{"id":651,"date":"2016-08-15T20:32:57","date_gmt":"2016-08-15T20:32:57","guid":{"rendered":"http:\/\/timss2015.org\/encyclopedia\/countries\/chile\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/"},"modified":"2016-10-17T14:48:49","modified_gmt":"2016-10-17T14:48:49","slug":"the-mathematics-curriculum-in-primary-and-lower-secondary-grades","status":"publish","type":"page","link":"http:\/\/timss2015.org\/encyclopedia\/countries\/chile\/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-chile\" class=\"carouselmenu\"><a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/chile\/\" 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\/chile\/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\/chile\/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\/chile\/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\/chile\/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\/chile\/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\/chile\/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\/chile\/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\/chile\/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>The current mathematics curriculum for fourth grade was implemented in 2012,<sup>9<\/sup> and the curriculum for eighth grade was implemented in 2013;<sup>10<\/sup> TIMSS 2015 was administered in Chile in 2014. Exhibits 1 and 2 present the content areas and fundamental objectives of the mathematics curriculum for Grades 4 and 8.<\/p>\n<p><strong>Exhibit 1: Mathematics Curriculum, Grade 4<\/strong><\/p>\n<table class=\"tableEncyc\" border=\"0\" width=\"100%\">\n<tbody>\n<tr class=\"heading\">\n<td>Content Area<\/td>\n<td>Fundamental Objectives<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight headingInside\" valign=\"top\">Numbers and Operations<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Represent and describe numbers from 0 to 10,000<\/li>\n<li>Describe and apply mental arithmetic strategies<\/li>\n<li>Demonstrate understanding of addition and subtraction up to 1,000<\/li>\n<li>Apply the properties of 0 and 1 for multiplication and the property of 1 for division<\/li>\n<li>Demonstrate understanding of the multiplication of three-digit numbers by one-digit numbers<\/li>\n<li>Demonstrate understanding of division with double-digit dividends and single-digit divisors<\/li>\n<li>Solve routine and non-routine problems in everyday contexts that involve money, selecting and using the proper operations<\/li>\n<li>Demonstrate understanding of fractions with denominators 100, 12, 10, 8, 6, 5, 4, 3, and 2<\/li>\n<li>Add and subtract fractions with the same denominator (100, 12, 10, 8, 6, 5, 4, 3, and 2) in concrete and pictorial ways in a problem solving context<\/li>\n<li>Identify, describe, and represent proper fractions and mixed numbers up to 5 in concrete, pictorial, and symbolic ways, in a problem solving context<\/li>\n<li>Describe and represent decimals (tenths and hundredths)<\/li>\n<li>Add and subtract decimals (with place value to the hundredth) in a problem solving context<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight headingInside\" valign=\"top\">Algebra and Patterns<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Identify and describe number patterns in tables that involve an operation, manually and\/or using educational software<\/li>\n<li>Solve equations and inequalities for values from 0 to 100 in one step, using addition and subtraction, checking the results in a pictorial and symbolic manner,\u00a0 and applying the inverse operation (addition or subtraction)<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight headingInside\" valign=\"top\">Geometry<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Describe the absolute location of an object on a simple map with informal coordinates (e.g., with letters and numbers) and the relative location in relation to other objects<\/li>\n<li>Determine the views of three-dimensional figures from the front, the side, and above<\/li>\n<li>Demonstrate understanding of line of symmetry<\/li>\n<li>Move, rotate, and mirror two-dimensional figures<\/li>\n<li>Construct angles using a protractor and compare them<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight headingInside\" valign=\"top\">Measuring<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Read and record various time measurements on analog and digital clocks, using the concepts of a.m., p.m., and 24 hours<\/li>\n<li>Convert among units of time in the context of problem solving (i.e., the number of seconds in a minute, the number of minutes in an hour, the number of days in a month, and the number of months in a year)<\/li>\n<li>Measure length in standardized units (m, cm) and convert between units (e.g., from m to cm and vice versa) in the context of problem solving<\/li>\n<li>Demonstrate understanding of the concept of area of rectangles and squares<\/li>\n<li>Demonstrate understanding of the concept of volume<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight headingInside\" valign=\"top\">Data and Probabilities<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Conduct surveys, analyze the data, and compare with the results of random tests, using charts and graphs<\/li>\n<li>Perform randomized experiments, tabulate the results, and represent them in graphs constructed manually and\/or using educational software<\/li>\n<li>Read and interpret pictographs and simple bar graphs with scale, and report findings<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Exhibit 2: Mathematics Curriculum, Grade 8<\/strong><\/p>\n<table class=\"tableEncyc\" border=\"0\" width=\"100%\">\n<tbody>\n<tr class=\"heading\">\n<td>Content Area<\/td>\n<td>Fundamental Objectives<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight headingInside\" valign=\"top\">Numbers<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Demonstrate understanding of multiplication and division of integers\n<ul class=\"subitem\">\n<li>Represent them in concrete, pictorial, and symbolic ways<\/li>\n<li>Apply procedures used in multiplication and division of natural numbers<\/li>\n<li>Apply the rule of order of operations<\/li>\n<li>Solve routine and nonroutine problems<\/li>\n<\/ul>\n<\/li>\n<li>Use multiplication and division of rational numbers in the context of problem solving\n<ul class=\"subitem\">\n<li>Represent them on the number line<\/li>\n<li>Use different number sets (fractions, decimals, and integers)<\/li>\n<\/ul>\n<\/li>\n<li>Explain multiplication, division, and the process of forming powers of numbers with natural number bases and\u00a0 exponents up to 3, in concrete, pictorial, and symbolic ways<\/li>\n<li>Demonstrate understanding of the square roots of natural numbers\n<ul class=\"subitem\">\n<li>Estimate them intuitively<\/li>\n<li>Represent them in concrete, pictorial, and symbolic ways<\/li>\n<li>Apply them in geometrical situations and in daily life<\/li>\n<\/ul>\n<\/li>\n<li>Solve problems involving percent changes in different contexts, using pictorial representations and recording the process symbolically (e.g., annual savings interest)<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight headingInside\" valign=\"top\">Algebra and Functions<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Demonstrate understanding of operations and algebraic expressions\n<ul class=\"subitem\">\n<li>Represent them in pictorial and symbolic ways<\/li>\n<li>Relate them to the area of squares and rectangles and the volume of parallelepipeds<\/li>\n<li>Determine factored forms<\/li>\n<\/ul>\n<\/li>\n<li>Demonstrate understanding of the concept of function in terms of linear change\n<ul class=\"subitem\">\n<li>Use tables<\/li>\n<li>Use machine metaphors<\/li>\n<li>Establish rules for <span class=\"formulas\">x<\/span>\u00a0and <span class=\"formulas\">y<\/span><\/li>\n<li>Graph them manually and\/or by using educational software (e.g., Cartesian plane, Venn diagrams)<\/li>\n<\/ul>\n<\/li>\n<li>Model situations in everyday life and in other academic subjects, using linear equations of the form <span class=\"formulas\">ax = b ;<\/span><span class=\"formulas\"><span class=\"fraction\"><span class=\"fup\">x<\/span><span class=\"bar\">\/<\/span><span class=\"fdn\">a<\/span><\/span> = b ;<\/span><span class=\"formulas\">a \u2260 0;<\/span><span class=\"formulas\">ax + b = c ;<\/span><span class=\"formulas\"><span class=\"fraction\"><span class=\"fup\">x<\/span><span class=\"bar\">\/<\/span><span class=\"fdn\">a<\/span><\/span> + b = c ;<\/span><span class=\"formulas\">x = b + cx ;<\/span> <span class=\"formulas\">a(x + b) = c ;<\/span><span class=\"formulas\">ax + b = cx + d (a, b, c, d, e) <\/span><\/li>\n<li>Solve linear inequalities with rational coefficients in the context of problem solving, using graphic representations and symbolic representations, generated manually and\/or by using educational software<\/li>\n<li>Demonstrate understanding of affine functions:\n<ul class=\"subitem\">\n<li>Generalize as the sum of a constant with a linear function<\/li>\n<li>Move linear functions in the Cartesian plane<\/li>\n<li>Determine the constant change from one interval to another, graphically and symbolically, manually and\/or by using educational software<\/li>\n<li>Link them to simple interest<\/li>\n<li>Use them to solve everyday life problems and in other academic subjects<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight headingInside\" valign=\"top\">Geometry<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Develop formulas for finding the surface area and volume of prisms with different bases and cylinders\n<ul class=\"subitem\">\n<li>Estimate surface area and volume<\/li>\n<li>Use nets to find the surface area of prisms<\/li>\n<li>Apply the formula for volume of a cube (base height) to different prisms and cylinders<\/li>\n<li>Apply these formulas to geometric problems and problem solving in daily life<\/li>\n<\/ul>\n<\/li>\n<li>Explain in concrete, pictorial, and symbolic ways the validity of the Pythagorean theorem, and apply the theorem to geometric problems and solving problems in daily life, manually and\/or by using educational software<\/li>\n<li>Describe the position and transformations (i.e., translations, rotations, and reflections) of two-dimensional figures in a coordinate plane, manually and\/or by using educational software, involving:\n<ul class=\"subitem\">\n<li>Vectors used in translations<\/li>\n<li>The axes of the Cartesian plane (e.g., lines of reflection)<\/li>\n<li>Points in a plane of rotation<\/li>\n<\/ul>\n<\/li>\n<li>Perform rotations, translations, and reflections in the Cartesian plane and in space, manually and\/or by using educational software; apply these transformations to the lines of symmetry of polygons and polyhedra, and in geometric problems related to art<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight headingInside\" valign=\"top\">Probability and Statistics<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Demonstrate an understanding of statistical measures of position (i.e., percentiles and quartiles)\n<ul class=\"subitem\">\n<li>Identify the population above or below the percentile<\/li>\n<li>Represent them in diagrams, manually and\/or by using educational software<\/li>\n<li>Use them to compare populations<\/li>\n<\/ul>\n<\/li>\n<li>Evaluate the way data is presented\n<ul class=\"subitem\">\n<li>Compare information from the same data set displayed in different types of graphs to determine the strengths and weaknesses of each<\/li>\n<li>Justify the choice of graph for a given situation and its corresponding data set<\/li>\n<li>Detect manipulation of graphics to represent data<\/li>\n<\/ul>\n<\/li>\n<li>Explain the multiplication principle of probability\n<ul class=\"subitem\">\n<li>In specific situations<\/li>\n<li>Represent it in regular tables and trees, generated manually and\/or by using educational software<\/li>\n<li>Use it to calculate the probability of compound events<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>The Mathematics Curriculum in Primary and Lower Secondary Grades The current mathematics curriculum for fourth grade was implemented in 2012,9 and the curriculum for eighth grade was implemented in 2013;10 TIMSS 2015 was administered in Chile in 2014. Exhibits 1 &hellip; <a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/chile\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/\">Continued<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":116,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-651","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/651","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=651"}],"version-history":[{"count":28,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/651\/revisions"}],"predecessor-version":[{"id":6899,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/651\/revisions\/6899"}],"up":[{"embeddable":true,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/116"}],"wp:attachment":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/media?parent=651"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}