Pascal's Triangle and Pathways with Learning Goals.notebook April 29, 2014
Tuesday April 29
1. Hand in permutations/combinations assignment
2. Lesson: Pascal's Triangle
3. Practice
4. Test Thursday/Practice Test
Pascal's Triangle and Pathways with Learning Goals.notebook April 29, 2014
MINDS ON1
1 11 12
1 13 31 4 6
Fill in the missing values in the pattern:
Pascal's Triangle and Pathways with Learning Goals.notebook April 29, 2014
Lesson goals Big Idea
Pascal's Triangle
I can investigate patterns in Pascal’s triangle and the relationship to combinations.
I can use these patterns to solve simple counting problems.
Pascal's Triangle and Pathways with Learning Goals.notebook April 29, 2014
11 1
1 2 11 3 3 1
1 4 6 4 1 1 5 10 10 5 1
1 6 15 20 15 6 1
Pascal's Triangle
1. What is the pattern used to create each row?
Each number is just the two number above it addes together.
1 + 3 = 4
Investigation 1
Pascal's Triangle and Pathways with Learning Goals.notebook April 29, 2014
1. What is the pattern in the second diagonal within Pascal’s triangle?
2. What is the pattern in the third diagonal?
11 1
1 2 11 3 3 1
1 4 6 4 1 1 5 10 10 5 1
1 6 15 20 15 6 1
The counting Numbers (1, 2, 3, ...)
The triangular numbers
2.
3.
Pascal's Triangle and Pathways with Learning Goals.notebook April 29, 2014
11 1
1 2 11 3 3 1
1 4 6 4 1 1 5 10 10 5 1
1 6 15 20 15 6 1
4. What do you notice about the horizontal sums? Is there a pattern?
The pattern doubles for each row. The powers of 2.
row 0
row 1
row 2
row 3
row 4
row 5
row 6
5. What conclusion could you make about the sum of the terms in the row and the row number?
20=121=222=423=824=16
2(row number) =HORIZONTAL SUM
Pascal's Triangle and Pathways with Learning Goals.notebook April 29, 2014
Naming conventions in Pascal's Triangle
Why is it so? With this way of naming the rows and elements, you can use combination notation to find any value in Pascal's Triangle!
Pascal's Triangle and Pathways with Learning Goals.notebook April 29, 2014
Investigation 2 Pathway ProblemsOn each grid, how many different paths can A take to get to B, assuming that you can only move to the right and down?
a) (b)
8C4 = 70
0
0
Pascal's Triangle and Pathways with Learning Goals.notebook April 29, 2014
Ataxicompanyistryingtoindthequickestrouteduringrushhourtraficfromthetrainstationtothefootballstadium.Howmanydifferentroutesmustbeconsideredifateachintersectionthetaximustalwaysmoveclosertothefootballstadium?
Pascal's Triangle and Pathways with Learning Goals.notebook April 29, 2014
SUMMARY
Pascal's Triangle and Pathways with Learning Goals.notebook April 29, 2014
Exit Card
For Option 2:
Determine the number of different ways Kipper can go home if he must avoid the fire hydrant.
Pascal's Triangle and Pathways with Learning Goals.notebook April 29, 2014
BACK
Pascal's Triangle and Pathways with Learning Goals.notebook April 29, 2014
Your task(s):
1. Page 289 # 1, 2, 7, 11, 12
2. Work on the probability unit practice test (we will go over it tomorrow)