The Jungle

1. Journey Through the Jungle Ajanis Notebook

2. Ajanis Notes Ajani knew he needed to get from Eagle Rock to the clearing, so he drew a grid of the land to help organize his path. The quickest way to get to the clearing would be on paths moving only north or east. 3. Ajanis Notes Ajani knew he needed to get from Eagle Rock to the clearing, so he drew a grid of the land to help organize his path. The quickest way to get to the clearing would be on paths moving only north or east.Eagle Rock The Clearing 4. Ajani knew he needed to get from Eagle Rock to the clearing, so he drew a grid of the land to help organize his path. The quickest way to get to the clearing would be on paths moving only north or east.He also knew he needed to steer clear of the wolves den and the watering hole.Ajanis Notes Eagle Rock The Clearing Watering Hole Wolves Den 5. Ajani knew he needed to get from Eagle Rock to the clearing, so he drew a grid of the land to help organize his path. The quickest way to get to the clearing would be on paths moving only north or east.He also knew he needed to steer clear of the wolves den and the watering hole.Ajanis Notes Eagle Rock The Clearing Watering Hole Wolves Den What Ajani wanted to know was: 6. Ajani knew he needed to get from Eagle Rock to the clearing, so he drew a grid of the land to help organize his path. The quickest way to get to the clearing would be on paths moving only north or east.He also knew he needed to steer clear of the wolves den and the watering hole.Ajanis Notes Eagle Rock The Clearing Watering Hole Wolves Den

What Ajani wanted to know was:

The probability he would pass the Wolves Den

7. Ajani knew he needed to get from Eagle Rock to the clearing, so he drew a grid of the land to help organize his path. The quickest way to get to the clearing would be on paths moving only north or east.He also knew he needed to steer clear of the wolves den and the watering hole.Ajanis Notes Eagle Rock The Clearing Watering Hole Wolves Den

The probability he would pass the watering hole

The probability he would pass both the wolves den and watering hole

How many different paths he could take that wouldnt bypass the wolves den and watering hole

The amount of time it will take to cross the jungle

11. Something to Think About; Pascals Triangle: 12. Something to Think About;

Pascals Triangle:

Arrangement of numbers where any number is the sum of two numbers above it

13. Something to Think About;

Pascals Triangle:

Arrangement of numbers whereany number is the sum of two numbers above it

Ex.3 + 3=6

14. Something to Think About;

Pascals Triangle:

Arrangement of numbers whereany number is the sum of two numbers above it

Ex.3 + 3=6

Can be applied to grid problems to illustrate the number of ways to reach any given point

15. Applying Pascals TrianglePascals Triangle can be applied to grid problems: 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 16. Applying Pascals TrianglePascals Triangle can be applied to grid problems: It can be used to illustrate the number of ways to reach a given point from another.1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 17. Applying Pascals TrianglePascals Triangle can be applied to grid problems: It can be used to illustrate the number of ways to reach a given point from another.For example from the bottom left hand corner there are 462 ways to reach the top right hand corner.1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 18. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability

19. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability

To find the probability of passing the wolves den Ajani needs to know how many ways there are from Eagle Rock to the wolves den and how many ways from the wolves den there are to the clearing.Using the grid it is easy to see there are 21 ways to reach the wolves den from eagle rock. 20. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability

To find the probability of passing the wolves den Ajani needs to know how many ways there are from Eagle Rock to the wolves den and how many ways from the wolves den there are to the clearing.Using the grid it is easy to see there are 21 ways to reach the wolves den from eagle rock. To find the number of ways from eagle rock to the clearing Ajani must reapply the triangle: 21. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityTo find the number of ways from eagle rock to the clearing Ajani must reapply the triangle: The Clearing Wolves Den 1 1 1 1 2 3 4 22. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityTo find the number of ways from eagle rock to the clearing Ajani must reapply the triangle: Therefore there are four ways to reach the clearing from the wolves den. The Clearing Wolves Den 1 1 1 1 2 3 4 23. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityThe Clearing Wolves Den 1 1 1 1 2 3 4

To find the total number of ways that pass through the wolves den:

Multiply the number of ways to get to the wolves den from eagle rock by the number of ways to get from the wolves den to the clearing:

24. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityThe Clearing Wolves Den 1 1 1 1 2 3 4

To find the total number of ways that pass through the wolves den:

Multiply the number of ways to get to the wolves den from eagle rock by the number of ways to get from the wolves den to the clearing:

P (passing den)=(21)(4)

P (passing den)= 84

= 2 11 25. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability

To reach the watering hole from eagle rock according to the diagram there are 56 ways

There is only one way to reach the clearing from the watering hole

1 1 1 1 The Clearing Watering Hole 28. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability

There is only one way to reach the clearing from the watering hole

1 1 1 1 The Clearing Watering Hole Therefore: P (passing hole)= (56)(1) 462 P (passing hole)= 56 462 = 4 33 29. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability

Since Ajani is only going North or East to save time it is not possible for him to pass both the wolves den AND the watering hole

Therefore:

the P (passing den and hole) =0

How many different paths he can take that wont bypass the wolves den and watering hole

Since he knows the number of ways that pass the wolves den and watering hole he can subtract that from the total number of paths to the clearing to calculate the number of paths that dont bypass the wolves den or watering hole

Number of paths that pass the wolves den:

Number of paths that pass the watering hole:

P (passing den)= 84 462 P (passing hole)= 56 462 36.

Number of paths that pass the wolves den:

Number of paths that pass the watering hole:

1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityP (passing den)= 84 462 P (passing hole)= 56 462 Total number of paths passing both the watering hole and wolves den= 84 462 + 56462 37.

1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityTotal number of paths passing both the watering hole and wolves den= 84 462 + 56462 = 140462 38.

1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityTotal number of paths passing both the watering hole and wolves den= 84 462 + 56462 = 140462 Number of paths that wont bypass the wolves den and watering hole= 462462 140462 - 39.

1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityNumber of paths that wont bypass the wolves den and watering hole= 462462 140462 - = 322462 40.

1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityNumber of paths that wont bypass the wolves den and watering hole= 462462 140462 - = 322462 Therefore, Ajani could take 322 different ways that would not pass the Wolves Den or Watering Hole. 41.

1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityNumber of paths that wont bypass the wolves den and watering hole= 462462 140462 - = 322462 Therefore, Ajani could take 322 different ways that would not pass the Wolves Den or Watering Hole. The probability of ways he could take that would not pass either place would be: P (passing neither )=322 462 = 2333 42.

Solving for Distance and Time Eagle Rock The Clearing 43. Solving for Distance and Time

The amount of time it would take to cross the jungle

Ajani drew his grid so that every line segment would represent 5m

Eagle Rock The Clearing 5m 5m 44. Solving for Distance and Time

From Eagle Rock to the Clearing on any given path is 11 line segments.

Eagle Rock The Clearing 5m 5m 45. Solving for Distance and Time

From Eagle Rock to the Clearing on any given path is 11 line segments.

Therefore:

11 line segments (5m)= 55m

The distance from Eagle Rock to the Clearing is 55m.

Eagle Rock The Clearing 5m 5m 46. Solving for Distance and Time The distance from Eagle Rock to the Clearing is 55m.If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Eagle Rock The Clearing 5m 5m 47. Solving for Distance and Time The distance from Eagle Rock to the Clearing is 55m.If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Ajanis pace:Distance to Clearing 0.25km55m 60 mintime Eagle Rock The Clearing 5m 5m First the 55m needs to be converted to km by dividing by 1000. 55m=0.055km 48. Solving for Distance and Time The distance from Eagle Rock to the Clearing is 55m.If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Ajanis pace:Distance to Clearing 0.25km0.055km 60 mintime Eagle Rock The Clearing 5m 5m By cross multiplying and dividing time can be calculated: (60 minutes)(0.055m)=(0.25km)(time) (60minutes)(0.055m)=time 0.25km 49. Solving for Distance and Time The distance from Eagle Rock to the Clearing is 55m.If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Ajanis pace:Distance to Clearing 0.25km0.055km 60 mintime Eagle Rock The Clearing 5m 5m By cross multiplying and dividing time can be calculated: (60 minutes)(0.055m)=(0.25km)(time) (60minutes)(0.055m)=time 0.25km Time=13.2 minutes 50. Solving for Distance and Time Eagle Rock The Clearing 5m 5m If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Time=13.2 minutes 51. Solving for Distance and Time Eagle Rock The Clearing 5m 5m If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Time=13.2 minutes The number of seconds: 1 minute0.2 minutes 60 secondsseconds 52. Solving for Distance and Time Eagle Rock The Clearing 5m 5m If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Time=13.2 minutes The number of seconds: 1 minute0.2 minutes 60 secondsseconds Cross multiply and divide to find the number of seconds: 53. Solving for Distance and Time Eagle Rock The Clearing 5m 5m If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Time=13.2 minutes The number of seconds: 1 minute0.2 minutes 60 secondsseconds Cross multiply and divide to find the number of seconds: (0.2minutes)(60seconds)=(1 minute)(seconds) (0.2minutes)60seconds)=Seconds 1 minute 54. Solving for Distance and Time Eagle Rock The Clearing 5m 5m If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Time=13.2 minutes The number of seconds: 1 minute0.2 minutes 60 secondsseconds Cross multiply and divide to find the number of seconds: (0.2minutes)(60seconds)=(1 minute)(seconds) (0.2minutes)60seconds)=Seconds 1 minuteSeconds=12 55. Solving for Distance and Time Eagle Rock The Clearing 5m 5m If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Time=13.2 minutes 0.2 minutes=12 seconds Therefore the amount of time it will take Ajani to cross the jungle at 0.25km/h is 13 minutes and 12 seconds approximately. 56. Solving for Distance and Time Eagle Rock The Clearing 5m 5m If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Time=13.2 minutes 0.2 minutes=12 seconds Therefore the amount of time it will take Ajani to cross the jungle at 0.25km/h is 13 minutes and 12 seconds approximately.The amount it would take to go to the clearing and back to eagle rock would be 26 minutes and 24 seconds since it would be twice the amount of time it took to get to the clearing.

The Jungle

Technology

Transcript of The Jungle