한국어

유럽

아시아

← Level 3 – Fraction kid

30 / 30 ⏱ 17 minutes

Fraction kid finale

A big recap of the level: ten challenges across everything you can do.

A parade of everything you can do now

Lesson thirty. Stop for a moment and look back: a month ago 0.5 was just “zero point five” for you and 3/4 just a piece of pizza. Now?

Decimal numbers: you read them, compare them, add in columns, move the point when multiplying and dividing. Fractions: you simplify, expand, add even with different denominators and translate them to decimal numbers. Divisibility: you see into numbers with no counting and you know primes. Angles: you measure, name, work out adjacent, vertically opposite and the third angle of a triangle. Solids: area, surface area, volume, units. Integers, coordinates, the mean: frost, maps and marks.

Today you will check it all at once. A decathlon waits — ten challenges, each from a different barrel. None is new. You have already handled them all, you just maybe do not know that you know.

Take paper, write methods, check with an estimate. Like a Fraction kid.

Ema, Adam, Tereza, Jonáš, Sofie and Filip sit at one table on Friday afternoon and Filip deals papers: “Decathlon. Who does all ten is a Fraction kid.” Tereza stretches her fingers like a pianist. Jonáš draws a number line in the corner, “just in case”. Sofie whispers: “Point under point, the denominator is a name…” Adam wants to start at once, Ema slows him: “An estimate. Always an estimate first.” In an hour six papers full of calculations, strips and plans lie on the table. Not everything came out first time — but every mistake they found themselves, with their own check. That is exactly what makes a pupil a Fraction kid.

💡

In the decathlon do not rush. Ten problems with a check is more than twenty without it — a mistake you find yourself counts double.

Before you go into the challenges, look at the map — Fraction kid was not a random list of topics, everything fits together:

Numbers with parts: decimal numbers and fractions are two languages for the same thing (0.5 = 1/2). Decimals can do a calculator and money, fractions can do exact thirds. Conversions between them = lesson eleven.

Fraction helpers: divisibility says what to simplify by. HCF simplifies in one blow, LCM builds common denominators. Primes are the bricks everything is built from.

Geometry: angles are first measured (a protractor), then calculated (180° on a line and in a triangle). Area is a grid of little squares (a × b), volume a grid of little cubes (a × b × c) — and units jump by 100 (area), by 1 000 (volume), because a length conversion is counted twice, or three times.

Tools for data and orientation: integers stretched the line to the left, coordinates crossed two axes into a map, the mean packs a list of numbers into one.

Who sees the links does not have to remember thirty rules — a few principles are enough: the same parts add, units convert by the number of dimensions, an estimate checks everything.

Decathlon, challenges 1–5 (numbers)

  1. Order from smallest: 2.3 — 2.08 — 2.25. (Pad to hundredths!)

  2. Work out: 15.6 + 8.75 and 4 × 2.25. (Point under point; hide the point and put it back.)

  3. Simplify 36/48 and decide which is more: 3/4, or 0.8.

  4. Work out 1/2 + 1/3. (Common denominator 6.)

  5. Is 87 a prime? And find HCF(24, 36).

Check the solutions yourself: 2.08 < 2.25 < 2.3 · 24.35 and 9 · 3/4 and 0.8, 0.8 leads · 5/6 · 87 = 3 × 29, it is not; HCF 12.

Decathlon, challenges 6–10 (geometry and data)

  1. A triangle has angles 48° and 90°. The third? And what is the adjacent angle to 48°?

  2. A rectangle 8 × 5 cm: perimeter and area. Do not mix the units!

  3. A cuboid 5 × 4 × 3 cm: volume and surface area.

  4. How many litres is 4 500 cm³? And how much is −7 + 12?

  5. The mean of marks 1, 3, 2, 2?

Checks: 42° and 132° · 26 cm and 40 cm² · 60 cm³ and 94 cm² · 4.5 l and 5 · mean 2. Ten out of ten? Fraction kid!

Bonus challenge: everything in one

Sofie buys a tank 40 × 25 × 30 cm for 850 Kč with a discount “you pay only 4/5 of the price”.

Volume: 40 × 25 × 30 = 30 000 cm³ = 30 litres (bridge : 1 000).

Price: 4/5 of 850 → 850 : 5 = 170, times 4 = 680 Kč.

Water to 4/5 of the height: 30 : 5 × 4 = 24 litres.

One problem, four lessons: volume, units, a fraction of a whole, a sense check (water < volume ✓). That is how maths looks outside — never one topic at a time.

⚠️

Do not forget the checks — even in the finale. An estimate before counting, a unit after the result, a check after dividing, the sum of angles 180°, the mean between the minimum and the maximum. Checks are not for weak counters; they are the tools of the best.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. 시작 with ten. When it goes well, add more.

Practise adding fractions — the flagship skill of Fraction kid. Write the answer as a fraction with a slash, for example 7/12.

Practise the questions

The final decathlon

Ten challenges from the examples in this lesson, on paper, with methods and checks. The Fraction kid badge is not given for speed, but for honesty.

  1. Solve challenges 1–5 (numbers): ordering decimals, adding and multiplying with a point, simplifying, comparing a fraction with a decimal number, a common denominator, a prime and HCF.

  2. Solve challenges 6–10 (geometry and data): angles in a triangle, perimeter and area, volume and surface area of a cuboid, converting to litres, integers and the mean.

  3. Check yourself against the results in the examples. By each mistake write in one sentence what happened (a lost point? added denominators?) — and solve it again correctly.

  4. Solve the bonus challenge with the tank and invent a similar “everything in one” problem for a friend or a parent.

Now you 💪

  1. I did at least 8 of 10 challenges — and for the rest I know exactly where the mistake was.
  2. By every result I have a unit and at least one check.
  3. I can say in my own words why 1/2 = 0.5 and why denominators are not added.
✅

Done when: You have gone through the decathlon across the whole level, you found mistakes with your own checks and fixed them — you are a Fraction kid.

What to take from this lesson

© 2026 Ing. Martin Polak / AlgoRhino · 콘텐츠 이용 약관