How to learn Elementary: Mathematics

Quebec curriculum: Mathematics, Elementary

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1. Arithmetic · Natural numbers

Rote counting to 100: Rote count forwards and backwards from 0 to 100, beginning from 0, 1, or any given number, by ones
Sorting into categories: Classify objects into given categories, count the number in each category, and sort the categories by count
Representing numbers with objects: Represent numbers using objects, pictorial representations, and the number line
Addition as combining or putting together two: Understand addition as combining or putting together two groups to find the total
Numbers up to 10 into pairs: Decompose numbers up to 10 into pairs in more than one way (part-part-whole)
Odd and even numbers: Recognise odd and even numbers
Numbers to 10,000: Identify, represent, and estimate numbers up to 10,000 using different representations
Positive and Negative Numbers: 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: Recognise and use relationships between operations including inverse operations; use these relationships to check answers and simplify calculations
Mental addition and subtraction (age 9+): Add and subtract numbers mentally with increasingly large numbers, using place-value knowledge and derived facts
Mental multiplication and division: 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: Add up to four two-digit numbers using strategies based on place value and properties of operations
Finding a missing number in addition: Understand subtraction as finding an unknown addend (e.g. 10 − 8 = ? is the same as 8 + ? = 10)
Arrays for multiplication: Use arrays to represent multiplication and division situations

2. Arithmetic · Fractions

Fractions of amounts: 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: 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): 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: Recognise and use fractions as numbers: place unit fractions and non-unit fractions with small denominators on a number line
Simple Fraction Sums: Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)
Understanding fractions: Write simple fractions (e.g. 1/2 of 6 = 3) and recognise the equivalence of 2/4 and 1/2
Comparing fractions (age 7+): Solve problems involving counting in tenths, fractions of quantities, equivalence, fraction addition/subtraction, and fraction comparison
Equivalent fractions: Recognise and show, using diagrams, equivalent fractions with small denominators
Decimals and fractions (age 10+): 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: Compare and order unit fractions, and fractions with the same denominator

3. Arithmetic · Decimals

Reading and writing numbers to 1000: Read and write numbers to 1000 in numerals, number names, and expanded form
Decimal equivalents of tenths and hundredths: 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: Round decimals with one decimal place to the nearest whole number
Decimal place value (age 8+): Compare numbers with the same number of decimal places up to two decimal places
Decimal place value: Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy
Tenths: 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: 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: Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide
Order of operations: Understand and apply the conventional order of operations (PEMDAS/BODMAS) to carry out calculations involving the four operations
Division with Decimals: 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: 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: 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: Recognise and name common 3-D shapes (cubes, cuboids, pyramids, spheres, cylinders, cones)
Building with 3-D Shapes: 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: 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+): 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: 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: 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: Recognise and name common 2-D shapes (circles, triangles, rectangles including squares)

8. Geometry · Patterns

Patterns & Sequences: Order and arrange combinations of mathematical objects in patterns and sequences
Translating and reflecting shapes: Draw and translate simple shapes on the coordinate plane; reflect shapes in the axes

9. Measurement · Lengths

Measuring length: Order three objects by length and compare the lengths of two objects indirectly using a third object
Comparing lengths by measuring: 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: 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: Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units
Estimating Lengths: Estimate lengths using units of inches, feet, centimetres, and metres
Measuring Perimeters: Measure the perimeter of simple 2-D shapes

10. Measurement · Surface areas

Understanding Area: 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: Measure and begin to record capacity and volume using non-standard and standard units

12. Measurement · Angles

Understanding angles: Recognise angles as a property of shape or a description of a turn

13. Measurement · Masses

Measuring mass and weight: Measure and begin to record mass/weight using non-standard and standard units

14. Measurement · Time

Telling time to the minute: Measure and begin to record time in hours, minutes, and seconds

15. Measurement · Temperatures

Choosing measurement units: 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: 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+): 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: 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: Calculate and interpret the mean as an average of a data set

17. Probability

The Probability Scale: 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: Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability