Pascal's Triangle Tree

THE TRIANGLE TREE

Click inside the triangle till you find a pattern.
When you find the pattern, point your mouse to the right spot, and type in the missing numbers.
Press the [ENTER] key when you finish typing a number in its place.
If you are right, the number will appear in its proper place.
After you have entered all the numbers possible, you are ready to answer the exercises below.
For a maximum of 10 points, screencopy and email me your completed tree
Plus answer the exercises below.
You receive no points for the answers without the completed tree,
And no points for the tree without the answers.
Due by noon on Tuesday.

Add the numbers in each row, and list them.
Find a pattern in the list you made for exercise 1, and describe it in English.
Write the formula that produces the sum of all the numbers on the nth row. The top row is ROW 0.
If this tree had one more row, what would the numbers be on that row? List the numbers on the next row immediately below the base of the triangle.
On what row, and in what position, is the number of ways to arrange 2 black aces among 3 red aces? Which number is it? Count positions from the left starting with 0 as the first position. Count rows from the top starting with 0.
Which row lists all the ways of making a pizza if you only have 6 toppings? Count rows from the top starting with 0.
What was the name of the web assignment where you listed the numbers on row 10? The top row is row 0.
What was the name of the problem where we studied the numbers in the diagonal that begins with 1, 3, 6, 10...?
Remember way back when we counted the regions made by intersecting lines in a circle? The figures below show how many regions can be made with circles containing 2 to 8 points. Compare the number of regions in each circle with the numbers in the triangle above. What is the connection between them? How many regions are possible with 9 points on a circle? Use the triangle tree to find the answer.
What was the name of the lab where we studied the sums of the numbers in the diagonals below?

Last Modified 10/24/08 6:29 PM