Level 5 free

Equation kid

Year 8: powers, Pythagoras, expressions and equations. 30 lessons.

Squares: the second power What a number to the power of two means, how to calculate it, and why a square of numbers is useful. ⏱ 15 minutes Practice
The square root A square root is a power backwards. How to find it, estimate it, and not get burned by negative numbers. ⏱ 16 minutes Practice
Powers with a natural exponent Cubes, fourth powers and higher. How to read and calculate aⁿ and why powers grow so fast. ⏱ 15 minutes Practice
Calculating with powers Multiplying and dividing powers with the same base, and a power of a power — three rules that save work. ⏱ 17 minutes Practice
Writing big numbers Millions and billions without counting zeros: writing numbers with powers of ten. ⏱ 15 minutes Practice
Pythagoras' theorem The most famous theorem in maths: c² = a² + b². What it means and how to find a missing side of a triangle with it. ⏱ 17 minutes Practice
Pythagoras in practice A ladder against a wall, a phone diagonal, a shortcut across a park. How to find a right-angled triangle in the real world. ⏱ 17 minutes Practice
An expression: calculating with letters Why letters show up in maths, what a variable is, and how to read the expression 3x + 2. ⏱ 15 minutes Practice
Substituting into an expression How to put a number in for a letter in an expression and calculate the value — including negative numbers and brackets. ⏱ 16 minutes Practice
Adding polynomials What a polynomial is, which terms you may add, and how to deal with a minus in front of brackets. ⏱ 16 minutes Practice
Multiplying polynomials Expanding brackets and multiplying two pairs of brackets: each with each, skip nothing. ⏱ 17 minutes Practice
Factoring out Expanding backwards: how to pull a common factor out of terms and put it in front of the brackets. ⏱ 16 minutes Practice
Formulae (a+b)², (a−b)², a²−b² Three formulae used all the time in algebra. Where they come from and how to calculate faster with them. ⏱ 18 minutes Practice
Equations: scales in balance What an equation is, what it means to solve it, and why both sides must change the same way. ⏱ 16 minutes Practice
Simple equations Two-step equations: ax + b = c. In what order to tidy, and why x must not be afraid of negative results. ⏱ 17 minutes Practice
Equations with brackets Expand first, then solve. How to deal with brackets and a minus in front of them. ⏱ 17 minutes Practice
Equations with fractions How to get rid of fractions in one move: multiply the whole equation by the common denominator. ⏱ 18 minutes Practice
Checking an equation L = R: how to write a check properly, why it is تم in the original equation, and how to find your own mistake. ⏱ 15 minutes Practice
Making a quantity the subject of a formula How to rearrange o = 2(a + b) or s = v · t so another quantity is the subject, not the one it was written for. ⏱ 17 minutes Practice
Word problems on equations How to translate a story into an equation: what to mark as x, how to build the equality, and how to answer in a full sentence. ⏱ 18 minutes Practice
Motion problems Distance, speed, time and equations: how to calculate two cars meeting and catching up with a friend on a bike. ⏱ 18 minutes Practice
Mixture and shared-work problems Mixing juice, pouring nuts and two painters on one fence: two classic problems, one method through an equation. ⏱ 18 minutes Practice
Circle and circumference The difference between a disc and a circumference, radius, diameter, chord, and how to draw a circle with compasses. ⏱ 15 minutes Practice
Circumference of a circle (π) Meeting the number π and the formula o = π · d. How far does a wheel go in one turn? ⏱ 17 minutes Practice
Area of a circle The formula S = π · r²: how much area fits into a circle and why pizza size grows faster than the diameter. ⏱ 17 minutes Practice
Cylinder: surface area and volume A tin, a mug and a barrel are cylinders. How to calculate how much fits into a cylinder and how much sheet metal is needed for it. ⏱ 18 minutes Practice
Thales' theorem Every triangle on the diameter of a circumference has a right angle. Why it holds and how to draw with it. ⏱ 16 minutes Practice
Statistics: mean, median, mode Three ways to describe a pile of data with one number — and why the mean is easy to fool. ⏱ 17 minutes Practice
Project: measure and calculate A big home project: a ruler, string and everything you have learned — Pythagoras, circles, cylinders and statistics on real things. ⏱ 18 minutes Practice
Equation kid finale A big review of the whole level: powers, Pythagoras, expressions, equations, circles and statistics in one final round. ⏱ 18 minutes Practice

Coding is still on the home page — this course does not replace it.