Project: measure and calculate · Martinとコード

A big home project: a ruler, string and everything you have learned — Pythagoras, circles, cylinders and statistics on real things.

Your flat is full of maths

Twenty-eight lessons of theory. Today no new topic — today you go measuring. You take a ruler, a tape measure or string and walk through the flat like a surveyor.

The project has four stations:

1. A diagonal — you measure a screen and check Pythagoras on a real thing.

2. Circles in the kitchen — a plate and a mug: circumference by calculating and with string.

3. A cylinder — the volume of a mug by calculating and a check with a measuring jug.

4. Household statistics — you collect data and calculate the mean and the median.

At each station write: what I measured, what I calculated, by how much the calculation differed from reality. Small differences are normal — a ruler is not a laser. Large differences mean a mistake in the calculation; and that is exactly why this project is 完了.

The result will be a paper that proves: maths from the lessons works on things you hold in your hand.

Ema made herself a project afternoon. Phone: screen 14.7 × 6.8 cm, Pythagoras says diagonal 16.2 cm — the maker gives 6.4 inches, so 16.3 cm. A millimetre difference, it fits. Plate: diameter 24 cm, circumference by calculating 75.4 cm; with string she measured 76 cm. Mug: she calculated 310 cm³, the measuring jug showed 300 ml. “Everything in tolerance,” she writes. She most enjoys the last line: a table of heights of the whole family and the finding that the family mean is spoiled (or improved?) by her younger brother.

💡

Write down at once while measuring, and with units. “24” without a unit is a mystery in an hour. “24 cm, plate diameter” is data.

Four stations of the project

Station 1: a screen diagonal. Measure the width and height of a screen (phone, monitor, TV). Pythagoras: diagonal = √(width² + height²). Convert to inches (divide by 2.54) and compare with the maker’s figure. A difference up to 2% is a success.

Station 2: a circle. Measure the diameter of a plate. Calculate the circumference (π · d) and the area (π · r²). Then check the circumference with string: wrap, straighten, measure. Write both numbers next to each other.

Station 3: a cylinder. A mug: diameter of the mouth → radius, height. Volume V = π · r² · v in cm³. Check: pour water with a measuring jug (1 ml = 1 cm³). Watch: a mug does not have completely straight walls — a small difference is fine.

Station 4: statistics. Collect at least 5 values of one kind: heights of family members, numbers of stairs between floors, prices of five things from shopping. Calculate the mean and the median and write a sentence why they do (not) differ.

Write-up format for each station: measured / calculated / reality / difference. Four columns, no novel.

Sample 1: write-up of the diagonal station

Measured: monitor 53.1 × 29.9 cm.

Calculation: √(53.1² + 29.9²) = √(2819.61 + 894.01) = √3713.62 ≈ 60.9 cm.

Inches: 60.9 : 2.54 ≈ 24.0.

Reality (box): 24 inches. Difference: practically zero.

Conclusion in one sentence: Pythagoras on the monitor fits to a tenth of an inch.

Sample 2: write-up of the cylinder station

Measured: mug — diameter 8 cm (r = 4 cm), inside height 9.5 cm.

Calculation: V = 3.14 · 16 · 9.5 = 477.28 cm³ ≈ 477 ml.

Reality: 450 ml fitted with the measuring jug.

Difference: 27 ml, about 6%. Explanation: the mug narrows towards the bottom, a cylinder is only an approximation.

This is the most valuable line of the project — seeing WHEN a formula is only a model of reality.

Sample 3: write-up of the statistics station

Data: family heights — 178, 165, 172, 138, 171 cm.

Mean: 824 : 5 = 164.8 cm.

Median: ordered 138, 165, 171, 172, 178 → the middle 171 cm.

Conclusion: the mean (164.8) is a lot lower than the median (171), because the younger brother’s height pulled it down — a classic extreme in small data. A typical family member is better described by the median.

⚠️

Do not measure “by eye” and do not round already while measuring. Write millimetres — you may round only the result. Anyone who rounds the inputs wonders why the check does not fit.

Practice: now you do it 🎲

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

Practise Pythagoras’ theorem before you go out to measure diagonals.

Practise the questions

Project: four stations

Set aside a quiet hour for this. Split the paper into four parts, each station has columns: measured / calculated / reality / difference.

Station 1: measure a screen (width, height), calculate the diagonal with Pythagoras, convert to inches and compare with the maker’s figure.
Station 2: measure the diameter of a plate, calculate circumference and area, check the circumference with string.
Station 3: measure a mug, calculate the volume of a cylinder and check with a measuring jug of water.
Station 4: collect at least 5 values (heights, prices, stairs), calculate the mean and the median and write a conclusion in one sentence.

Now you 💪

Every measurement I have written with a unit.
At every station I have a calculation and a comparison with reality.
I can say why the calculation and reality can differ a little.

✅

Done when: You have a paper with four stations: diagonal, circle, cylinder and statistics — everywhere measured, calculated and compared.

What to take from this lesson

Formulae work on real things — and you can check it.
The format measured / calculated / reality / difference holds the project together.
A small difference is normal; a large one means a mistake in the calculation.
A formula is a model: a mug is not a perfect cylinder and that is fine.
Measure exactly, round only the result.