pascal's triangle maths investigation

Pascal’s Triangle

WALT: investigate and describe patterns

What is Pascal’s triangle? 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“

It is used to solve problems of probability

FUNCTION – How does it work? What is the rule? Use the rule to

complete a triangle.

What can you see?

Here is a hint to help you finish the triangle.

You may use a calculator.

Finding patterns

Find the total of each row and record this. What do you notice? Can you use exponents to record this

number sequence? Can you write a general statement for

this number sequence?

Explore diagonal patterns within the triangle.

Look at the diagonals: Is there a pattern

along each diagonal?

Describe the pattern and its rule.

More Diagonal Patterns2nd diagonal = triangular

numbers AND the adjacent numbers make square numbers

3rd diagonal = tetrahedral numbers (add the layers) AND the adjacent numbers make pyramid numbers (add the layers.)

Investigate Pascal’s triangle – ODDS and EVENS

Shade in all the even numbers in Pascal’s triangle. What do you notice?

This called - The Sierpinski Triangle

Are there more odd or even numbers?

Can you remember the addition properties of odd and even numbers?

ODD + ODD = EVEN + ODD =EVEN +EVEN = How can you relate this to your

prediction?

Are there more odd or even numbers?

Design a table or graph to record your data in two ways:

By rowAccumulative Challenge! What is the ratio of even to odd

numbers after 3, 7,15 rows?

Find your own patterns!

Colour multiples of nine What do you see?

Try multiples of other numbers are there repeating patterns?

More information

http://www.mathsisfun.com/pascals-triangle.html