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Mathematics Basics

Easy to follow, grades 7–10 (all school types).

Tip: The videos also have an English audio track. On YouTube, open ⚙ Settings → Audio track.

12:52

Episode 1

Negative Numbers & Order of Operations Explained

What you will learn

  • order and compare negative numbers on the number line
  • plus and minus as movement – no rules to memorise
  • why 3 − (−4) is the same as 3 + 4
  • why minus times minus is plus – derived, not just claimed
  • order of operations (PEMDAS / BODMAS) and brackets
  • the four mistakes that cost the most points in tests
Watch on YouTube
12:25

Episode 2

Fractions & Percentages Explained

What you will learn

  • what numerator and denominator mean
  • why 2/4 is the same as 1/2 – equivalent fractions
  • turning fractions into decimals (3/4 = 0.75)
  • percent means “out of a hundred”: 25 % = 1/4 = 0.25
  • the 1 % trick for any percentage
  • the four most common mistakes with fractions and percentages
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12:31

Episode 3

Algebraic Expressions Explained

What you will learn

  • what a variable is – a placeholder for a number
  • why 3x means “3 times x”, not “3 plus x”
  • substituting numbers and evaluating an expression
  • collecting like terms: x with x, numbers with numbers
  • minus signs in expressions – the sign moves with its term
  • expanding brackets: multiply every term inside
  • the four most common mistakes with expressions
Watch on YouTube
11:34

Episode 4

Solving Equations Explained

What you will learn

  • what the equals sign really means
  • solving an equation with a balance scale
  • inverse operations: plus ⇄ minus, times ⇄ divide
  • two-step equations
  • turning words into an equation (number riddles, escape-room codes)
  • phone bills, saving up and taxi fares
  • the four most common mistakes
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11:18

Episode 5

Linear Functions Explained

What you will learn

  • plotting points: x first, then y
  • what a function is – the function machine
  • tables of values and graphs
  • b, the y-intercept, and m, the slope
  • falling lines: a phone battery
  • the equation of a line through two points
  • the four most common mistakes
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10:59

Episode 6

Systems of Equations Explained

What you will learn

  • why two unknowns need two equations
  • turning a word problem into two equations
  • elimination by subtracting or adding
  • substitution and checking in both equations
  • the solution as an intersection point
  • the classic chickens-and-rabbits puzzle
  • the four most common mistakes
Watch on YouTube
11:35

Episode 7

Powers & Square Roots Explained

What you will learn

  • what a power is: base and exponent
  • why 2⁴ = 16, not 8
  • square numbers up to 15² – and why they are called “squared”
  • the square root: from area back to side length
  • powers of ten: 8 · 10⁹ people, 8E9 on your calculator
  • estimating roots: √20 lies between 4 and 5
  • (−3)² = 9, but −3² = −9
Watch on YouTube
11:16

Episode 8

Perimeter, Area & Volume Explained

What you will learn

  • perimeter (fence) versus area (floor)
  • why area = length · width
  • the triangle as half a rectangle
  • circles and π: circumference and area
  • 1 m² = 10,000 cm² and 1 m³ = 1,000 litres
  • volume of a pool, an aquarium and a moving box
  • the pizza duel: one large versus two small
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10:37

Episode 9

Pythagorean Theorem Explained

What you will learn

  • hypotenuse and legs
  • why 9 + 16 = 25 is no coincidence
  • the four-triangle proof
  • finding the hypotenuse (add)
  • finding a leg (subtract)
  • is it a right triangle? The 3-4-5 rope
  • screen diagonals, kites, straight-line distance
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9:59

Episode 10

Quadratic Equations Explained

What you will learn

  • x² means x · x – the area of a square
  • x² = 25 has two solutions: 5 and −5
  • choosing the solution that makes sense
  • rearrange first, then solve
  • zero product property: (x − 2) · (x + 3) = 0
  • factoring: x² − 4x = 0
  • the parabola y = x² and where it meets a line
  • braking distance and pizza: double means four times
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11:16

Episode 11

Sine, Cosine & Tangent Explained

What you will learn

  • opposite, adjacent, hypotenuse – seen from the angle
  • same angle, same ratio
  • sin = O/H, cos = A/H, tan = O/A (SOH-CAH-TOA)
  • a ladder against a wall with cosine
  • the height of a tree with tangent
  • calculator in DEG mode and the inverse key
  • a 10 % slope is only 5.7°
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10:11

Episode 12

Statistics & Probability Explained

What you will learn

  • probability = favourable : possible outcomes
  • a die has no memory (gambler’s fallacy)
  • chance evens out only over many trials
  • absolute and relative frequency
  • the mean – like a seesaw
  • the median: sort, take the middle
  • outliers: why the median is often more honest
  • range
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9:42

Episode 13

Limits & Infinity Explained

What you will learn

  • keep halving: the rest approaches 0
  • a limit = getting arbitrarily close
  • ½ + ¼ + ⅛ + … = 1
  • why 0.999… is exactly 1
  • Achilles and the tortoise
  • π with polygons like Archimedes
  • limits in everyday life: tea, battery, dice
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11:46

Episode 14

Planning a Skatepark with Math

What you will learn

  • area and perimeter of the plot: 600 m² and a 100 m fence
  • 10 % for planning → construction budget €72,000
  • cost function K(x) = 2,000 + 150x and solving an equation
  • rail and box: prices from two offers
  • the ramp: 3.7 m riding surface and an incline of almost 19°
  • survey: why the median fits better than the mean
  • the budget check: €64,800 – reserve €7,200
Watch on YouTube