Pascal's Triangle Lesson

Pascal's Triangle

Named after Blaise Pascal.
Add together numbers that are beside each other. Starting with 1.

How Pascal's Triangle Works?

Multiple Choice

What is the next row?

1 5 10 10 5 1

• 1 2 3 4 5 6 7 8

• 1 6 20 30 20 6 1

• 1 6 15 20 15 6 1

• 1 5 15 20 15 5 1

Second Diagonal -
counting numbers
Third Diagonal -
Equilateral Triangles
Fourth Diagonal - Tetrahedral Numbers

Diagonal Patterns

Multiple Choice

What diagonal is the 3D triangle pattern in and what is it called?

• First

  Equilateral

• Fourth

  Equilateral

• Fourth

  Tetrahedral

• Third

  Counting numbers

The sum of all the numbers in one row is equal to 2 to the power of the row number.

Powers of 2

​Sum of n row = 2ⁿ

Multiple Choice

What is the sum of all the numbers in the highlighted row?

• 2⁵

• 2¹⁰

• 2⁹

• 2⁸

Binomial Expansion

Multiple Choice

What is (a+b)⁵?

• a+b

• a⁴+4a³b+6a²b²+4ab³+b⁴

• a⁵+5a⁴b+10a³b²+10a²b³+5ab⁴+b⁵

If you were to shade in all the odd numbers you would get the fractal, Sierpinski's Triangle.

​Sierpinski Triangle

Multiple Choice

What is the fractal that you get from shading in all the odd numbers in Pascal's Triangle?

• Sierpinski's Triangle

• Pascal's Triangle

• Pythagorean Theorem

• Blaise Triangle

Open Ended

What do you know about Pascal's Triangle now?