Math practice · Unit #09 · 8th grade · Meet the periodic table

Mendeleev's Report Card

In 1871 Mendeleev left a gap in his table and predicted the missing element's density and melting point. Four years later gallium was found — and it melts in your palm. Grade the great man's predictions: percent error.

skills: percent error scatter patterns weighted averages ≈ 35 min
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Name Period Date
PART A

Grading eka-aluminum

% error = |predicted − actual| ÷ actual × 100
Mendeleev called the missing element "eka-aluminum." Here are his predictions (rounded for grading) next to gallium's actual measured values.

Predicted vs. actual (gallium, discovered 1875)
PropertyMendeleev's predictionActual% error
Density (g/cm³)6.05.91
Melting point (°C)3029.8
Atomic mass (g/mol)6869.7

  1. Compute all three percent errors (round to one decimal). What letter grade would you give a prediction machine this accurate — and why is predicting properties of something never seen more impressive than measuring them?

PART B

The pattern, as data

Melting points of elements 3–10 (in °C). Plot them (atomic number on x, melting point on y) and the table's hidden wave appears.

Melting points, elements 3–10
ElementAtomic #MP (°C)
Li3180
Be41,287
B52,075
C63,550
N7−210
O8−218
F9−220
Ne10−249

  1. Range of the dataset (max − min, signs included):

  2. Describe the shape: where does it rise, where does it crash? The next element, Na (#11), has MP 98 °C — low again, like Li. What does that restart tell you about why the table is called periodic?

PART C

Why chlorine weighs 35.5

The table says chlorine's atomic mass is 35.5 — but no chlorine atom weighs 35.5. About 75% are Cl-35 and 25% are Cl-37. The table reports a weighted average.

  1. Compute it: (35 × 0.75) + (37 × 0.25) = ?

  2. Why isn't the answer 36 — the plain average of 35 and 37? Use the word weighted in your answer.

  3. Magnesium: 79% Mg-24, 10% Mg-25, 11% Mg-26. Compute the table's value. (0.79×24 + 0.10×25 + 0.11×26)

PART D

Two pies, same universe

Earth's crust: O 46.6% · Si 27.7% · Al 8.1% · Fe 5.0% · everything else 12.6%.
Human body: O 65% · C 18% · H 10% · N 3% · everything else 4%.

  1. Check both pies: do they each sum to 100%? Show it.

  2. Silicon is the crust's #2 element at 27.7% — and barely appears in your body. Carbon is your #2 — and barely appears in the crust. One sentence: what does the comparison say about how life selects its ingredients rather than just grabbing what's around?

Answer key — teachers

Part A

Density: 0.09/5.91 ≈ 1.5% · MP: 0.2/29.8 ≈ 0.7% · mass: 1.7/69.7 ≈ 2.4%.

  1. A-grade work: sub-3% errors on a never-seen element. Predicting beats measuring because it proves the pattern has power — the table knew chemistry it had never met.

Part B

  1. 3,550 − (−249) = 3,799 °C
  2. Rises Li→C (peak 3,550), crashes at N→Ne (all below −200). Na restarting LOW like Li = the pattern repeats — that's what periodic means: the wave comes around again every row.

Part C

  1. 26.25 + 9.25 = 35.5 ✓ matches the table.
  2. Plain average weights both isotopes equally; the real mix is 3:1 toward 35, so the weighted average leans toward the common isotope.
  3. 18.96 + 2.5 + 2.86 = 24.32 (matches the table's 24.3).

Part D

  1. 46.6+27.7+8.1+5.0+12.6 = 100 ✓ · 65+18+10+3+4 = 100 ✓
  2. Life is selective: it builds from reactive light elements (C, H, N) rather than mirroring the crust's abundance — chemistry chosen for function, not availability.