Math library
Learn the idea. Then practise it in more than one way.
Worked examples, common mistakes, varied practice and complete answers for elementary learners.
Start with Grade 2 math basicsPictographs and Tally Charts: Read the Key, Count Whole and Half Symbols
Read a pictograph key, count whole and half symbols, use tally bundles of five, and compare data. Includes 30 practice questions with explanations.
Mean, Median and Mode: Describe a Data Set
Order data, find the mode, median and mean, see the mean as a fair share, and choose the measure that best describes a data set.
Divide a 2-Digit Number by 1 Digit: Area Model, Partial Quotients
Break a two-digit number into friendly parts, divide by one digit with an area model and partial quotients, check by multiplying, and solve word problems.
Multiply a 2-Digit Number by a 1-Digit Number: Area Model and Partial Products
Break a two-digit number into tens and ones, use an area model and partial products, regroup correctly, estimate to check, and solve multiplication word problems.
Factors, Multiples, Primes: Common Factors and Multiples
Find all the factors of a number, list multiples, tell prime from composite, use divisibility tests, and solve problems with common factors and multiples.
Place Value to 100,000: Digit Value, Expanded Form, Compare, Order
Read, write and compare numbers up to 100,000 by place value, use zeros as placeholders, and see what happens to digits when you multiply or divide by 10.
Multiplication and Division Facts: Arrays, Fact Families, Break Apart
Use arrays and fact families to link multiplication and division, and break hard facts like 7 × 8 into easier ones you already know.
Add and Subtract With Regrouping: Trade, Then Check
Add and subtract 3- and 4-digit numbers by regrouping, handle zeros in the middle, and check every answer with an estimate or the inverse operation.
Estimate Sums and Differences: Round First, Then Check
Round to the nearest ten or hundred to estimate sums and differences, compare front-end estimates, and decide whether an exact answer is reasonable.
Rounding to 10, 100 and 1000: Then Estimate and Check
Round whole numbers to the nearest 10, 100 or 1000 on a number line, use the halfway rule, avoid rounding twice, and estimate to check answers.
Volume of Boxes: Count Cubes in Layers, Then Multiply
Find the volume of rectangular prisms: count 1 cm cubes in one layer, multiply by the number of layers, use l × w × h and write the answer in cm³.
Perimeter of L-Shapes: Find Missing Sides, Then Add
Find the perimeter of L-shapes and other composite figures: work out missing sides from opposite sides, add every edge once and compare perimeter with area.
Area of L-Shapes: Split, Add or Subtract
Find the area of L-shapes and other composite figures: split them into rectangles, subtract a missing corner, find missing sides and avoid double counting.
Lines of Symmetry: Fold, Match and Count
Find lines of symmetry by folding, count them in squares, triangles and letters, reflect points across a mirror line, and spot the diagonal trap in rectangles.
Classify Triangles and Quadrilaterals by Sides and Angles
Name triangles by sides and angles, sort squares, rectangles, rhombuses, parallelograms and trapezoids, and read tick marks and right-angle marks.
Angles: Acute, Right, Obtuse, Straight and the Protractor
Name acute, right, obtuse and straight angles, estimate with 45°, 90° and 180°, read the right protractor scale and find clock-hand angles.
Probability: Impossible, Unlikely, Likely or Certain? Spinners, Bags and Fair Games
Describe chance with words and fractions, compare spinners and bags, catch the 'it's due' mistake and test whether a game is fair. Includes 28 original Grade 3–5 questions with explanations.
Mass and Capacity: Grams, Kilograms, Millilitres and Litres
Tell mass from capacity, choose a sensible metric unit, estimate with everyday benchmarks and convert with the same 1000 pattern. Includes 28 original Grade 3–5 questions with explanations.
Remove One Pair of Parentheses: Smart Arithmetic Without Traps
Learn when parentheses can be safely removed, when minus signs reverse terms, how multiplication distributes, and why division over a grouped sum is different. Includes 28 original Grade 4–5 questions with worked explanations.
Bar Graph Word Problems: Totals, Differences and Evidence
Use one accurate bar graph to solve two-step word problems, calculate totals and averages, and explain why a chart of book loans cannot prove the number of borrowers.
Division Remainders: Share, Pack, or Round Up?
Use equal-group pictures and inverse multiplication to decide whether a remainder means leftovers, another container, or an impossible exact split.
Multiplication Shortcuts: Valid Distributive Steps or Traps?
Tell a valid distributive calculation from a convincing but incorrect shortcut; explain what must be multiplied and why.
Mental Addition & Subtraction: When Is a Shortcut Worth It?
Choose when to make ten, split numbers, double, compensate or use straightforward arithmetic; explain why an adjustment is valid.
Money Problems: Total Cost, Change, Unit Price and a Reasonableness Check
Solve meaningful Canadian dollar-and-cent problems: combine prices, compare per-item cost, plan a small budget and use estimates to catch mistakes.
Metric Length: Estimate, Convert and Keep the Units
Learn how millimetres, centimetres, metres and kilometres relate, choose a sensible unit, and defend comparisons rather than guessing from the digits alone.
Elapsed Time: Read Clocks, Cross the Hour, Check a Schedule
Grade 3–4 time reasoning: calculate elapsed minutes across an hour, work backward, compare swim and school schedules, and explain your answer with a timeline.
Bar Graphs: Read Scales, Compare Data, Challenge a Claim
Grades 3–4 practice with bars, pictograph keys, frequency tables, rainfall units, averages, zero baselines and careful claims using clearly labelled invented data.
Two-Step Word Problems: Find the Unknown, Choose the Operation, Check
Grade 3–4 reasoning with equal groups, comparisons, two-step problems, misleading keywords, remainders and missing-information traps.
Dilations & Scale Factor: Enlarge, Reduce, Coordinates & Similar Figures
Build on rigid transformations by using scale factors to enlarge or reduce lengths and coordinate figures, identify similar figures, and predict how perimeter and area change.
Coordinate Transformations: Translations, Reflections & Rotations
Build on ordered pairs by translating, reflecting and rotating points and simple figures on the coordinate plane, then describe each transformation with precise coordinate rules.
Coordinate Plane: Ordered Pairs, Quadrants, Reflections & Distance
Extend input–output tables into the full coordinate plane by reading and plotting ordered pairs, identifying quadrants, measuring horizontal and vertical distance, and reflecting points across axes.
Patterns & Functions: Input–Output Tables, Rules, Coordinates, Predict
Move from equations and inequalities into function thinking by reading input–output tables, applying and reversing rules, writing ordered pairs, plotting points and predicting values.
Inequalities: Boundaries, Number Lines, Solve and Check
Move from equations to inequalities by interpreting <, >, ≤ and ≥, finding boundary values, solving two-step inequalities with positive multipliers/divisors, graphing solution sets and checking boundary cases.
Two-Step Equations: Undo in Reverse Order, Balance, Solve, Check
Build on one-step equations by undoing two operations in reverse order, preserving equality on both sides and checking each solution by substitution.
Variables & One-Step Equations: Inverse Operations, Balance, Solve, Check
Move from numerical expressions to equations by representing unknowns with variables, undoing one operation with its inverse, preserving equality and checking solutions by substitution.
Expressions & Order of Operations: Parentheses, Exponents, Multiply, Divide, Add, Subtract
Read and evaluate numerical expressions reliably by grouping first, handling exponents, then multiplying/dividing and adding/subtracting from left to right, with estimation and inverse-operation checks.
Integers: Positive & Negative Numbers, Opposites, Absolute Value, Compare & Coordinate Plane
Extend number sense below zero: place integers on a number line, identify opposites, use absolute value, compare signed numbers and reason with coordinates and real-world contexts.
Percent: Benchmarks, Percent of a Quantity, Discounts & Tax
Build percent meaning from fractions and decimals, use benchmark percents, find percents of quantities, and solve discount, tax, tip and percent-change problems.
Ratios & Unit Rates: Equivalent Ratios, Tables, Double Number Lines, Compare
Move from fraction division into ratios and rates: read ratio language, build equivalent ratios, use tables and double number lines, find unit rates and compare real-world rates.
Divide Fractions: Meaning, Reciprocals, Mixed Numbers, Estimate, Check
Move from fraction multiplication into division: interpret how-many-groups situations, use reciprocals with meaning, divide mixed numbers, estimate size and check by multiplication.
Multiply Fractions: Whole Numbers, Fractions of Quantities, Estimate, Check
Move from fraction addition into multiplication: fractions of whole-number quantities, fraction × fraction, mixed numbers, simplification, reverse problems and reasonableness checks.
Add & Subtract Fractions: Common Denominators, Mixed Numbers, Estimate, Check
Move from equivalent fractions into addition and subtraction with common denominators, mixed numbers, estimation, reverse problems and reasonableness checks.
Add & Subtract Decimals: Align Place Value, Estimate, Check
Move from decimal place value to accurate addition and subtraction through alignment, regrouping, estimation, money contexts, missing values and reasonableness checks.
Decimals as Numbers: Tenths, Hundredths, Compare, Round
Build Grade 4–5 decimal sense by connecting tenths and hundredths to fractions, place value, number lines, comparison and simple rounding.
Fractions as Numbers: Equivalent Fractions, Compare, Number Line
Build Grade 4–5 fraction sense by locating fractions on number lines, creating equivalents, comparing values, and moving between improper fractions and mixed numbers.
Division That Makes Sense: Quotients, Remainders, Estimate, Check
Build reliable Grade 4–5 division with inverse multiplication, partial quotients, sensible remainders, estimation and 40 original practice questions.
Multiply Smarter: Break Apart, Regroup, Estimate, Check
Build reliable multi-digit multiplication with distributive thinking, friendly-number regrouping, estimation, partial products and 40 original Grade 4–5 practice questions.
Perimeter vs Area: The Mistake That Changes the Whole Answer
Learn how perimeter measures the distance around a shape while area measures the space inside it, with worked examples, common traps and 36 original Grade 4 practice questions.
Multiply 2-Digit Numbers: Area Model and Four Partial Products
Multiply a two-digit number by a two-digit number with an area model, add the four partial products, estimate to check, and solve word problems.
Quick number-sense starter
Make the numbers work together.
A shortcut is useful only when you can explain why it works.
Regroup 25 × 16
Write 16 as 4 × 4. The value has not changed; you have just exposed a useful factor.
Try the same idea with 25 × 24. Because 24 = 4 × 6, the calculation becomes 100 × 6 = 600.
Watch the extra addend
25 × 9 + 9 is not 25 × 10. To add one more group of 25, you need +25, not +9. The first expression is 225 + 9 = 234; the second is 250.