View
11.532
Download
4
Embed Size (px)
DESCRIPTION
This is lesson where students can guide themselves through exploring and investigating patterns in Pascal's triangle.
Citation preview
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