Visual representation of the periodic table highlighting element classifications.

Problem Description:

The task involves completing a simplified version of the Periodic Table of Elements by categorizing elements into three groups: Metals, Metalloids, and Nonmetals. The table is partially filled, and the goal is to determine the correct classification for each element based on its position in the periodic table.

Solution Approach:

1. Understand the Categories:
- Metals: Elements that are typically shiny, malleable, and good conductors of heat and electricity. They are located on the left side of the periodic table.
- Nonmetals: Elements that lack metallic properties and are generally poor conductors of heat and electricity. They are located on the right side of the periodic table.
- Metalloids: Elements that have properties intermediate between metals and nonmetals. They are located along the "stair-step" line separating metals and nonmetals.

2. Identify the Stair-Step Line:
- The stair-step line runs diagonally from boron (B) to astatine (At). Elements above this line are generally nonmetals, while those below it are metals. Metalloids lie along this line.

3. Fill in the Table:
- Use the known positions of elements in the periodic table to classify them.
- Refer to standard periodic table patterns for guidance.

Step-by-Step Classification:

#### Period 1:
- Element 1 (H): Hydrogen is a nonmetal.
- Element 2 (He): Helium is a nonmetal (noble gas).

#### Period 2:
- Element 3 (Li): Lithium is a metal.
- Element 4 (Be): Beryllium is a metal.
- Element 5 (B): Boron is a metalloid.
- Element 6 (C): Carbon is a nonmetal.
- Element 7 (N): Nitrogen is a nonmetal.
- Element 8 (O): Oxygen is a nonmetal.
- Element 9 (F): Fluorine is a nonmetal.
- Element 10 (Ne): Neon is a nonmetal (noble gas).

#### Period 3:
- Element 11 (Na): Sodium is a metal.
- Element 12 (Mg): Magnesium is a metal.
- Element 13 (Al): Aluminum is a metal.
- Element 14 (Si): Silicon is a metalloid.
- Element 15 (P): Phosphorus is a nonmetal.
- Element 16 (S): Sulfur is a nonmetal.
- Element 17 (Cl): Chlorine is a nonmetal.
- Element 18 (Ar): Argon is a nonmetal (noble gas).

#### Period 4:
- Element 19 (K): Potassium is a metal.
- Element 20 (Ca): Calcium is a metal.
- Element 21 (Sc): Scandium is a metal.
- Element 22 (Ti): Titanium is a metal.
- Element 23 (V): Vanadium is a metal.
- Element 24 (Cr): Chromium is a metal.
- Element 25 (Mn): Manganese is a metal.
- Element 26 (Fe): Iron is a metal.
- Element 27 (Co): Cobalt is a metal.
- Element 28 (Ni): Nickel is a metal.
- Element 29 (Cu): Copper is a metal.
- Element 30 (Zn): Zinc is a metal.
- Element 31 (Ga): Gallium is a metal.
- Element 32 (Ge): Germanium is a metalloid.
- Element 33 (As): Arsenic is a metalloid.
- Element 34 (Se): Selenium is a nonmetal.
- Element 35 (Br): Bromine is a nonmetal.
- Element 36 (Kr): Krypton is a nonmetal (noble gas).

#### Period 5:
- Element 37 (Rb): Rubidium is a metal.
- Element 38 (Sr): Strontium is a metal.
- Element 39 (Y): Yttrium is a metal.
- Element 40 (Zr): Zirconium is a metal.
- Element 41 (Nb): Niobium is a metal.
- Element 42 (Mo): Molybdenum is a metal.
- Element 43 (Tc): Technetium is a metal.
- Element 44 (Ru): Ruthenium is a metal.
- Element 45 (Rh): Rhodium is a metal.
- Element 46 (Pd): Palladium is a metal.
- Element 47 (Ag): Silver is a metal.
- Element 48 (Cd): Cadmium is a metal.
- Element 49 (In): Indium is a metal.
- Element 50 (Sn): Tin is a metal.
- Element 51 (Sb): Antimony is a metalloid.
- Element 52 (Te): Tellurium is a metalloid.
- Element 53 (I): Iodine is a nonmetal.
- Element 54 (Xe): Xenon is a nonmetal (noble gas).

#### Period 6:
- Element 55 (Cs): Cesium is a metal.
- Element 56 (Ba): Barium is a metal.
- Element 57 (La): Lanthanum (start of lanthanides).
- Element 72 (Hf): Hafnium is a metal.
- Element 73 (Ta): Tantalum is a metal.
- Element 74 (W): Tungsten is a metal.
- Element 75 (Re): Rhenium is a metal.
- Element 76 (Os): Osmium is a metal.
- Element 77 (Ir): Iridium is a metal.
- Element 78 (Pt): Platinum is a metal.
- Element 79 (Au): Gold is a metal.
- Element 80 (Hg): Mercury is a metal.
- Element 81 (Tl): Thallium is a metal.
- Element 82 (Pb): Lead is a metal.
- Element 83 (Bi): Bismuth is a metal.
- Element 84 (Po): Polonium is a metalloid.
- Element 85 (At): Astatine is a nonmetal.
- Element 86 (Rn): Radon is a nonmetal (noble gas).

#### Lanthanides (Period 6, f-block):
- These are all metals.

#### Actinides (Period 7, f-block):
- These are all metals.

Final Classification:

Using the above reasoning, the completed periodic table would look like this (colors correspond to the legend):

- Metals: Light blue
- Metalloids: Gray
- Nonmetals: Orange

Final Answer:

\[
\boxed{\text{See the detailed classification above.}}
\]