the periodic table
The periodic table is the single most useful chart in all of chemistry and materials science: a grid of every known element arranged so that atoms with similar behaviour line up together. It works because chemistry repeats. As you add electrons one by one, the outer-shell pattern cycles over and over, so elements a fixed distance apart behave alike — the property is periodic, hence the name.
Reading it is straightforward once you know the layout. Rows (called periods) go left to right in order of increasing atomic number, and each new row starts a new electron shell. Columns (called groups) stack elements with the same number of valence electrons: group 1 all have 1 outer electron (the reactive alkali metals like sodium), group 17 all have 7 (the grabby halogens like chlorine), and group 18 all have full shells (the inert noble gases). Metals dominate the left and centre, nonmetals the upper right, with a staircase of in-between metalloids like silicon and germanium separating them.
For a materials engineer the table is a map of raw ingredients and their tendencies. It tells you at a glance which elements will donate electrons and which will accept them (and therefore what kind of bond they will form), where the semiconductors live, and which neighbours might substitute for one another in an alloy. The next term, electronegativity, is essentially a number added onto this map.
Copper, silver, and gold all sit in the same column (group 11), and sure enough all three are soft, dense, excellent electrical conductors used in wiring and contacts — a family resemblance you can read straight off the table.
Same column, same valence, similar properties.
The table predicts trends and tendencies, not exact values. Position tells you an element is likely to be, say, a soft reactive metal, but the actual melting point or strength still depends on how the atoms bond and pack in the solid.