{"id":993,"date":"2016-08-15T20:33:00","date_gmt":"2016-08-15T20:33:00","guid":{"rendered":"http:\/\/timss2015.org\/encyclopedia\/countries\/serbia\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/"},"modified":"2016-10-06T20:55:24","modified_gmt":"2016-10-06T20:55:24","slug":"the-mathematics-curriculum-in-primary-and-lower-secondary-grades","status":"publish","type":"page","link":"http:\/\/timss2015.org\/encyclopedia\/countries\/serbia\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/","title":{"rendered":"The Mathematics Curriculum in Primary and Lower Secondary Grades"},"content":{"rendered":"<div class=\"carouselwrap\"><div id=\"menu-serbia\" class=\"carouselmenu\"><a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/serbia\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>Introduction<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/serbia\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>The Mathematics Curriculum in Primary and Lower Secondary Grades<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/serbia\/the-science-curriculum-in-primary-and-lower-secondary-grades\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>The Science Curriculum in Primary and Lower Secondary Grades<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/serbia\/teachers-teacher-education-and-professional-development\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>Teachers, Teacher Education, and Professional Development<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/serbia\/instruction-for-mathematics-and-science-in-primary-and-lower-secondary-grades\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>Instruction for Mathematics and Science in Primary and Lower Secondary Grades<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/serbia\/monitoring-student-progress-in-mathematics-and-science\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>Monitoring Student Progress in Mathematics and Science<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/serbia\/use-and-impact-of-timss\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>Use and Impact of TIMSS<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/serbia\/suggested-readings\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>Suggested Readings<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/serbia\/references\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>References<\/span><\/a><\/li>\n<\/div><\/div>\t<style>\n\t\t.carouselwrap{\n\t\t\tbackground: #e5eaef;\n\t\t}\t\t\n\t\t.owl-item a{\n\t\t\tbackground: #ffffff;\n\t\t\tborder: 4px #00b2cc solid;\n\t\t\tcolor: #000000;\n\t\t}\t\t\n\t\t.owl-item a:hover,\n\t\t.owl-item a:focus,\n\t\t.owl-item a.current-menu-item{\n\t\t\tbackground: #00667f;\n\t\t\tborder: 4px #00b2cc solid;\n\t\t\t\n\t\t\tcolor: #ffffff;\n\t\t}\n\t<\/style>\n\t\n<h2>The Mathematics Curriculum in Primary and Lower Secondary Grades<sup>a<\/sup><\/h2>\n<p>The goals of the mathematics curriculum for primary school are stated as follows: \u201cProviding students with basic mathematical knowledge and the ability to apply that knowledge to solving problems in everyday life; laying a foundation for continuing students\u2019 mathematical education and self-education; and developing students\u2019 mental abilities and their ability to form a scientific view of the world, as well as the overall development of their personality.\u201d<sup>13<\/sup><\/p>\n<p>In the curriculum, there are teaching objectives and operational tasks prescribed for each grade. It offers descriptions of knowledge and skills that students are expected to obtain by the end of each grade in primary school. Standards for achievement in mathematics are specified in four areas of knowledge\u2014Numbers and Operations, Geometry, Fractions, and Measuring and Measurements\u2014at three levels: basic, intermediate, and advanced.<sup>14<\/sup><\/p>\n<p>Standards for achievement in mathematics at the end of the second cycle of primary education also are specified at basic, intermediate, and advanced levels for each of the following areas: Numbers and Numerical Operations, Algebra and Functions, Geometry, and Measuring and Data Analysis.<sup>15<\/sup><\/p>\n<p>Exhibit 1 presents the competencies students are expected to attain in mathematics in Grades 1 to 8.<\/p>\n<p><strong>Exhibit 1: Mathematics Curriculum, Grades 1\u20138<\/strong><\/p>\n<table border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"100%\" class=\"tableEncyc\">\n<tr class=\"heading\">\n<td>\n      Grade Level <\/td>\n<td>\n      Competencies\n    <\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" class=\"headingInside borderBottom borderRight\" width=\"20%\">\n      Grades 1\u20134<sup style=\"font-weight:normal;\">16,17,18<\/sup>\n    <\/td>\n<td valign=\"top\" class=\"borderBottom\">\n<ul>\n<li>Understand   natural numbers including zero <\/li>\n<li>Perform   operations with natural numbers and understand numerical expressions   including equations and inequalities <\/li>\n<li>Identify   and measure geometric shapes<\/li>\n<li>Understand   the metric system, measure objects in the environment, and understand the   relationship between familiar units of measurement<\/li>\n<li>Solve   word problems with increasing levels of complexity<\/li>\n<li>Use   mathematical language, including basic symbols, expressions, and formulas<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" class=\"headingInside borderBottom borderRight\">\n      Grade 5<sup>19<\/sup>\n    <\/td>\n<td valign=\"top\" class=\"borderBottom\">\n<ul>\n<li>Create   and display sets and their subsets graphically; perform operations related to   sets; understand the meaning of &ldquo;and,&rdquo; &ldquo;or,&rdquo; &ldquo;no,&rdquo; &ldquo;every,&rdquo; and &ldquo;some&rdquo; in   mathematical contexts; and recognize familiar geometric objects (e.g., lines,   line segments, rays, planes, circles, and angles)<\/li>\n<li>Understand   the properties of angles formed by parallel lines and a transversal, and   angles formed in figures with parallel sides<\/li>\n<li>Draw   lines parallel to a given line<\/li>\n<li>Understand   the basic rules of divisibility and how to divide natural numbers<\/li>\n<li>Determine   the least common multiple and greatest common factor<\/li>\n<li>Understand   the concept of fractions, know how to write fractions in different ways,   convert fractions from one mode to another, compare fractions, and present   fractions on the number line<\/li>\n<li>Read,   compose, and calculate simple numerical expressions<\/li>\n<li>Solve   simple equations and inequalities with fractions<\/li>\n<li>Recognize   mathematical content in narrative form and express it in mathematical   language<\/li>\n<li>Understand   axial symmetry and its properties<\/li>\n<li>Identify   the center of a line segment<\/li>\n<li>Construct   angle bisectors and lines perpendicular to another line through a given point<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" class=\"headingInside borderBottom borderRight\">\n      Grade 6<sup>20<\/sup>\n    <\/td>\n<td valign=\"top\" class=\"borderBottom\">\n<ul>\n<li>Understand   negative numbers, the structure of the sets of integers and rational numbers,   and the absolute value of numbers<\/li>\n<li>Perform   basic arithmetic operations with integers and rational numbers<\/li>\n<li>Read   simple expressions containing rational numbers and calculate their numerical   value<\/li>\n<li>Solve   simple equations and inequalities on the set of rational numbers<\/li>\n<li>Express   percentages and use them in practice; classify triangles and rectangles and   know their basic properties; understand congruence and its properties, and   know how to apply it when constructing triangles and rectangles<\/li>\n<li>Calculate   the area of triangles, parallelograms, and rectangles<\/li>\n<li>Apply   rules for calculating the area of triangles and rectangles in a variety of   practical tasks<\/li>\n<li>Use   deductive reasoning (e.g., defining statements and using the words &ldquo;and,&rdquo;   &ldquo;or,&rdquo; &ldquo;if\u2026then\u2026,&rdquo; and &ldquo;if and only if\u2026&rdquo;)<\/li>\n<li>Understand   the need for presenting evidence in proofs and know how to do so in simple   cases<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" class=\"headingInside borderBottom borderRight\">\n      Grade 7<sup>21<\/sup>\n    <\/td>\n<td valign=\"top\" class=\"borderBottom\">\n<ul>\n<li>Understand   the concepts of squaring and finding square roots of rational numbers<\/li>\n<li>Find   the approximate value of the square root of a rational number<\/li>\n<li>Understand   the concept of exponentiation and operations with natural number exponents <\/li>\n<li>Perform   basic arithmetic operations with polynomials<\/li>\n<li>Understand   the rectangular coordinate system and its application<\/li>\n<li>Understand   direct and inverse proportionality and its practical application<\/li>\n<li>Understand   the Pythagorean theorem and how to apply it to geometric figures that contain   a right triangle<\/li>\n<li>Recognize   the most important properties of polygons and circles<\/li>\n<li>Construct   regular polygons with 3, 4, 6, 8, and 12 sides and draw other regular   polygons<\/li>\n<li>Recognize   central angles and draw them using a protractor; understand the most   important properties of polygons and circles and apply them in problems<\/li>\n<li>Understand   the concepts of scale and proportion<\/li>\n<li>Translate   word problems into mathematical language and solve them<\/li>\n<li>Use   elements of deductive reasoning in simple proofs<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" class=\"headingInside borderBottom borderRight\">\n      Grade 8<sup>22<\/sup>\n    <\/td>\n<td valign=\"top\" class=\"borderBottom\">\n<ul>\n<li>Solve   linear equations (including inequalities) and systems of linear equations in   one or two unknowns and interpret solutions graphically<\/li>\n<li>Represent   word problems using mathematical language and solve them<\/li>\n<li>Identify   functional dependencies and display them in different ways<\/li>\n<li>Understand   the concept of functions and graphical representations of functions<\/li>\n<li>Understand   linear functions and their properties <\/li>\n<li>Draw   and interpret linear functions<\/li>\n<li>Interpret   data presented in graphs and tables<\/li>\n<li>Construct   a table and draw appropriate graphs and diagrams from the data <\/li>\n<li>Calculate   the median of a data set<\/li>\n<li>Understand   the relationships among points, lines, and planes in space<\/li>\n<li>Understand   projections in a plane and the elements and properties of solid figures   (e.g., prism, pyramid, cylinder, cone, and sphere)<\/li>\n<li>Calculate   the surface area and volume of a solid figure<\/li>\n<li>Apply   knowledge of solid figures in practice, linking the content of mathematics   and other areas<\/li>\n<li>Apply   elements of deductive reasoning in proofs<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>The Mathematics Curriculum in Primary and Lower Secondary Gradesa The goals of the mathematics curriculum for primary school are stated as follows: \u201cProviding students with basic mathematical knowledge and the ability to apply that knowledge to solving problems in everyday &hellip; <a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/serbia\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/\">Continued<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":166,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"1"},"class_list":["post-993","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/993","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/comments?post=993"}],"version-history":[{"count":9,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/993\/revisions"}],"predecessor-version":[{"id":6858,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/993\/revisions\/6858"}],"up":[{"embeddable":true,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/166"}],"wp:attachment":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/media?parent=993"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}