{"id":669,"date":"2016-08-15T20:32:57","date_gmt":"2016-08-15T20:32:57","guid":{"rendered":"http:\/\/timss2015.org\/encyclopedia\/countries\/croatia\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/"},"modified":"2016-10-06T20:19:09","modified_gmt":"2016-10-06T20:19:09","slug":"the-mathematics-curriculum-in-primary-and-lower-secondary-grades","status":"publish","type":"page","link":"http:\/\/timss2015.org\/encyclopedia\/countries\/croatia\/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-croatia\" class=\"carouselmenu\"><a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/croatia\/\" 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\/croatia\/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\/croatia\/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\/croatia\/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\/croatia\/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\/croatia\/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\/croatia\/special-initiatives-in-mathematics-and-science-education\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>Special Initiatives in Mathematics and Science Education<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/croatia\/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\/croatia\/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\/croatia\/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<\/h2>\n<p>In 2005, the MSES began to implement a school reform project known as the Croatian National Education Standard <em>(Hrvatski nacionalni obrazovni standard)<\/em>,<sup>6<\/sup> after which the Syllabus for Primary School <em>(Nastavni plan i program za osnovnu \u0161kolu)<\/em><sup>7<\/sup> was designed and implemented in August 2006. The syllabus contains the educational work plan for subjects in Grades 1 to 8. It is not presented in the form of a curriculum, but as a catalog, with education goals enumerated separately for each subject, grade, and teaching unit.<\/p>\n<p>According to the syllabus, students should be able to do the following by the end of fourth grade:<\/p>\n<ul>\n<li>Number\n<ul class=\"subitem\">\n<li>Whole numbers\u2014Add, subtract, and compare whole numbers up to 1 million; demonstrate knowledge of place values; find values on a number line; add and subtract using a number line; differentiate between natural and ordinal numbers; estimate and round two-digit numbers to the nearest 10<sup class=\"nonSup\">th<\/sup>; recognize multiples and factors of numbers; learn the multiplication table up to 10 \u00d7 10; multiply a two-digit number by 100; divide multiples of 100 by 100; multiply a two-digit number by a number with more than two digits; divide a number of three or more digits by a two-digit number; perform operations with and without brackets; perform money calculations (in <em>kuna<\/em> and <em>lipa<\/em>); know units for measuring liquid (deciliter and liter) and convert between them; know units for measuring mass (gram, dekagram, and kilogram) and convert between them; and learn basic algebraic terms, and that letters represent numbers in algebraic equations<\/li>\n<li>Fractions and decimals\u2014Use words to express fractions (e.g., one-third of an apple, or 5 is half of 10) and divide with a remainder<\/li>\n<li>Number sentences with whole numbers\u2014Solve word problems and simple equations<\/li>\n<li>Patterns and relationships\u2014Find a missing term in a sequence<\/li>\n<\/ul>\n<\/li>\n<li>Geometric Shapes and Measures\n<ul class=\"subitem\">\n<li>Points, lines, and angles\u2014Differentiate among and draw flat, curved, and broken lines; draw and label lengths, and mark terminal points of lines; draw horizontal and vertical lines; draw straight lines that intersect and determine their point of intersection; differentiate between points that belong to a line and points that do not; recognize and draw right, acute, and obtuse angles; use informal coordinate systems (square grids) to locate points on a plane; draw circles with a compass<\/li>\n<li>Two- and three-dimensional shapes\u2014Identify two-dimensional geometric shapes (circle, triangle, rectangle, and square); identify three-dimensional geometric shapes (sphere, cylinder, cube, parallelepiped, and pyramid); draw and identify triangles according to shape (scalene, isosceles, and equilateral); draw right triangles; measure the perimeter of triangles; measure the perimeter and area of rectangles and squares; know units of area (cm<sup class=\"nonSup\">2<\/sup>, dm<sup class=\"nonSup\">2<\/sup>, and m<sup class=\"nonSup\">2<\/sup>); use a square grid to measure area; estimate area and volume; calculate the volume of cubes and parallelepipeds; and know units of volume (cm<sup class=\"nonSup\">3<\/sup> and dm<sup class=\"nonSup\">3<\/sup>)<\/li>\n<li>Data display\u2014Read, interpret, organize, and represent data in simple tables, compare information from bar graphs, and draw conclusions from data<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>By the end of eighth grade, students should be able to do the following:<\/p>\n<ul>\n<li>Number\n<ul class=\"subitem\">\n<li>Whole numbers\u2014Compare, round, add, subtract, multiply, and divide whole numbers; find numbers on a number line; determine the absolute value of a whole number; write, read, compare, add, subtract, and multiply natural numbers larger than 1 million; divide by two-digit numbers; use the commutative, associative, and distributive properties of multiplication; know the properties of divisibility; determine common multiples; use pocket calculators; and find square roots using a calculator<\/li>\n<li>Fractions and decimals\u2014Find fractions, decimals, and rational numbers on a number line; compare, add, subtract, multiply, and divide fractions; write equivalent fractions; convert fractions to mixed numbers; understand decimal places; compare, round, add, subtract, multiply, and divide decimals; convert decimal numbers to decimal fractions and vice versa; and write rational numbers as fractions and decimal numbers and compare them<\/li>\n<li>Integers\u2014Differentiate between positive and negative integers; find integers on a number line; compare, add, subtract, multiply, and divide integers; and determine the absolute value of an integer<\/li>\n<li>Ratio, proportion, and percent\u2014Recognize proportional quantities and apply ratios and proportionality in simple everyday situations; present proportionality graphically; calculate percentages; and determine interest<\/li>\n<\/ul>\n<\/li>\n<li>Algebra\u2014Solve simple mathematical formulas and expressions containing one variable; solve simple linear equations and simple two-variable systems of two linear equations, and use substitution to verify the accuracy of solutions; substitute numerical values for variables in formulas and calculate the value of remaining variables; present simple numerical relationships (e.g., linear, pure quadratic, and square root) using appropriate vocabulary, associated value tables, equations, and graphics; convert simple word problems into algebraic notation (e.g., numerical sentences, linear equations, and systems of two linear equations), plan and execute solutions, and understand their significance; solve equations graphically and algebraically; graph linear functions; calculate with exponents; and perform calculations using scientific notation<\/li>\n<li>Geometry\u2014Measure and draw angles; construct angles using the properties of angle bisectors; identify, create, compare, and classify two-dimensional and three-dimensional geometric shapes, and recognize and describe their geometrical properties, including translation, axis symmetry, central symmetry, and rotation; recognize congruence, similarity, and symmetry in two-dimensional and three-dimensional forms; apply Thales\u2019 theorem for right angles inscribed in circles; apply the Pythagorean theorem as it relates to the measurable features of squares, rectangles, equilateral triangles, isosceles triangles, rhombuses, and trapezoids; use the Cartesian coordinate system and read the coordinates of points in the system; determine perpendicular lines and planes; and apply formulas to determine length, area, surface area, perimeter, and volume<\/li>\n<li>Data and Chance\u2014Collect, classify, and interpret data using tables, frequency diagrams, bar graphs, and pie charts; determine the number of possible and favorable outcomes in simple situations; apply the terminology of probability; draw frequency and relative frequency histograms and find the arithmetic mean, median, quartiles, mode, range, and interquartile range of a series of numerical data; and calculate the probabilities of random events and explain them as relative frequencies<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>The Mathematics Curriculum in Primary and Lower Secondary Grades In 2005, the MSES began to implement a school reform project known as the Croatian National Education Standard (Hrvatski nacionalni obrazovni standard),6 after which the Syllabus for Primary School (Nastavni plan &hellip; <a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/croatia\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/\">Continued<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":118,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-669","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/669","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=669"}],"version-history":[{"count":12,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/669\/revisions"}],"predecessor-version":[{"id":6845,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/669\/revisions\/6845"}],"up":[{"embeddable":true,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/118"}],"wp:attachment":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/media?parent=669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}