average

Average calculation and questions related to the properties of the average

d. Polygons

Investigating properties of the quadrilateral family
Using connections between square, rhombus, rectangle and parallelogram
Construction and identification of height in triangles and the family of parallelograms
Identifying angles, comparing angles, estimating angles
Knowing the terms: polygon, triangle, quadrilateral, pentagon…, angle, ray, elevation, altitude in a triangle, altitude in a parallelogram, right triangle, right-angled triangle, obtuse-angled triangle, different-sided triangle, isosceles triangle, equilateral triangle, parallelogram, rhombus, delton, trapezoid, rectangle, square, parallel sides, perpendicular sides, adjacent sides, opposite sides, diagonal

God. Area measurements

Using the formulas for the area of ​​a rectangle, parallelogram and triangle
Calculations of areas and perimeters including finding the area and perimeter of complex shapes
Use of agreed units of measure: mm, cm, m, km, square meter, square meter

Fifth grade math

What the student should know in light of the curriculum
A. Simple fractions and decimal fractions

Arrange fractions (including fractions greater than 1 and mixed numbers) by size
Comparing fractions
expansion and contraction
Adding and subtracting fractions
Fraction addition and subtraction questions
Research tasks in the field of addition and subtraction of fractions
Knowing the terms: simple fraction, mixed number, common denominator
Reading and using different representations of a decimal number (area, number line, simple fraction)
Comparing decimal numbers
Simple addition and subtraction exercises
Knowing the terms: decimal number, basic series: 1/100, 1/10, 1, 10, 100
Questions with decimal numbers

B. Arithmetic operations with natural numbers

Operations with natural numbers including the use of the order of operations, use of parentheses
Multi-step verbal questions

third. Data exploration, average

Average calculation and questions related to the properties of the average

d. Polygons

Investigating properties of the quadrilateral family
Using connections between square, rhombus, rectangle and parallelogram
Construction and identification of height in triangles and the family of parallelograms
Identifying angles, comparing angles, estimating angles
Knowing the terms: polygon, triangle, quadrilateral, pentagon…, angle, ray, elevation, altitude in a triangle, altitude in a parallelogram, right triangle, right-angled triangle, obtuse-angled triangle, different-sided triangle, isosceles triangle, equilateral triangle, parallelogram, rhombus, delton, trapezoid, rectangle, square, parallel sides, perpendicular sides, adjacent sides, opposite sides, diagonal

God. Area measurements

Using the formulas for the area of ​​a rectangle, parallelogram and triangle
Calculations of areas and perimeters including finding the area and perimeter of complex shapes
Use of agreed units of measure: mm, cm, m, km, square meter, square meter

Sixth grade math

What the student should know in light of the curriculum
fractions

Transition from fractions to mixed numbers and vice versa
Operations on simple fractions
Placement of fractions – simple and decimal – on the number line
Completing and exploring series of fractions
Finding a part pays off
Questions involving different representations of numbers
Operations with decimal fractions
Transition from decimal representation to representation as a simple fraction

percentage

Percent is another name for one hundredth
Finding a part of a quantity – given in percentages – in calculation exercises and simple situations
Exploration tasks dealing with operations with simple fractions, decimal fractions and percentages

third. ratio

Finding a ratio, comparing ratios, finding a missing figure in situations based on relationships between numbers
Small – also through the representation of the ratio as a fraction
Dividing a quantity according to a given ratio
Questions of ratio and scale

d. Decimal measurements

Transitions between different decimal units of measure

God. Scale

Questions of ratio and scale

and. Numbers and operations – expansion and deepening, inclusive (integrative) questions

Transitions between different representations of numbers: natural numbers, simple fractions, decimal fractions, percentages
Activities that require an overall view of the learned numbers (natural, fractions, decimals, percentages) as one consistent system
Multi-step questions with mixed representation of numbers

G. inclusive (integrative) questions

Two-step and multi-step questions in natural numbers
Traffic and provider questions

H. Data exploration and probability analysis

Frequency, relative frequency
Probability analysis
Using the term “more likely” while relying on relative frequency calculations. First use of the term “chance is…”

ninth. Bodies

Bodies: attribute analysis, layouts
Knowing the terms: prism, pyramid, cylinder, cone, envelope, profession, base of the cylinder, base of the cone
The base of the pyramid, the bases of the prism

J. Measurements

Using the circle area and circumference formulas in exercises and questions
Knowing the terms: circle, circle, chord, radius, diameter
Volume calculations of boxes and cylinders
Using a formula to calculate the volume of prisms based on the area of ​​the base and the height
Knowing volume units: cc, m3, liter

Seventh grade

A. Algebraic domain

Variables, algebraic expressions and generalization of numerical phenomena
Algebraic variables and expressions
Placing numbers in algebraic expressions and calculating the numerical value of the resulting arithmetical expressions
Equality between algebraic expressions
Assembly of similar organs

Solving equations and verbal questions

Equations and their solution
Solving equations of the first degree in one variable
Verbal questions that can be solved using equations of the first degree in one variable

functions

Useful graphs – reading and drawing
Introduction to functions
Different representations of a function
Change of function
Increase and decrease of a function
Variation of a function at a uniform rate and at a non-uniform rate

Verbal equations and questions

Solving linear equations
Verbal questions combined with linear equations

B. numeric domain

Arithmetic operations and their laws, powers and square roots

Account operation rules
The substitution and grouping rules of the connection operation
The substitution and grouping laws of the multiplication operation
Not divisible by zero
neutral organs
Reverse numbers
The law of division
Subtraction of a sum: a – (b + c) = a – b – c
Subtraction of the difference: a – (b – c) = a – b + c
Multiplying the divisor: a : (b × c) = (a : b) : c
Dividing the divisor: a : (b : c) = (a : b) × c
Powers with natural exponent
Square root

Negative, positive and zero numbers

Displaying negative numbers on the number line, order on the number line, opposite numbers
Four arithmetic operations with directed numbers
The integration of the algebraic field in the study of directed numbers
Powers with a natural exponent and a power base that is an integer
Coordinate system
Marking points and reading points

third. Geometric domain

Rectangle, box, perpendicularity and parallelism

rectangle
extras
parallel lines
overlapping shapes
Properties of the rectangle
Square
Perimeter and area of ​​a rectangle
perimeter of a rectangle
Whitespace
box
surface area of ​​a box
volume of a box
Box layout

territories

Areas of polygons
Triangles
Parallelism
trapezoids
General polygons
Circumference of a circle and area of ​​a circle

angle

angle
Equal angles and comparing angles
sum and difference of angles
Measuring angles
adjacent angles
Vertex angles
Cross-angle
Alternate angles and corresponding angles
Alternate angles between parallels
Corresponding angles between parallels

triangular

triangular
Knowing the triangle
the angles of the triangle
angles in a square
angles in polygons
Sides of the triangle

triangular prism

Right triangular prism
Getting to know the body
Calculation of surface area
Volume calculation
Deployment

Eight grade math

A. Algebraic domain

linear function
the linear function
Representation of phenomena using linear functions

inequality
Linear inequalities
Solving first degree equations (deepening), appropriate verbal questions and algebraic technique

Solving first degree equations
Appropriate verbal questions
algebraic technique

System of Equations of Two Equations of the First Degree, Matching Verbal Questions, Absolute Value, Inequalities

B. numeric domain

ratio, proportion and scale (including algebraic uses)

ratio between numbers
Division in a given ratio
proportion
Straight attitude
Scale
Reverse ratio

Percentages, statistics and probability

percentage
Collecting data and organizing it in different ways of representation: list, table, column diagram, pie diagram, pictogram and points on a system of axes
prevalence and relative prevalence
data range
Central indices: common, median, average
probability
The probability of receiving a result is a pre-determination of the degree of possibility that the result will occur on a scale between 0 and 1.
Properties of probability in symmetric situations
The estimate for the probability of obtaining a result can be obtained by checking the relative frequency of the same result when repeating the same experiment a large number of times.

Square root and irrational number

third. Geometric domain

Congruent triangles, secondary and isosceles triangles

Overlapping triangles
exterior angle of a triangle
median in a triangle
An isosceles triangle

Similarity of polygons

Similar triangles
similar polygons

Pythagorean theorem in plane and space
Roll (straight roll only)

Getting to know the body
Calculation of surface area
Shell area calculation
Volume calculation
Deployment

Ninth grade math

A. algebra

Strengths and roots

Powers with natural exponent
Extending the concept of power to exponents that are zero and negative integers
Formula 1
square roots

probability
conditional probability
Probability of two events
Probability of foreign events
Probability of independent events
Probability of dependent events
algebraic technique
The multiplication formulas (multiplying two terms by two terms)
Opening brackets
Factorization
Solving quadratic equations by completing the square
Decomposition of a quadratic trinomial (quadratic trinomial) x2 + bx + c
Solving quadratic equations
quadratic functions
The function f(x) = x2 and its graphical representation
Functions of the form f(x) = ax2 where a ¹ 0 – stretching, shrinking and mirroring
Functions of the form f(x) = ax2 + c where a ¹ 0 – vertical shifts
Composition of horizontal, vertical, stretching and contraction movements of the function f(x) = x2
Functions whose algebraic expression is:
g(x) = (x – p) 2, m(x) = a(x – p)2, t(x) = a(x – p)2 + k (where a ¹ 0)
The quadratic function and its different algebraic representations
Solving quadratic equations
Solving verbal questions
Quadratic inequalities
A system of nonlinear equations of two equations in two vanishings and solving verbal questions

B. Geometry

Dalton and isosceles triangle
A convex Dalton consists of two isosceles triangles with a common base.
The main diagonal of the delton is an axis of symmetry.
The main diagonal of the delton crosses the angles of the head.
The major diagonal of the delton intersects the minor diagonal.
The diagonals in the Dalton are perpendicular to each other.
The side angles in Dalton are equal to each other.
The area of ​​the delta is equal to half the product of the diagonals.
Basic constructions
Copying a section
Adding segments or subtracting them (including multiplying a given segment by a natural number)
Angle copy
Adding or subtracting angles (including multiplying a given angle by a natural number)
Crossing a section
Elevating the middle meridian to the segment and elevating the meridian to the line from a point on the line
You lowered yourself to the right from a point outside the right
crossing an angle
Constructing a triangle according to data that matches each of the known overlap theorems
Construction of a triangle according to data that corresponds to one of the well-known overlap theorems in relation to its partial triangle: construction of a triangle by the length of an angle bisector and the two angles formed at its ends with the sides of the triangle, construction of a triangle by the length of a side, the length of the middle of that side and the length of another side, construction of a triangle by the length of a side, length The height to the same side and the length of another side, building an isosceles triangle according to the length of the base and the length of the height to the base
Parallel lines and trapezoids
parallel and other contents that can be proven using its properties
Properties of the parallelogram and understanding how they arise from its definition: the diagonal divides the parallelogram into two congruent triangles, opposite sides are equal to each other, opposite angles are equal to each other, the sum of adjacent angles is 180°, bisectors of adjacent angles are perpendicular to each other, the diagonals intersect each other, rotational symmetry of the parallelogram around the point of intersection of the diagonals
Results arising from the properties of the parallelogram: in an isosceles trapezoid the base angles are equal to each other, a trapezoid where the base angles are equal to each other is an isosceles trapezoid, a trapezoid where the diagonals are equal to each other is an isosceles trapezoid.
Identifying features of a parallelogram and their equivalence to definition:
If the sum of any two adjacent angles in a quadrilateral is 180°, then the quadrilateral is a parallelogram.
If in a quadrilateral all two opposite angles are equal to each other, then the quadrilateral is a parallelogram.
A square where the diagonals cross each other is a parallelogram.
A quadrilateral where the opposite sides are equal to each other is a parallelogram.
A quadrilateral in which two opposite sides are equal and parallel is a parallelogram.
The properties of a midsection in a triangle and a trapezoid and how they derive from the properties of the parallelogram:
A midsection in a triangle is parallel to the third side and equal to half of it.
A middle section of a trapezoid is parallel to the bases and equal to half their sum.
A segment starting from the middle of a side of a triangle and parallel to another side intersects the third side.
A section coming out of the middle of one leg of a trapezoid and parallel to its bases also crosses the other leg.
A rectangle and other contents that can be proved using its properties
Construction of a rectangle given two adjacent sides or given a side and a diagonal
The properties of the rectangle and understanding how they arise from its definition:
A rectangle is a parallelogram, therefore all the properties of a parallelogram exist in it.
The diagonals of a rectangle are equal to each other.
The rotational symmetry of the rectangle around the point of intersection of the diagonals, its two axes of symmetry
Identifying properties of a rectangle and their equivalence to definition:
A parallelogram that has a right angle is a rectangle.
A parallelogram in which the diagonals are equal to each other is a rectangle.
Results arising from the properties of the rectangle and the ways to identify it
Proof by way of negation
Rhombus and square
Construction of a square given a side
Construction of a rhombus given a side and an angle between the sides
Features of the rhombus:
A rhombus is a parallelogram, therefore all the properties of a parallelogram exist in it.
The diagonals in a rhombus are perpendicular to each other.
The diagonals in the rhombus intersect the angles.
Features of the square:
A square is a parallelogram, so all the properties of a parallelogram exist in it.
A square is a rectangle, therefore all the properties of a rectangle exist in it.
A square is a rhombus, therefore all the properties of a rhombus exist in it.
The rotational symmetries of the rhombus and the square around the point of intersection of the diagonals, all their axes of symmetry
Identifying features of a rhombus and their equivalence for definition:
A parallelogram in which two adjacent sides are equal is m