# Elementary: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 63 concepts ready. In the app: https://ai.page/roadmap/ca-qc-elementary Part of: [Quebec: Mathematics](https://ai.page/roadmap/ca-qc.md) Goal: Quebec curriculum: Mathematics, Elementary ## 1. Arithmetic · Natural numbers - [Rote counting to 100](https://ai.page/c/rote-counting-to-100/index.md): Rote count forwards and backwards from 0 to 100, beginning from 0, 1, or any given number, by ones - [Sorting into categories](https://ai.page/c/sorting-into-categories/index.md): Classify objects into given categories, count the number in each category, and sort the categories by count - [Representing numbers with objects](https://ai.page/c/representing-numbers-with-objects/index.md): Represent numbers using objects, pictorial representations, and the number line - [Addition as combining or putting together two](https://ai.page/c/addition-as-combining-or-putting-together-two/index.md): Understand addition as combining or putting together two groups to find the total - [Numbers up to 10 into pairs](https://ai.page/c/numbers-up-to-10-into-pairs/index.md): Decompose numbers up to 10 into pairs in more than one way (part-part-whole) - [Odd and even numbers](https://ai.page/c/odd-and-even-numbers/index.md): Recognise odd and even numbers - [Numbers to 10,000](https://ai.page/c/numbers-to-10-000/index.md): Identify, represent, and estimate numbers up to 10,000 using different representations - [Positive and Negative Numbers](https://ai.page/c/positive-and-negative-numbers/index.md): Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances - [Using inverse operations](https://ai.page/c/using-inverse-operations/index.md): Recognise and use relationships between operations including inverse operations; use these relationships to check answers and simplify calculations - [Mental addition and subtraction (age 9+)](https://ai.page/c/mental-addition-and-subtraction-age-9/index.md): Add and subtract numbers mentally with increasingly large numbers, using place-value knowledge and derived facts - [Mental multiplication and division](https://ai.page/c/mental-multiplication-and-division/index.md): Use place value, known and derived facts to multiply and divide mentally, including multiplying by 0 and 1, dividing by 1, and multiplying together three numbers - [Adding numbers](https://ai.page/c/adding-numbers/index.md): Add up to four two-digit numbers using strategies based on place value and properties of operations - [Finding a missing number in addition](https://ai.page/c/finding-a-missing-number-in-addition/index.md): Understand subtraction as finding an unknown addend (e.g. 10 − 8 = ? is the same as 8 + ? = 10) - [Arrays for multiplication](https://ai.page/c/arrays-for-multiplication/index.md): Use arrays to represent multiplication and division situations ## 2. Arithmetic · Fractions - [Fractions of amounts](https://ai.page/c/fractions-of-amounts/index.md): Recognise, find, name, and write fractions 1/3, 1/4, 2/4, and 3/4 of a length, shape, set of objects, or quantity - [Fractions of a whole](https://ai.page/c/fractions-of-a-whole/index.md): Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a/b as a parts of size 1/b - [Dividing fractions (unit fractions)](https://ai.page/c/dividing-fractions-unit-fractions/index.md): Interpret and compute division of a unit fraction by a non-zero whole number (e.g. 1/3 ÷ 4 = 1/12); use visual models and the relationship between multiplication and division to explain the result - [Fractions on a number line](https://ai.page/c/fractions-on-a-number-line/index.md): Recognise and use fractions as numbers: place unit fractions and non-unit fractions with small denominators on a number line - [Simple Fraction Sums](https://ai.page/c/simple-fraction-sums/index.md): Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7) - [Understanding fractions](https://ai.page/c/understanding-fractions-maths/index.md): Write simple fractions (e.g. 1/2 of 6 = 3) and recognise the equivalence of 2/4 and 1/2 - [Comparing fractions (age 7+)](https://ai.page/c/comparing-fractions-age-7/index.md): Solve problems involving counting in tenths, fractions of quantities, equivalence, fraction addition/subtraction, and fraction comparison - [Equivalent fractions](https://ai.page/c/equivalent-fractions/index.md): Recognise and show, using diagrams, equivalent fractions with small denominators - [Decimals and fractions (age 10+)](https://ai.page/c/decimals-and-fractions-age-10/index.md): Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts - [Comparing fractions](https://ai.page/c/comparing-fractions/index.md): Compare and order unit fractions, and fractions with the same denominator ## 3. Arithmetic · Decimals - [Reading and writing numbers to 1000](https://ai.page/c/reading-and-writing-numbers-to-1000/index.md): Read and write numbers to 1000 in numerals, number names, and expanded form - [Decimal equivalents of tenths and hundredths](https://ai.page/c/decimal-equivalents-of-tenths-and-hundredths/index.md): Recognise and write decimal equivalents of any number of tenths or hundredths (e.g. 3/10 = 0.3, 27/100 = 0.27) - [Decimal place value](https://ai.page/c/decimal-place-value/index.md): Round decimals with one decimal place to the nearest whole number - [Decimal place value (age 8+)](https://ai.page/c/decimal-place-value-age-8/index.md): Compare numbers with the same number of decimal places up to two decimal places - [Decimal place value](https://ai.page/c/decimal-place-value-3/index.md): Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy - [Tenths](https://ai.page/c/tenths/index.md): Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and from dividing one-digit numbers or quantities by 10 - [Fractions on a number line](https://ai.page/c/fractions-on-a-number-line-maths/index.md): Move fluently between real-world situations, diagrams, number lines, and symbolic equations involving multiplication, fractions, and decimals, explaining what each representation shows - [Properties of Operations](https://ai.page/c/properties-of-operations/index.md): Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide - [Order of operations](https://ai.page/c/order-of-operations/index.md): Understand and apply the conventional order of operations (PEMDAS/BODMAS) to carry out calculations involving the four operations - [Division with Decimals](https://ai.page/c/division-with-decimals/index.md): Use written division methods in cases where the answer has up to two decimal places; divide decimals to hundredths by whole numbers ## 4. Arithmetic · Using Numbers - [Percentages as Fractions](https://ai.page/c/percentages-as-fractions/index.md): Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100% ## 5. Geometry · Space - [Plotting points in the first quadrant](https://ai.page/c/plotting-points-in-the-first-quadrant/index.md): Plot and read ordered pairs in the first quadrant of the coordinate plane; represent real-world and mathematical problems by graphing points and interpreting coordinate values in context ## 6. Geometry · Solids - [3-D shapes](https://ai.page/c/3-d-shapes/index.md): Recognise and name common 3-D shapes (cubes, cuboids, pyramids, spheres, cylinders, cones) - [Building with 3-D Shapes](https://ai.page/c/building-with-3-d-shapes/index.md): Compose three-dimensional shapes (cubes, right rectangular prisms, right circular cones, right circular cylinders) and create composite shapes; build new shapes from component shapes - [2-D faces on 3-D shapes](https://ai.page/c/2-d-faces-on-3-d-shapes/index.md): Identify 2-D shapes on the surface of 3-D shapes (e.g. a circle on a cylinder, a triangle on a pyramid) - [3-D shapes (age 11+)](https://ai.page/c/3-d-shapes-age-11/index.md): Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections - [Nets of 3-D Shapes](https://ai.page/c/nets-of-3-d-shapes/index.md): Identify, draw, and interpret nets of common 3-D shapes — cubes, cuboids, triangular prisms, and square-based pyramids — by predicting which 3-D shape a given flat arrangement of faces will fold into, checking whether a net will close completely, and sketching a net from a description or 3-D model; understand the relationship between the number of faces and the structure of the net ## 7. Geometry · Plane figures - [Lines, Rays & Angles](https://ai.page/c/lines-rays-and-angles/index.md): Draw and identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines; identify these in two-dimensional figures - [2-D shapes](https://ai.page/c/2-d-shapes/index.md): Recognise and name common 2-D shapes (circles, triangles, rectangles including squares) ## 8. Geometry · Patterns - [Patterns & Sequences](https://ai.page/c/patterns-and-sequences/index.md): Order and arrange combinations of mathematical objects in patterns and sequences - [Translating and reflecting shapes](https://ai.page/c/translating-and-reflecting-shapes/index.md): Draw and translate simple shapes on the coordinate plane; reflect shapes in the axes ## 9. Measurement · Lengths - [Measuring length](https://ai.page/c/measuring-length/index.md): Order three objects by length and compare the lengths of two objects indirectly using a third object - [Comparing lengths by measuring](https://ai.page/c/comparing-lengths-by-measuring/index.md): Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit - [Measuring with different units](https://ai.page/c/measuring-with-different-units/index.md): Measure the length of an object using two different length units and describe how the measurements relate to the size of the unit chosen - [Calculating with measurements](https://ai.page/c/calculating-with-measurements/index.md): Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units - [Estimating Lengths](https://ai.page/c/estimating-lengths/index.md): Estimate lengths using units of inches, feet, centimetres, and metres - [Measuring Perimeters](https://ai.page/c/measuring-perimeters/index.md): Measure the perimeter of simple 2-D shapes ## 10. Measurement · Surface areas - [Understanding Area](https://ai.page/c/understanding-area/index.md): Understand that a unit square has one square unit of area and that the area of a plane figure is the number of unit squares that cover it without gaps or overlaps ## 11. Measurement · Volumes - [Capacity and volume](https://ai.page/c/capacity-and-volume/index.md): Measure and begin to record capacity and volume using non-standard and standard units ## 12. Measurement · Angles - [Understanding angles](https://ai.page/c/understanding-angles/index.md): Recognise angles as a property of shape or a description of a turn ## 13. Measurement · Masses - [Measuring mass and weight](https://ai.page/c/measuring-mass-and-weight/index.md): Measure and begin to record mass/weight using non-standard and standard units ## 14. Measurement · Time - [Telling time to the minute](https://ai.page/c/telling-time-to-the-minute/index.md): Measure and begin to record time in hours, minutes, and seconds ## 15. Measurement · Temperatures - [Choosing measurement units](https://ai.page/c/choosing-measurement-units/index.md): Choose and use appropriate standard units to measure length (m/cm), mass (kg/g), temperature (°C), and capacity (litres/ml) to the nearest appropriate unit ## 16. Statistics - [Sorting Data into Categories](https://ai.page/c/sorting-data-into-categories/index.md): Organise and represent data with up to three categories by counting objects in each category and sorting categories by quantity - [Pictograms and tally charts (age 11+)](https://ai.page/c/pictograms-and-tally-charts-age-11/index.md): Construct and interpret frequency tables, bar charts, pie charts, pictograms, and vertical line charts for both categorical and grouped numerical data, choosing appropriate representations for the data type - [Picture & Bar Graphs](https://ai.page/c/picture-and-bar-graphs/index.md): Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories; solve put-together, take-apart, and compare problems using information presented in a bar graph - [Calculating the Mean](https://ai.page/c/calculating-the-mean/index.md): Calculate and interpret the mean as an average of a data set ## 17. Probability - [The Probability Scale](https://ai.page/c/the-probability-scale/index.md): Understand probability as a measure on a scale from 0 (impossible) to 1 (certain); use the language of probability including likely, unlikely, certain, and impossible - [Experimental probability](https://ai.page/c/experimental-probability/index.md): Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability ## Health: 0 of 100 Of its 63 own concepts: 0 have an explanation, 0 have practice, 0 have a measurement question, 0 have a checked version. Findings (each is a task for anyone's AI): - Rote counting to 100 has no explanation yet - Sorting into categories has no explanation yet - Representing numbers with objects has no explanation yet - Addition as combining or putting together two has no explanation yet - Numbers up to 10 into pairs has no explanation yet - Odd and even numbers has no explanation yet - Numbers to 10,000 has no explanation yet - Positive and Negative Numbers has no explanation yet - Using inverse operations comes before Order of operations, which it needs - Using inverse operations has no explanation yet - Mental addition and subtraction (age 9+) has no explanation yet - Mental multiplication and division has no explanation yet - Adding numbers has no explanation yet - Finding a missing number in addition has no explanation yet - Arrays for multiplication has no explanation yet - Fractions of amounts has no explanation yet - Fractions of a whole has no explanation yet - Dividing fractions (unit fractions) has no explanation yet - Fractions on a number line has no explanation yet - Simple Fraction Sums has no explanation yet - Understanding fractions has no explanation yet - Comparing fractions (age 7+) has no explanation yet - Equivalent fractions has no explanation yet - Decimals and fractions (age 10+) has no explanation yet - Comparing fractions has no explanation yet - Reading and writing numbers to 1000 has no explanation yet - Decimal equivalents of tenths and hundredths has no explanation yet - Decimal place value has no explanation yet - Decimal place value (age 8+) has no explanation yet - Decimal place value has no explanation yet - Tenths has no explanation yet - Fractions on a number line has no explanation yet - Properties of Operations has no explanation yet - Order of operations has no explanation yet - Division with Decimals has no explanation yet - Percentages as Fractions has no explanation yet - Plotting points in the first quadrant has no explanation yet - 3-D shapes has no explanation yet - Building with 3-D Shapes has no explanation yet - 2-D faces on 3-D shapes comes before 2-D shapes, which it needs - 2-D faces on 3-D shapes has no explanation yet - 3-D shapes (age 11+) has no explanation yet - Nets of 3-D Shapes has no explanation yet - Lines, Rays & Angles has no explanation yet - 2-D shapes has no explanation yet - Patterns & Sequences has no explanation yet - Translating and reflecting shapes has no explanation yet - Measuring length has no explanation yet - Comparing lengths by measuring has no explanation yet - Measuring with different units has no explanation yet Credit: The structure of Quebec curriculum: Mathematics (https://www.education.gouv.qc.ca/en/teachers/programs/mathematics/); concepts from the Marble Skill Taxonomy (v1), © Generative Spark, Inc. (withmarble.com), text CC BY-SA 4.0, database ODbL 1.0: https://github.com/withmarbleapp/os-taxonomy, mapped to its standards by Marble.