Learn
Short, clear lessons on every topic in the game. Each one explains the idea in simple words, works through examples step by step, and ends with questions to try.
53 lessons
Arithmetic
Mental math with whole numbers, fractions, decimals and percentages.
- Adding and subtracting in your headAdd and subtract two-digit numbers in your head by splitting them into tens and ones, and find doubles and halves fast.Read the lesson
- Times tables and multiplyingLearn the times tables with patterns that make them easy, multiply bigger numbers by splitting them, and use tricks like 25 × 4 = 100.Read the lesson
- DivisionWhat dividing means, how it undoes multiplying, and how to divide in your head using the times tables you already know.Read the lesson
- Order of operationsWhy 3 + 4 × 2 is 11 and not 14: brackets first, then powers, then multiplying and dividing, then adding and subtracting.Read the lesson
- Squares and powersWhat 13² and 2¹⁰ mean, the squares worth knowing by heart, and a quick way to square numbers like 45 in your head.Read the lesson
- Negative numbersAdd and subtract with numbers below zero using the number line, and see why taking away a negative is the same as adding.Read the lesson
- FractionsFind a fraction of a number, like 3/4 of 60, and add fractions with different bottoms by finding a common denominator.Read the lesson
- DecimalsLine up the decimal point to add decimals without mistakes, and divide by a decimal like 0.6 by moving the point first.Read the lesson
- PercentagesWhat "per cent" means, and how to find 10%, 25%, 50% and 15% of any number in your head.Read the lesson
Algebra
Letters that stand for numbers, and how to solve equations.
- Expressions and variablesWhat a letter like x stands for, how to put a number in its place, how to collect like terms, and how to turn words into algebra.Read the lesson
- Solving simple equationsSolve equations like 2x + 5 = 17 by doing the same thing to both sides, one step at a time, until x is alone.Read the lesson
- Equations with x on both sidesMove every x to one side and every number to the other, solve equations with fractions, and rearrange a formula.Read the lesson
- Word problems into equationsTurn a story about ages, numbers in a row or a rectangle into an equation, then solve it and check the answer.Read the lesson
- Expanding brackets and factoringMultiply out 3(x + 4) and (x + 3)(x + 5) term by term, and go back the other way by factoring.Read the lesson
- Powers in algebraThe rules for powers, like x³ times x⁴ = x⁷, how to solve 2ˣ = 32, and why x² = 144 means x = 12.Read the lesson
- Quadratic equationsSolve equations like x² − 5x + 6 = 0 by factoring, find the sum of the solutions, and use the special products of a and b.Read the lesson
- Inequalities and absolute valueSolve inequalities like 2x + 1 > 7, see why the sign flips when you divide by a negative, and solve |x − 3| = 5.Read the lesson
- Two equations, two unknownsFind x and y when you have two equations, by adding the equations together or by putting one into the other.Read the lesson
- Functions and slopeWhat f(x) means and how to work out f(3), and how to find the slope of a line through two points.Read the lesson
Probability
How likely something is: coins, dice, marbles and cards.
- What probability meansProbability as a number from 0 to 1, the words impossible, unlikely, even, likely and certain, and the chance of a coin or a die.Read the lesson
- Bags, cards and spinnersFind a probability by counting: the outcomes you want divided by all the outcomes, with marbles, cards, letters and spinners.Read the lesson
- The chance that something does not happenWhy the chance of "not" is 1 minus the chance of "yes", and how it turns "at least one six" into an easy question.Read the lesson
- Two things at onceThe chance of heads AND a six, two coins, two dice, and taking marbles with and without putting them back.Read the lesson
- Counting outcomesCount every possible result with a table or a tree: two dice, totals like 7, and the orders of books on a shelf.Read the lesson
- What to expectHow many heads to expect in 100 flips, and the expected value of a die: the average you get over many tries.Read the lesson
- Probability puzzlesPuzzles that fool almost everyone, solved by counting carefully, including the famous Monty Hall problem.Read the lesson
Geometry
Angles, shapes, areas, circles and solids.
- AnglesRight angles, angles on a straight line, angles around a point, and two angles that make a right angle.Read the lesson
- Angles in a triangleThe three angles of any triangle add up to 180°. Use it to find a missing angle, also in an isosceles triangle.Read the lesson
- PolygonsThe names of shapes from triangle to decagon, their sides, their lines of symmetry, their diagonals and their perimeter.Read the lesson
- Angles in polygonsWhat the inside angles of any polygon add up to, the size of each angle in a regular polygon, and exterior angles.Read the lesson
- Area and perimeter of rectanglesThe perimeter is the distance around; the area is the space inside. Find both for rectangles and squares, and work backwards to a side.Read the lesson
- Area of triangles and trapezoidsWhy a triangle is half a rectangle, and how a trapezoid uses the average of its two parallel sides.Read the lesson
- The Pythagorean theoremIn a right triangle, a² + b² = c². Find a missing side, learn the famous triples like 3, 4, 5, and find diagonals.Read the lesson
- CirclesRadius and diameter, the circumference 2πr, the area πr², half circles, and the angles inside a circle.Read the lesson
- Cubes, boxes and cylindersFaces, edges and corners, the volume of a cube, a box and a cylinder, and the total area of a cube’s six faces.Read the lesson
- Making shapes biggerDouble every side of a square and the area does not double: it grows four times. See why, for areas and volumes.Read the lesson
- Angles on a clockFind the angle between the hands of a clock at any time, and see how often the two hands meet in a day.Read the lesson
Logic
Puzzles about time, calendars, ages and clever counting.
- Days and calendarsWhat day it will be in 10 days, which day was yesterday if tomorrow is Friday, months, leap years and dates.Read the lesson
- Reading clocks and adding timeRead the time on a clock face, and find when a film ends or what time it will be in 45 minutes.Read the lesson
- Fence posts and gapsPosts and gaps, cuts and pieces, pages counted from 12 to 30: why the answer is so often one more or one less than you think.Read the lesson
- Counting digitsHow many times do you write the digit 1 from 1 to 20? How many digits from 1 to 100? Count them in groups.Read the lesson
- Age puzzlesEveryone gets older at the same speed. Use that to solve puzzles about ages now, years ago and years from now.Read the lesson
- Speed, rates and working togetherTrains that meet, a train in a tunnel, the average speed of a trip, people working together, and the snail in the well.Read the lesson
- Trick questionsQuestions that are easy once you read every word: all but 9, the bat and the ball, the brick and a half, and more.Read the lesson
- Ordering, odd ones out and liarsPut people in order from clues, find the odd one out, and work out who is lying, with a little reasoning at each step.Read the lesson
- Counting cleverlyHandshakes at a party, squares in a grid, socks in the dark, the fewest coins, and finding a heavy coin with a balance.Read the lesson
Patterns
Number patterns: find the rule, then the next number.
- Patterns that add the same numberFind the next number when the same amount is added each time, fill a gap, write the rule, and jump to the 10th number.Read the lesson
- Patterns that multiplyDoubling, halving and multiplying by 3: patterns that grow fast, how to fill a gap in them, and their 10th number.Read the lesson
- Square, cube and triangle numbersSquare numbers, cube numbers, triangle numbers and their cousins, and how to find the 15th one without listing them all.Read the lesson
- Patterns with growing gapsWhen the gaps between numbers are not the same, look at the gaps themselves, or try "double it and add one".Read the lesson
- Fibonacci, primes and other famous patternsAdd the two numbers before, list the primes, multiply by 1, 2, 3, 4, and read the look-and-say pattern aloud.Read the lesson
- Two patterns in onePatterns that take turns, signs that flip from plus to minus, and how to spot the one number that does not fit.Read the lesson
- Quick sumsAdd 1 + 2 + 3 + ... + 20 in seconds, the way young Gauss did, and see why the odd numbers always add up to a square.Read the lesson