Percent kid finale

A closing circuit: everything Percent kid can do

Lesson thirty. Look at everything you can do from the start of the level:

Rational numbers and fractions: multiplying, dividing, compound fractions. Percentages in all three directions, discounts, interest and per mille. Ratio and sharing in a ratio, map scale. Proportions direct and inverse and the rule of three with arrows. And geometry: triangles with everything, quadrilaterals, areas, prisms and point symmetry.

Today nothing new. A closing circuit waits — a series of questions across the whole level. The goal is not speed, but certainty: with every question spotting which tool to pull out.

That is the biggest skill you take from Percent kid. Formulas can be googled. But deciding whether in front of you is a question for the ladder via 1%, for the rule of three, or for the area of a trapezium — that is a craft. And you have that in your hands.

The whole gang — Ema, Adam, Tereza, Jonáš, Sofie and Filip — sits at a table on Friday and plays a homemade game: cards with questions from the whole level, a die, tokens. Adam draws: “Share 720 Kč in the ratio 4 : 5.” He writes for a moment: “320 and 400.” He moves three squares. Sofie: “After 20% off it costs 480 — how much originally?” — “600!” Tereza gets a triangle construction and draws on her knee for a while. Filip loses by two squares and frowns: “Next time I want more cards with prisms.” Ema laughs: “Next time? Next time is Equation kid.”

A map of Percent kid tools

Go through the map — and by each tool answer in your head whether you can pull it out.

Fractions: multiplying (top times top), dividing (flip and multiply), a compound fraction (the main bar = divide).

Percentages — three questions: How much is the part? (base × percent.) What is the whole? (ladder: divide by the percent, times 100.) How many percent? (part : whole × 100.) Plus a discount (times 0.8), a rise (times 1.15), interest (a percent of a deposit for a year) and per mille (a thousandth).

Ratio: simplify and expand, share a whole (add the parts → one part → multiples), map scale (1 cm = the scale number in cm).

Proportions: direct (a constant quotient, via one), inverse (a constant product), the rule of three with arrows as a universal writing.

Geometry: kinds of triangles and the sum of angles 180°, SSS construction, heights and medians, the circumcircle (perpendicular bisectors of sides) and the incircle (angle bisectors), quadrilaterals and 360°, area of a triangle (a × v : 2), a parallelogram (a × v), a trapezium (average of the bases × v), prisms (V = Sp × v, S = 2Sp + lateral surface), point symmetry (through the centre, equally far).

Where you hesitated, go back — each lesson has its practice and training. The circuit below will tell you where.

A spotting quiz: which question wants which tool?

a) “How much do 7 notebooks cost when 3 cost 54 Kč?” → the rule of three, direct proportion.

b) “After 25% off it costs 450 Kč. Original price?” → the ladder: 450 is 75%, divide by 75, times 100 → 600 Kč.

c) “Share 91 sweets in the ratio 3 : 4.” → sharing in a ratio: 7 parts of 13 → 39 and 52.

d) “How much canvas for a tent in the shape of a triangular prism?” → surface area of a prism: 2 bases + lateral surface.

Notice: spotting took a few seconds and then the calculations run on their own. That is exactly how your head should look in a test.

A combined question: a trip with a map and a till

A route on a map 1 : 50 000 measures 16 cm. A bus costs 45 Kč a person and there are 6 of you; a shared spend of 540 Kč you share in the ratio 4 : 5 between snacks and tickets.

Map: 16 × 0.5 = 8 km on foot.

Bus: 6 × 45 = 270 Kč together.

Sharing: 4 + 5 = 9 parts, one part 540 : 9 = 60. Snacks 240 Kč, tickets 300 Kč.

Three tools in one question — scale, multiplying, ratio. The real world mixes topics with no warning; you already know how to untangle them.

A closing trick: percentages there and back

A question from the party: “They raised the price by 25% and then took 25% off. Are we at the original price?”

Answer by calculating: coefficients 1.25 × 0.75 = 0.9375. The new price is 93.75% of the original — 6.25% is missing.

On numbers: 400 Kč → 500 Kč → 375 Kč.

Why: 25% off took from a higher base (500) than the one the rise added from (400). Who can explain this to a younger sibling really understands percentages — and is ready for Equation kid.

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.

Revise a percent of a number — the flagship of the level. Write only the number without %.

Practise the questions

A closing circuit on paper

Eight minutes, four stations. At each first name the tool, then calculate.

1. Fractions and percentages: calculate 3/4 × 8/9, then 5/6 : 10/3, and finally 18% of 550.

2. The ladder and a ratio: 35% of an amount is 210 Kč — what is the whole amount? Then share 960 Kč in the ratio 5 : 7.

3. The rule of three: 4 tractors plough a field in 9 hours. How long will 6 tractors plough it? Draw arrows.

4. Geometry: calculate the area of a trapezium with bases 12 and 8 cm and height 5 cm; then the volume of a cuboid 8 × 5 × 4 cm.

Now you 💪

1. For every question on the circuit I first named the tool and then calculated.
2. I managed the circuit without looking in earlier lessons.
3. I know which topics I will still practise, and I have them written down.

What to take from this lesson

• The biggest skill of Percent kid: spotting which tool a question wants.
• Percentages: three questions, three methods, one ladder via 1%.
• The rule of three with arrows handles direct and inverse proportion.
• Areas and volumes sit on the pair side + perpendicular height.
• What you recognise but cannot finish counting is not skill — go back and finish counting.

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