Free Printable Pascal's Triangle Sheets
Print Pascal's triangle with a few numbers missing. The triangle starts from a single 1, every row begins and ends with 1, and each inner number totals the pair of numbers right above it, so every blank is one addition away.
Three sizes are offered, 8, 12 and 16 rows, hiding six, nine and twelve numbers respectively. Once the triangle is full, coloring its odd numbers draws the Sierpinski triangle, a pattern that repeats inside itself. Each set of sheets is gathered in a workbook, and the Pascal's triangle generator draws new sheets with a key that fills in the blanks and circles the odd cells.
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Last updated on Tue, 03 Nov 2026 01:24:02 GMT
About the Pascal's triangle sheets
How the triangle grows
Pascal's triangle is built row by row from a 1 at the top. Each row opens and closes with 1, and every number between them adds up its two neighbors on the row above. The rows soon hold large numbers: 1, 4, 6, 4, 1 on the fifth row, and 462 in the middle of the twelfth.
From numbers to a pattern
On these sheets, a child first fills the blanks, each found from the two numbers just above it. Then the odd numbers get a color and the even ones stay white. Since odd plus even gives odd and two odds or two evens give even, the colored cells form triangles inside triangles: the Sierpinski triangle.
Picking a size
Eight rows suit a first try, with small numbers and large hexagons to color. Twelve rows bring numbers of up to three digits to find. Sixteen rows give the fullest pattern, one step beyond the eight-row picture, in smaller cells.
A triangle with many names
Blaise Pascal wrote about it in a treatise published in 1665, but the triangle was known long before: it is Yang Hui's triangle in China, Khayyam's triangle in Iran and Tartaglia's triangle in Italy.
