##### 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