Work program in mathematics 5th grade Federal State Educational Standard Vilenkin
use the rules of politeness in communication;
use simple speech means to convey your opinion;
control your actions in team work;
understand the content of questions and reproduce questions;
monitor the actions of other participants in the process of collective cognitive activity.
Subject results:
Integers. Fractions. Rational numbers.
The student will learn:
understand the features of the decimal number system;
compare and order natural numbers;
perform calculations with natural numbers, combining oral and written calculation techniques, using a calculator;
use concepts and skills related to percentages when solving mathematical problems, and perform simple practical calculations.
Measurements, approximations, estimates
The student will learn:
use elementary concepts associated with approximate values of quantities when solving problems.
Equations
The student will learn:
solve simple equations with one variable;
understand the equation as the most important mathematical model for describing and studying a variety of real situations, solve word problems using the algebraic method;
Inequalities
The student will learn:
understand and apply terminology and symbolism associated with the relationship of inequality;
apply the apparatus of inequalities to solve problems.
Descriptive statistics.
The student will learn
use the simplest ways to present and analyze statistical data.
Combinatorics
The student will learn
solve combinatorial problems to find the number of objects or combinations.
Visual geometry
The student will learn:
recognize flat and spatial geometric shapes in drawings, drawings, models and in the surrounding world;
recognize the development of a cube, a rectangular parallelepiped;
build developments of a cube and a rectangular parallelepiped;
calculate the volume of a rectangular parallelepiped.
Geometric figures
The student will learn:
use the language of geometry to describe objects in the surrounding world and their relative positions;
recognize and depict geometric shapes and their configurations in drawings and drawings;
find the lengths of linear figures, the degree measure of angles from 0 to 180°;
solve simple construction problems.
Measurement of geometric quantities
The student will learn:
use the properties of measuring lengths, areas and angles when solving problems of finding the length of a segment, the degree measure of an angle;
calculate the area of a rectangle, square;
calculate the lengths of linear elements of figures and their angles, formulas for the areas of figures;
solve problems using the formula for the area of a rectangle or square.
SOSHI "Umid"
Mathematics (ancient Greek μᾰθημᾰτικά < ancient Greek μάθημα - study, science) is the science of structures, order and relationships, historically developed on the basis of the operations of counting, measuring and describing the shape of objects. Mathematical objects are created by idealizing the properties of real or other mathematical objects and writing these properties in a formal language.
Mathematics does not belong to the natural sciences, but is widely used in them both for the precise formulation of their content and for obtaining new results. Mathematics is a fundamental science that provides (general) language tools to other sciences; Thus, it reveals their structural relationship and contributes to the discovery of the most general laws of nature.
We present to your attention a dictionary of mathematical terms.
Abscissa - (Latin word abscissa - “cut off”). Borrowing from French language at the beginning of the 19th century Franz. abscisse - from lat. This is one of the Cartesian coordinates of a point, usually the first, denoted by x. In the modern sense, T. was first used by the German scientist G. Leibniz (1675).
Additivity - (Latin word additivus - “added”). The property of quantities, consisting in the fact that the value of the quantity corresponding to the whole object is equal to the sum of the values of quantities corresponding to its parts for any division of the object into parts.
Adjunct - (Latin word adjunctus - “attached”). This is the same as algebraic complement.
Axiom - (Greek word axios- valuable; axioma - “acceptance of position”, “honor”, “respect”, “authority”). In Russian - since Peter's times. This is a basic proposition, a self-evident principle. T. is first found in Aristotle. Used in Euclid's Elements. An important role was played by the work of the ancient Greek scientist Archimedes, who formulated axioms related to the measurement of quantities. Contributions to axiomatics were made by Lobachevsky, Pash, Peano. A logically impeccable list of geometry axioms was indicated by the German mathematician Hilbert at the turn of the 19th and 20th centuries.
Axonometry - (from the Greek words akon - “axis” and metrio - “I measure”). This is one of the ways to depict spatial figures on a plane.
Algebra - (Arabic word "al-jabr"). This is a part of mathematics that develops in connection with the problem of solving algebraic equations. T. first appears in the work of the outstanding mathematician and astronomer of the 11th century, Muhammad ben Musa al-Khwarizmi.
Analysis - (Greek word analozis - “decision”, “resolution”). T. "analytic" goes back to Vieta, who rejected the word "algebra" as barbaric, replacing it with the word "analysis".
Analogy - (Greek word analogia - “correspondence”, “similarity”). This is an inference based on the similarity of particular properties of two mathematical concepts.
Antilogarithm - (Latin word nummerus - “number”). This number, which has a given table value of the logarithm, is denoted by the letter N.
Antier - (French word entiere - “whole”). This is the same as the integer part of a real number.
Apothem - (Greek word apothema, apo - “from”, “from”; thema - “attached”, “delivered”). 1. In a regular polygon, an apothem is a perpendicular segment dropped from its center to any of its sides, as well as its length. 2. In a regular pyramid, the apothem is the height of any of its side faces. 3. In a regular truncated pyramid, the apothem is the height of any of its side faces.
Applicata - (Latin word applicata - “attached”). This is one of the Cartesian coordinates of a point in space, usually the third, denoted by the letter Z.
Approximation - (Latin word approximo - “approximating”). Replacement of some mathematical objects with others, in one sense or another close to the original ones.
Function argument (Latin word argumentum – “object”, “sign”). This is an independent variable whose values determine the values of the function.
Arithmetic (Greek word arithmos - “number”). This is the science that studies operations with numbers. Arithmetic originated in the countries of Dr. East, Babylon, China, India, Egypt. Special contributions were made by: Anaxagoras and Zeno, Euclid, Eratosthenes, Diophantus, Pythagoras, L. Pisansky and others.
Arctangent, Arcsine (prefix “arc” - the Latin word arcus - “bow”, “arc”). Arcsin and arctg appear in 1772 in the works of the Viennese mathematician Schaeffer and the famous French scientist J.L. Lagrange, although they had already been considered somewhat earlier by D. Bernoulli, but who used different symbolism.
Asymmetry (Greek word asymmetria - “disproportion”). This is the absence or violation of symmetry.
Asymptote (Greek word asymptotes - “non-coincident”). This is a straight line to which the points of a certain curve approach indefinitely as these points move away to infinity.
Astroid (Greek word astron - “star”). Algebraic curve.
Associativity (Latin word associatio - “connection”). Combination law of numbers. T. was introduced by W. Hamilton (1843).
Billion (French word billion, or billion – milliard). This is a thousand million, a number represented by one followed by 9 zeros, i.e. number 10 9. In some countries, a billion is a number equal to 10 12.
Binom (Latin words bi - “double”, nomen - “name) is the sum or difference of two numbers or algebraic expressions, called members of a binomial.
Bisector (Latin words bis - “twice” and sectrix - “secant”). Borrowing In the 19th century from French language where bissecrice – goes back to lat. phrase. This is a straight line passing through the vertex of the angle and dividing it in half.
Vector (Latin word vector – “carrying”, “carrier”). This is a directed segment of a straight line, one end of which is called the beginning of the vector, the other end is called the end of the vector. This term was introduced by the Irish scientist W. Hamilton (1845).
Vertical angles (Latin word verticalis - “vertex”). These are pairs of angles with a common vertex, formed by the intersection of two straight lines so that the sides of one angle are a continuation of the sides of the other.
Hexahedron (Greek words geks - “six” and edra - “face”). This is a hexagon. This T. is attributed to the ancient Greek scientist Pappus of Alexandria (3rd century).
Geometry (Greek words geo – “Earth” and metreo – “I measure”). Old Russian borrowed from Greek The part of mathematics that studies spatial relationships and shapes. T. appeared in the 5th century BC. in Egypt, Babylon.
Hyperbole (Greek word hyperballo - “going through something”). Borrowing in the 18th century from lat. language This is an open curve of two unlimitedly extending branches. T. was introduced by the ancient Greek scientist Apollonius of Perm.
Hypotenuse (Greek word gyipotenusa - “contracting”). Deputy from lat. language in the 18th century, in which hypotenusa – from the Greek. the side of a right triangle that lies opposite the right angle. The ancient Greek scientist Euclid (3rd century BC) wrote instead of this term, “the side that subtends a right angle.”
Hypocycloid (Greek word gipo - “under”, “below”). The curve that a point on a circle describes.
Goniometry (Latin word gonio - “angle”). This is the study of "trigonometric" functions. However, this name did not catch on.
Homothety (Greek word homos - “equal”, “same”, thetos - “located”). This is an arrangement of figures that are similar to each other, in which the straight lines connecting the corresponding points of the figures intersect at the same point, called the center of homothety.
Degree (Latin word gradus - “step”, “step”). A unit of measurement for a plane angle equal to 1/90 of a right angle. The measurement of angles in degrees appeared more than 3 years ago in Babylon. Designations reminiscent of modern ones were used by the ancient Greek scientist Ptolemy.
Graph (Greek word graphikos - “inscribed”). This is a graph of a function - a curve on a plane depicting the dependence of the function on the argument.
Deduction (Latin word deductio - “deduction”). This is a form of thinking through which a statement is derived purely logically (according to the rules of logic) from some given statements - premises.
Deferents (Latin word defero - “carry”, “move”). This is the circle around which the epicycloids of each planet rotate. For Ptolemy, the planets rotate in circles - epicycles, and the centers of the epicycles of each planet rotate around the Earth in large circles - deferents.
Diagonal (Greek word dia - “through” and gonium - “angle”). This is a straight line connecting two vertices of a polygon that do not lie on the same side. T. is found in the ancient Greek scientist Euclid (3rd century BC).
Diameter (Greek word diametros - “diameter”, “through”, “measuring” and the word dia - “between”, “through”). T. “division” in Russian is first found in L.F. Magnitsky.
Directress (Latin word directrix - “director”).
Discreteness (Latin word discretus – “divided”, “discontinuous”). This is discontinuity; opposed to continuity.
Discriminant (Latin word discriminans - “discriminating”, “separating”). This is an expression made up of quantities defined by a given function, the reversal of which to zero characterizes one or another deviation of the function from the norm.
Distributivity (Latin word distributivus – “distributive”). Distributive law connecting addition and multiplication of numbers. T. was introduced by the French. scientist F. Servois (1815).
Differential (Latin word differento- “difference”). This is one of the basic concepts of mathematical analysis. This T. is found by the German scientist G. Leibniz in 1675 (published in 1684).
Dichotomy (Greek word dichotomia - “division in two”). Method of classification.
Dodecahedron (Greek words dodeka - “twelve” and edra - “base”). This is one of the five regular polyhedra. T. is first encountered by the ancient Greek scientist Theaetetus (4th century BC).
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