Math Basics — Simply Explained

Each skill explained clearly — with everyday examples

The belt colors correspond to the Dojo Mode in the Math Fighter app. Both modes (KIDS and STUDENT) have all 8 belts with different difficulty levels. Topics are aligned with common school curricula.

For kids aged 6 to 12. All 8 belts are playable! Tasks are age-appropriate — with pictures, stories, and simple language.

Belt Grade Topics Difficulty
White Belt 1–2 Addition, Subtraction, Doubles, Halves (1–20) — with apples, candies and fingers 🟢 Easy
Yellow Belt 2–3 Addition & Subtraction up to 100 — step by step with carrying 🟢 Easy
Orange Belt 3–5 Times tables, Division, simple percent (50%, 25%) 🟠 Medium
Green Belt 4–6 Order of Operations, Parentheses — kid-friendly examples 🟠 Medium
Blue Belt 5–6 Fractions, Decimals, Conversion 🟠 Challenging
Brown Belt 5–7 Geometry (Area, Perimeter), Powers 🔴 Hard
Black Belt 7–8 Simple equations (find x), Summation 🔴 Very hard
2nd DAN 8–9+ Simple functions f(x) — plug in values 🔴 Very hard

For students and adults aged 13 to 99. More direct explanations, higher numbers, and more complex tasks. All belts in Math Fighter are achievable.

Belt Grade Topics Difficulty
White Belt 1–2 Addition, Subtraction, Doubles, Halves (1–20) 🟢 Easy
Yellow Belt 2–3 Addition & Subtraction up to 100 (with carrying) 🟢 Easy
Orange Belt 3–5 Multiplication, Division, Percent Basics 🟠 Medium
Green Belt 4–6 Order of Operations, Parentheses 🟠 Medium
Blue Belt 5–6 Fractions, Decimals, Conversion 🟠 Medium
Brown Belt 5–7 Geometry, Powers 🔴 Hard
Black Belt 7–8 Algebra, Equations, Summation (Σ) 🔴 Hard
2nd DAN 8–9+ Functions f(x), Inverse Functions 🔴 Hard

Grade 1–2

White Belt

Addition (Adding)

Difficulty:

What is it? Adding two or more numbers together.

🍎🍎 + 🍎🍎🍎 = 🍎🍎🍎🍎🍎
You have 2 apples. Your grandmother gives you 3 more apples. How many apples do you have now?
2 + 3 = 5

💡 Tip: Use your fingers to count — everyone does it at the beginning!

Subtraction (Taking Away)

Difficulty:

What is it? Taking one number away from another.

🍬🍬🍬🍬🍬🍬 - 🍬🍬 = 🍬🍬🍬🍬
You have 6 candies. You eat 2 of them. How many candies do you have left?
6 - 2 = 4

💡 Tip: Imagine giving something away — what's left?

⚪⚪

Doubles & Halves

Difficulty:

What is it? Multiplying a number by 2 (doubling) or dividing by 2 (halving).

You have 6 marbles. Your friend gives you the same amount. Double!
⚪⚪ 6 = 12
⚪⚪ = Double (×2)   |   ◔ = Half (÷2)

💡 Tip: Doubling means adding the number to itself! 6 + 6 = 12.

Grade 2–3

Yellow Belt
🔢

Carrying & Borrowing (up to 100)

Difficulty: ⭐⭐

What is it? Addition and subtraction with two-digit numbers — with carrying over tens.

You have 47 trading cards and get 38 more. 7 + 8 = 15 — write 5, carry 1!
47 + 38 = 85
You have 83 stickers and give away 27. 3 - 7 doesn't work — borrow a ten!
83 - 27 = 56

💡 Tip: Break down hard problems: 83 - 27 → first 83 - 7 = 76, then 76 - 20 = 56.

Grade 3–5

Orange Belt

Multiplication (Times)

Difficulty: ⭐⭐

What is it? Quick addition of equal groups.

Every person has 2 shoes. 3 friends come to visit. How many shoes are at the door?
3 × 2 = 6

💡 Tip: Multiplication is like fast addition — 3 × 2 is the same as 2 + 2 + 2!

Division (Sharing)

Difficulty: ⭐⭐

What is it? Sharing fairly into equal groups.

You have a birthday cake with 8 slices. There are 4 children. How many slices does each child get?
8 ÷ 4 = 2

💡 Tip: Division is the opposite of multiplication — fair sharing!

%

Percent Basics

Difficulty: ⭐⭐

What is it? Calculating parts of 100 — the most common: 10%, 25%, 50%.

A game costs 80 euros. You get a 25% discount. How much do you save?
25% von 80 = 20
25% = one quarter. 80 ÷ 4 = 20.

💡 Tip: 50% = half, 25% = quarter, 10% = tenth. Remember these three!

Grade 4–6

Green Belt
🔢

Order of Operations

Difficulty: ⭐⭐⭐

What is it? The rule that multiplication and division are always calculated BEFORE addition and subtraction.

You buy 3 bags with 2 gummy bears each and get 4 extra gummy bears as a gift. How many do you have in total?
3 × 2 + 4 = 10
First 3 × 2 = 6, then 6 + 4 = 10. Not 3 × 6 = 18!

💡 Tip: Remember: multiply and divide first, then add and subtract!

( )

Parentheses

Difficulty: ⭐⭐⭐

What is it? Parentheses change the order — what's inside parentheses is calculated first.

Compare: 3 + 4 × 5 versus (3 + 4) × 5 — same numbers, different result!
3 + 4 × 5 = 23
(3 + 4) × 5 = 35

💡 Tip: Parentheses are the boss — they are ALWAYS calculated first!

Grade 5–6

Blue Belt
½

Fractions

Difficulty: ⭐⭐⭐

What is it? Parts of a whole — a pizza cut into 4 slices, 1 slice = 1/4.

You eat 1/2 pizza and your friend eats 1/4 pizza. How much did you eat together?
1/2 + 1/4 = 3/4
1/2 = 2/4, so 2/4 + 1/4 = 3/4

💡 Tip: Adding fractions: first find the same denominator, then add the numerators!

0.5

Decimals

Difficulty: ⭐⭐⭐

What is it? Fractions written as decimal numbers. 1/2 = 0.5 and 3/4 = 0.75.

How do you write 3/4 as a decimal? Divide 3 by 4!
3/4 = 0,75

💡 Tip: Remember: 1/2 = 0.5 | 1/4 = 0.25 | 3/4 = 0.75 | 1/5 = 0.2

Grade 5–7

Brown Belt

Geometry: Area & Perimeter

Difficulty: ⭐⭐⭐⭐

What is it? Area = how much space a shape takes up. Perimeter = how long the edge is.

6 × 4 = 24 squares
A rectangle is 6 cm long and 4 cm wide.
Area = 6 × 4 = 24 cm²
Perimeter = 2 × (6 + 4) = 20 cm

💡 Tip: Area = length × width. Perimeter = add all sides together!

Powers & Exponents

Difficulty: ⭐⭐⭐⭐

What is it? Multiplying a number by itself. 3² = 3 × 3. 2³ = 2 × 2 × 2.

3² = 9
2³ = 8
A square with side length 5 — what is the area? 5 to the power of 2!
5² = 5 × 5 = 25
2³ = 2 × 2 × 2 = 8

💡 Tip: The small number on top (exponent) tells you how many times to multiply!

Grade 7–8

Black Belt
x

Algebra & Equations

Difficulty: ⭐⭐⭐⭐⭐

What is it? Finding unknown numbers (x) by solving equations.

If 3x + 5 = 20, what is x? Subtract 5, divide by 3!
3x + 5 = 20 → x = 5
3x = 15 → x = 15 ÷ 3 = 5

💡 Tip: Goal: get x alone on one side! Do the same thing on both sides.

Σ

Summation (Σ)

Difficulty: ⭐⭐⭐⭐⭐

What is it? A shorthand for 'add all numbers from ... to ...'.

Add all numbers from 1 to 5:
Σ(i, i=1..5) = 1+2+3+4+5 = 15

💡 Tip: Σ is just an abbreviation for many plus signs in a row!

Grade 8–9+

2nd DAN
f(x)

Functions f(x)

Difficulty: ⭐⭐⭐⭐⭐

What is it? A formula that takes a number (x) and calculates a result.

The function f(x) = 2x + 3. What is f(4)?
f(4) = 2×4 + 3 = 11
Reverse: f(x) = 2x + 3 and f(x) = 11. What is x?
2x + 3 = 11 → x = 4

💡 Tip: Plug in the number for x and calculate step by step!

Everyday Math

🎮 Tutorials in the app
🕛

Reading the Clock

Difficulty:

What is it? Telling the time on a clock with hands. The short hand shows the hour, the long hand shows the minutes.

🕒 → 🕞
The short hand is just past 3, the long hand points to 6. Half an hour has gone by since 3 o'clock.
🕞 = 3:30

💡 Tip: Long hand on 12 = o'clock, on 3 = quarter past, on 6 = half past, on 9 = quarter to.

💰

Money & Change

Difficulty: ⭐⭐

What is it? Knowing what coins and notes are worth, adding them up, and working out the change.

🪙🪙🪙 + 💵
An ice cream costs 4. You pay with a 10 note. How much change do you get back?
10 - 4 = 6

💡 Tip: Start counting with the biggest coin — it is quicker and you make fewer mistakes.

🌡

Temperature

Difficulty: ⭐⭐

What is it? Reading a thermometer and calculating with degrees Celsius (°C).

🌡 4°C → 17°C
In the morning it is 4°C. By midday the thermometer shows 17°C. How much warmer did it get?
17 - 4 = 13 °C

💡 Tip: Water freezes at 0°C and boils at 100°C — between those two marks you can estimate everything else.

The AI Tutor

🤖 Pro feature
🤖

Learning with the AI Tutor

What is it? A tutor inside the app that teaches in a conversation, instead of only marking answers right or wrong.

It first works out what you already know, then explains the next topic — and asks a control question to check that it really landed. From your answers it plans what comes next, and brings topics back days later so they stick.
Ask it anything in between — it answers your question and then picks the plan back up where you left off.

💡 Good to know: The tutor is a Pro feature — the first message is free with 20 trial credits, Pro includes 300 credits a month. For children, a parent has to agree before it can be used.

Practice these skills playfully with Math Fighter!

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