This pattern is named after the French mathematician Blaise Pascal (1623-62), who brought the triangle to the attention of Western mathematicians (it was known as early as 1300 in China, where it was known as the “Chinese Triangle”).
The triangle itself is made by arranging numbers. Each number in the triangle is the sum of the pair of numbers directly above it (to the above left and above right). The first four rows are as follows (the 1 at the top is considered to be Row 0):
The worksheet below shows the above triangle and then asks the children to try and work out how the triangle is made. They are then required to complete the next five rows of the triangle, which are as follows:
When the children have completed all of the triangles, they should look for patterns. The questions at the bottom of the worksheet focus the children’s attention on different aspects of the triangle (e.g. even and odd numbers, diagonal lines, a total of the numbers in each row).