Field
Mathematics
Learn secondary-school maths by being curious and experimenting, not by memorising: fractions, angles, ratio, proportion and percentages, data and probability, powers. Every lesson starts with a question from real life and ends with an interactive simulation and a short quiz.
Fractions and decimals
Starting from splitting a whole into equal parts, this unit takes you through equivalent fractions, comparing fractions, decimal notation, and adding and subtracting fractions.
- The fraction model and unit fractions
What happens when you split a whole into equal parts? Explore what the numerator and denominator mean, what unit fractions are, and why 1/8 is smaller than 1/4, using pizza and chocolate.
- 15 min
- 1 simulation
- Mini quiz
- Equivalent fractions
Are 1/2 and 2/4 the same amount? Learn to find equivalent fractions by multiplying or dividing the numerator and denominator by the same number, to simplify fractions, and to find the simplest form.
- 15 min
- 1 simulation
- Mini quiz
- Comparing and ordering fractions
Which is bigger, 3/5 or 2/3? Learn to compare and order fractions by making the denominators equal, by using unit fractions and one half as benchmarks, or by converting to decimals.
- 20 min
- 1 simulation
- Mini quiz
- Adding and subtracting fractions
Why isn't 1/2 + 1/3 equal to 2/5? Learn to add fractions with equal denominators, to bring different denominators to a common denominator, and to subtract fractions from a whole, using recipes and walks.
- 20 min
- 1 simulation
- Mini quiz
Angles and geometry
From clock hands to skateboard ramps: find out what an angle is, how to measure it with a protractor, the types of angle, adjacent, complementary and supplementary angles, and the interior angles of a triangle.
- What is an angle and how do you measure it?
Does the size of an angle depend on the length of its arms or on how far it turns? Learn the parts of an angle, the degree as a unit, and how to measure accurately with a protractor, using clocks and skateboards as examples.
- 15 min
- 1 simulation
- Mini quiz
- Types of angle
Acute, right, obtuse, straight and full angles: learn to classify angles by their measure, test for a right angle with the corner of a sheet of paper, and find out why a rotated right angle is still a right angle.
- 15 min
- 1 simulation
- Mini quiz
- Adjacent, complementary and supplementary angles
When a road splits in two, how are the angles it makes related? Explore adjacent angles, complementary angles that add up to 90° and supplementary angles that add up to 180°, using cycle lanes and ramps.
- 20 min
- 1 simulation
- Mini quiz
- Interior angles of a triangle
Tiny or huge, pointy or flat: why do the interior angles of every triangle add up to 180°? Find out with a paper triangle experiment, and learn to find a missing angle and spot impossible triangles.
- 20 min
- 1 simulation
- Mini quiz
Ratio, proportion and percentages
From shooting accuracy to recipes, from maps to discounts: learn to compare two quantities by dividing, work with direct and inverse proportion, calculate percentages and take a first look at interest.
- What is a ratio?
Is the player who scores more baskets the more accurate one? Learn to compare two quantities by dividing, how to write a ratio, why order matters, and unit rates such as km/h, with examples from sport and shopping.
- 15 min
- 1 simulation
- Mini quiz
- Direct proportion
How do the ingredients in a recipe change when more guests come? Discover why the ratio of directly proportional quantities stays constant, the unit rate, the relationship y = kx and map scales.
- 20 min
- 1 simulation
- Mini quiz
- Inverse proportion
Why does a job finish sooner when more people work on it? Learn why the product of inversely proportional quantities stays constant, solve speed-time and worker-day problems, and see why not every decreasing relationship is inverse proportion.
- 20 min
- 1 simulation
- Mini quiz
- Percentages in everyday life
Is 20% off a better deal than 50 TL off? Learn that a percentage is a ratio with denominator 100, work out discounts and price rises, avoid the trap of successive percentages, and take a first look at simple interest.
- 20 min
- 1 simulation
- Mini quiz
Data and probability
From match scores to dice rolls: learn to summarise data with the mean, median and mode, count possible outcomes, calculate the probability of simple events and see how experiment and theory meet.
- Reading data: mean, median and mode
If a team scores "10 points on average", did every player score 10? Learn to calculate the mean, median and mode, and see how outliers affect each of these measures.
- 20 min
- 1 simulation
- Mini quiz
- Possible outcomes
How many different results can there be when you roll a dice, toss two coins or choose a meal from the canteen? Learn about experiments, outcomes and events, listing outcomes, tree diagrams and the multiplication principle.
- 15 min
- 1 simulation
- Mini quiz
- Probability of simple events
What are your chances of drawing a red marble from a bag? Learn to calculate probability when outcomes are equally likely, why probability lies between 0 and 1, impossible and certain events, and the "it either happens or it doesn't, so 50%" fallacy.
- 20 min
- 1 simulation
- Mini quiz
- Experiment and theory: experimental probability
If you toss a coin 10 times and get 7 heads, is the coin biased? Compare experimental and theoretical probability, see why results get closer to theory as the number of trials grows, and meet the gambler's fallacy.
- 20 min
- 1 simulation
- Mini quiz
Powers and exponential growth
From grains of rice on a chessboard to a lily pond: explore multiplying a number by itself again and again, the rules of exponents, doubling, and the difference between linear, exponential and logistic growth.