{"id":1119,"date":"2016-08-15T20:33:01","date_gmt":"2016-08-15T20:33:01","guid":{"rendered":"http:\/\/timss2015.org\/encyclopedia\/benchmarking-participants\/quebec-canada\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/"},"modified":"2016-10-18T19:52:16","modified_gmt":"2016-10-18T19:52:16","slug":"the-mathematics-curriculum-in-primary-and-lower-secondary-grades","status":"publish","type":"page","link":"http:\/\/timss2015.org\/encyclopedia\/benchmarking-participants\/quebec-canada\/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-quebec-canada\" class=\"carouselmenu\"><a href=\"http:\/\/timss2015.org\/encyclopedia\/benchmarking-participants\/quebec-canada\/\" 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\/benchmarking-participants\/quebec-canada\/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\/benchmarking-participants\/quebec-canada\/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\/benchmarking-participants\/quebec-canada\/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\/benchmarking-participants\/quebec-canada\/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\/benchmarking-participants\/quebec-canada\/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\/benchmarking-participants\/quebec-canada\/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\/benchmarking-participants\/quebec-canada\/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\/benchmarking-participants\/quebec-canada\/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\/benchmarking-participants\/quebec-canada\/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>Mathematics is a compulsory subject in Qu\u00e9bec throughout elementary and secondary school.<sup>1,2,3,4<\/sup> The mathematics programs comprise prescribed concepts and processes. The concepts are grouped by cycle in the three cycles of elementary school and in Secondary Cycle I, and by year for each of the three years of Secondary Cycle II. Three learning profiles or \u201coptions\u201d are available to students in Secondary IV and V: the Cultural, Social, and Technical option, the Technical and Scientific option, and the Science option. Students who wish to pursue studies in science or certain technical training programs in college (i.e., the 12th and 13th years of study) must complete the appropriate option.<\/p>\n<p>Learning mathematics enables students to:<\/p>\n<ul>\n<li>Use mathematical reasoning to make conjectures and to criticize, justify, or refute a proposition by drawing on an organized body of mathematical knowledge<\/li>\n<li>Communicate (i.e., interpret, produce, and convey) messages in contexts in which the subject and purpose of the message, as well as the target audience, play a significant role<\/li>\n<li>Solve situational problems by using various strategies for understanding, organizing, solving, validating, and communicating<\/li>\n<\/ul>\n<p>Thus, students develop their ability to interpret reality, anticipate, generalize, and make decisions in a changing world.<\/p>\n<p>Exhibits 1 and 2 present the mathematics content objectives for Elementary Cycle II (Grade 4) and Secondary Cycle I (Grade 8) in Qu\u00e9bec.<\/p>\n<p><strong>Exhibit 1: Mathematics Content Objectives for Elementary Cycle II (Grade 4) in Qu\u00e9bec <\/strong><\/p>\n<table class=\"tableEncyc\" border=\"0\" width=\"100%\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr class=\"heading\">\n<td>Content Area<\/td>\n<td>Main Topics<\/td>\n<td>Content Objectives<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside borderRight\" rowspan=\"3\" valign=\"top\">Arithmetic<\/td>\n<td class=\"borderRight borderBottom\" valign=\"top\">Understanding and writing numbers<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Natural numbers less than 100,000\u2014Reading, writing, counting, representing, comparing, classifying, ordering numbers, writing equivalent expressions, writing numbers in expanded form, writing patterns, understanding properties (e.g., even and odd numbers, squares, prime numbers, and compound numbers), and estimating values<\/li>\n<li>Fractions based on a whole or a collection of objects\u2014Reading, writing, and understanding numerator, denominator, various representations (using objects or pictures), equivalent parts, isometric parts, and comparison with 0, \u00bd, and 1<\/li>\n<li>Decimals up to two decimal places\u2014Reading, writing, understanding various representations, ordering, writing equivalent expressions, writing numbers in expanded form, comparing, and estimating<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderRight borderBottom\" valign=\"top\">Meaning of operations involving numbers<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Natural numbers and decimals\u2014Choice of operation and operation sense (addition, subtraction, multiplication, division); meaning of an equality relation; meaning of an equivalence relation; relationships between the operations (addition, subtraction); properties of operations (commutative law, associative law)<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderRight borderBottom\" valign=\"top\">Operations involving numbers<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Natural numbers\u2014Approximating operation results, acquiring processes for mental computation, and memorizing operations (addition, subtraction); acquiring conventional processes for written computation (i.e., adding two 4-digit numbers and subtracting a 4-digit number from a 4-digit number such that the difference is greater than 0); acquiring processes for written computation (i.e., multiplying a three-digit number by a one-digit number and dividing a three-digit number by a one-digit number); and working with patterns<\/li>\n<li>Decimals\u2014Written computation (i.e., addition and subtraction where the result does not go beyond the second decimal place)<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside borderRight\" rowspan=\"4\" valign=\"top\">Geometry<\/td>\n<td class=\"borderRight borderBottom\" valign=\"top\">Space<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Locating objects on an axis<\/li>\n<li>Locating objects in a plane<\/li>\n<li>Locating objects in a Cartesian plane<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderRight borderBottom\" valign=\"top\">Solids<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Comparing, constructing, and identifying spheres, cones, cubes, cylinders, prisms, and pyramids<\/li>\n<li>Describing prisms and pyramids in terms of faces, vertices, and edges<\/li>\n<li>Classifying prisms and pyramids and using nets for prisms and pyramids<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderRight borderBottom\" valign=\"top\">Plane figures<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Comparing, identifying, and describing squares, rectangles, triangles, rhombuses, trapezoids, parallelograms, and circles<\/li>\n<li>Describing convex and non-convex polygons<\/li>\n<li>Describing and classifying quadrilaterals (e.g., parallel segments, perpendicular segments, right angles, acute angles, obtuse angles, and congruent sides)<\/li>\n<li>Identifying and constructing parallel lines and perpendicular lines<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderRight borderBottom\" valign=\"top\">Frieze patterns and tessellations<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Identifying congruent figures<\/li>\n<li>Observing and producing patterns using geometric figures<\/li>\n<li>Observing and producing frieze patterns and tessellations by means of reflections<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside borderRight\" rowspan=\"5\" valign=\"top\">Measurement<\/td>\n<td class=\"borderRight borderBottom\" valign=\"top\">Length<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Estimating and measuring\u00a0 with conventional units (e.g., m, dm, cm, mm)<\/li>\n<li>Understanding relationships among units of measurement (e.g., m, dm, cm, mm)<\/li>\n<li>Calculating perimeter<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderRight borderBottom\" valign=\"top\">Surface area<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Estimating and measuring with unconventional units<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderRight borderBottom\" valign=\"top\">Volume<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Estimating and measuring with unconventional units<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderRight borderBottom\" valign=\"top\">Angles<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Comparing angles (e.g., right, acute, and obtuse)<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderRight borderBottom\" valign=\"top\">Time<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Estimating and measuring time and duration with conventional units (e.g., day, hour, minute, second, daily cycle, weekly cycle, and yearly cycle)<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside borderRight\" valign=\"top\">Probability and Statistics<\/td>\n<td class=\"borderRight borderBottom\" valign=\"top\"><\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Enumerating the possible outcomes of simple random experiments<\/li>\n<li>Interpreting and displaying data using data tables, bar graphs, pictographs, and broken-line graphs<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Exhibit 2: Mathematics Content Objectives for Secondary Cycle I (Grade 8) in Qu\u00e9bec<\/strong><\/p>\n<table class=\"tableEncyc\" border=\"0\" width=\"100%\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr class=\"heading\">\n<td>Content Area<\/td>\n<td>Main Topics<\/td>\n<td>Content Objectives<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside borderRight\" rowspan=\"2\" valign=\"top\">Arithmetic<\/td>\n<td class=\"borderBottom borderRight\" valign=\"top\">Number sense with regard to decimal and fractional notation and operation sense<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Reading, writing, various representations, patterns, and properties of numbers\u2014Order of magnitude, comparison of numbers, and decomposition of numbers (e.g., additive and multiplicative)<\/li>\n<li>Fractional, decimal, and exponential (integral exponent) notation, percentage, and square root\u2014Recognizing the different meanings of fractions (e.g., part of a whole, division, ratio, operator, and measurement), switching from one way of writing numbers to another, and simplifying and reducing fractions<\/li>\n<li>Approximation (i.e., estimating, rounding off, and truncating)<\/li>\n<li>Properties of divisibility\u2014Determining the divisibility of a number (by 2, 3, 4, 5, 6, 8, 9, and 10) and using properties of divisibility (by 2, 3, 4, 5, and 10) in different situations<\/li>\n<li>Rules of signs for numbers written in decimal notation<\/li>\n<li>Equality relations: meaning, properties, and rules for transforming numerical equalities (balancing equalities)\n<ul>\n<li>Transforming arithmetic equalities<\/li>\n<\/ul>\n<\/li>\n<li>Inverse operations: addition, subtraction, multiplication, and division, and square and square root\u2014Expressing situations using operations; mental computation with numbers written in decimal notation; written computation with numbers written in decimal notation or with positive numbers written in fractional notation<\/li>\n<li>Properties of operations\u2014Commutative and associative properties, distributive property of multiplication over addition or subtraction, and factoring out the common factor; and simplifying the terms of an operation<\/li>\n<li>Order of operations and the use of no more than two levels of parentheses in different contexts<\/li>\n<li>Locating numbers on a number line or in a Cartesian plane<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Understanding proportionality<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Ratio and rate\u2014Ratios and equivalent rates; unit rate; comparison of ratios and rates; and expressing situations using ratio or rate<\/li>\n<li>Proportion\u2014Equality of ratios and rates; ratios and coefficients of proportionality; recognizing and solving proportional situations by referring to their context, tables of values, or graphs<\/li>\n<li>Percentage\u2014Finding a specified percentage of a number and values corresponding to 100 percent<\/li>\n<li>Variation\u2014Direct and inverse<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside borderRight\" rowspan=\"4\" valign=\"top\">Geometry<\/td>\n<td class=\"borderRight\" valign=\"top\">Geometric figures and spatial sense<sup>a<\/sup><\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Plane figures<\/li>\n<li>Triangles, quadrilaterals, and regular convex polygons\u2014Segments and lines (e.g., bisector, perpendicular bisector, median, altitude, base, and height)<\/li>\n<li>Circles and sectors\u2014Radius, diameter, chord, arc, and central angle<\/li>\n<li>Measurement\u2014Degree (angle and arc), length, perimeter, circumference, area, lateral area, total area, choice of unit of measurement for length and area, and relationship between SI units of length and SI units of area<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderRight\" valign=\"top\"><\/td>\n<td class=\"borderBottom \" valign=\"top\">\n<ul>\n<li>Angles\u2014Complementary and supplementary; angles formed by two intersecting lines (e.g., vertically opposite and adjacent); and angles formed by a transversal intersecting two other lines (e.g., alternate interior, alternate exterior, and corresponding)<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderRight\" valign=\"top\"><\/td>\n<td class=\"borderBottom \" valign=\"top\">\n<ul>\n<li>Solids\u2014Right prisms, right pyramids, and right cylinders; using possible nets of solids to calculate surface area; and decomposable solids<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\"><\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Congruent and similar figures\u2014Translation, rotation, reflection, and dilatation<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside borderRight\" rowspan=\"2\" valign=\"top\">Algebra<\/td>\n<td class=\"borderBottom borderRight\" valign=\"top\">Understanding algebraic expressions<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Algebraic expressions\u2014Understanding variables, coefficients, degrees, terms, and like terms; constructing and interpreting algebraic expressions; finding equivalent algebraic expressions; and performing numerical evaluation of algebraic expressions<\/li>\n<li>Operations on algebraic expressions\u2014Addition, subtraction, multiplication of first-degree monomials, and division by a constant<\/li>\n<li>Equality, equations, and unknowns<\/li>\n<li>First-degree equations with one unknown expressed in the form <span class=\"formulas\">ax+b=cx+d<\/span><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Dependence between variables<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Analyzing situations using different types of representation (e.g., graphs, tables of values, words, etc.); and representing situations using graphs<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside borderRight\" rowspan=\"4\" valign=\"top\">Probability<\/td>\n<td class=\"borderBottom borderRight\" valign=\"top\">Random experiments<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Random experiments involving one or more steps (with or without replacement and with or without order); enumerating possible outcomes of random experiments using different types of representations (e.g., tree diagrams, networks, tables, and Venn diagrams); and sample spaces<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Events<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Certain, probable, and impossible events; simple, complementary, compatible, incompatible, dependent, and independent events; calculating the probability of an event; and interpreting probabilities<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Types of probability<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Theoretical probability and experimental probability<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Interpretation<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Interpreting the resulting probabilities<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside borderRight\" valign=\"top\">Statistics<\/td>\n<td class=\"borderBottom borderRight\" valign=\"top\">Statistical reports<\/td>\n<td class=\"borderBottom\" valign=\"top\">\n<ul>\n<li>Population and sample\u2014Sample surveys, polls, and censuses; representative samples; sampling methods (e.g., simple random and systematic); and sources of bias<\/li>\n<li>Data\u2014Gathering data, qualitative variables, discrete or continuous quantitative variables, comparing distributions, minimum and maximum, arithmetic mean, and range<\/li>\n<li>Tables\u2014Characteristics, population, and frequencies<\/li>\n<li>Reading and drawing graphs\u2014Bar graphs, broken-line graphs, and circle graphs<\/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 Mathematics is a compulsory subject in Qu\u00e9bec throughout elementary and secondary school.1,2,3,4 The mathematics programs comprise prescribed concepts and processes. The concepts are grouped by cycle in the three cycles of &hellip; <a href=\"http:\/\/timss2015.org\/encyclopedia\/benchmarking-participants\/quebec-canada\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/\">Continued<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":226,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"1"},"class_list":["post-1119","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/1119","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=1119"}],"version-history":[{"count":10,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/1119\/revisions"}],"predecessor-version":[{"id":6945,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/1119\/revisions\/6945"}],"up":[{"embeddable":true,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/226"}],"wp:attachment":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/media?parent=1119"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}