Mathematics curriculum in Poland Overview : fourth to sixth classes

Aims Broad objectives: Calculating skills Students make simple memory operations: addition, substraction, multiplication,division using the positive integers (whole numbers), integers and fractions. They know and use algorithms to make calculations. Students can use acquired concepts, skills and processes in real problem-solving situations. Making and using mathematical information Students interpret text, number and graphical information. They know the basic mathematical concepts and are able to explain the meaning of them. Students formulate answers and write the results in a correct way. Mathematical modelling Students adjust correct mathematical formulae to simple situations. Students explore, perceive, use and appreciate mathematical patterns in order to convert the text of the exercise into simple, arithmetic equation. Understanding and making of strategies Students use acquired simple concepts, establish the sequence of doings (including calculations) in the process of problem-solving. Students plan, monitor and evaluate solutions.They can also draw conclusions using different kind of information and facts provided or learnt.

The content of teaching- strands The positive integers in decimal system. The student : reads and writes the multi-digit integers (whole numbers) reads and writes the multi-digit integers (whole numbers) interprets the integers on a number line interprets the integers on a number line compares the integers compares the integers round whole numbers e.g round whole numbers to nearest ten, hundred, thousand round whole numbers e.g round whole numbers to nearest ten, hundred, thousand changes decimals up to 30 into Roman numerals and vice versa changes decimals up to 30 into Roman numerals and vice versa Whole number calculations The student: explores and identifies place value in whole numbers explores and identifies place value in whole numbers adds and substracts multi-digit numbers and solves simple problems adds and substracts multi-digit numbers and solves simple problems knows and recalls addition and subtraction facts knows and recalls addition and subtraction facts solves word problems involving addition and subtraction solves word problems involving addition and subtraction develops an understanding of multiplication as repeated addition and vice versa. develops an understanding of multiplication as repeated addition and vice versa. adds and subtracts whole numbers without and with a calculator adds and subtracts whole numbers without and with a calculator multiplies and divides integres by other whole numbers, without and with a calculator multiplies and divides integres by other whole numbers, without and with a calculator identifies whole numbers divided by 2, 3, 5, 9, 10, 100 identifies whole numbers divided by 2, 3, 5, 9, 10, 100 identifies and explores square and cube roots identifies and explores square and cube roots divides two-digit numbers into prime factors divides two-digit numbers into prime factors

The content of teaching- strands Directed numbers The student:  identifies positive and negative numbers in context  identifies positive and negative numbers on the number line  calculates the absolute value  compares directed numbers  makes simple memory calculations usind directed numbers Fractions and decimal fractions The student:  calculates a unit fraction of a number and calculates a number, given a unit fraction of the number  reduces or simplifies the fractions  finds common denominator to fractions  expresses improper fractions as mixed numbers and vice versa  rounds decimal fractions  adds and subtracts simple fractions and simple mixed numbers  compares and orders fractions and decimals  multiplies a fraction by a whole number and a fraction by a fraction  expresses tenths, hundredths and thousandths in both fractional and decimal form Fraction and decimal fraction calculations The student:  adds and subtracts whole numbers and decimals without and with a calculator  multiplies and divides a decimal by a whole number, without and with a calculator  makes simple calculations using fractions and decimal fractions  estimates the results of calculations  compares fractions differentially  identifies and explores square roots and cube roots of fractions  computes the integer fraction

The content of teaching- strands Elements of Algebra The student:  identifies positive and negative numbers in context  identifies positive and negative numbers on the number line  adds simple positive and negative numbers on the number line

The content of teaching- strands Straight lines and sections (lenghts) The student:  identifies, describes figures: point, straight,ray, length  identifies, describes and classifies vertical, horizontal and parallel lines  identifies, describes and classifies oblique and perpendicular lines  measures the length with an accuracy of 1 millimeter  knows if he wants to find the distance from a point to a line he must find the length of the perpendicular line Angles The student:  recognises, classifies and describes angles, their rays and vertex  measures angles less than 180 degrees with accuracy of 1 degree  draws an angle less than 180 degrees  classifies angles as acute, obtuse and right angles  estimates angle sizes  recognises and uses features of apex and adjacent angles

The content of teaching- strands 2-D shapes The student:  classifies and describes triangles and quadrilaterals  identifies, describes and classify 2-D shapes: equilateral, isosceles and scalene triangle, rectangle, parallelogram, rhombus, trapesoid  explores, describes and compares the properties (sides, angles, parallel and non-parallel lines) of 2-D shapes  identifies the properties of the circle: diameter, radius and chord circle  uses the assertion of the sum of angles in a triangle 3-D shapes The student:  identifies, describes and classifies 3-D shapes, including cube, cuboid, cylinder, cone, sphere, triangular prism, pyramid  recognises the nets of prisms and pyramids  draws the nets of simple 3-D shapes (prisms)

The content of teaching- strands Calculating area, length, and other geometric properties The student:  calculates the perimeter a polygon  calculates the area of the square, rhombus, parallelogram, triangle and trapezium presented on a drawing and in practical situations  estimates and measures length using appropriate metric units  calculates area using acres and hectares  estimates and measures capacity using appropriate metric units  calculates angle measures

The content of teaching- strands Practical calculations The student:  develops an understanding of simple percentages and relate them to fractions and decimals  solves problems involving operations with whole numbers, fractions, decimals and simple percentages  solves and completes practical tasks and problems involving times and dates  reads the temperature on the Celsius scale  renames the measures of weight and length  identifies given scale and draws items to a larger or smaller scale.  in the practical situation calculates the length of the road at a given speed and given time and so forth

The content of teaching- strands Elements of mathematical statistics The student:  compiles and uses simple data sets  uses charts, graphs and tables to read and interpret data Problem-solving activities The student:  reads with understanding a simple text which includes number information  can extract important information and data from the activity, makes auxiliary drafts before solving the operation  notices the relationship between the information and data provided  selects appropriate concepts, methods and techniques to apply to mathematical problems.  makes connections and begins to reason deductively in geometry, number and algebra, including using geometrical constructions  verifies the outcome of the execise, judging its meaningfulness