1. Journey Through the Jungle… Ajani’s Notebook

2. Ajani’s 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. Ajani’s 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. Ajani’s 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. Ajani’s Notes Eagle Rock The Clearing Watering Hole Wolves Den What Ajani wanted to know was:

11. Something to Think About; Pascal’s Triangle:

15. Applying Pascal’s Triangle Pascal’s 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 Pascal’s Triangle Pascal’s 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 Pascal’s Triangle Pascal’s 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

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 Probability To 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 Probability To 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

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? Ajani’s pace: Distance to Clearing 0.25km 55m 60 min time 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? Ajani’s pace: Distance to Clearing 0.25km 0.055km 60 min time 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? Ajani’s pace: Distance to Clearing 0.25km 0.055km 60 min time 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 minute 0.2 minutes 60 seconds seconds

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 minute 0.2 minutes 60 seconds seconds 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 minute 0.2 minutes 60 seconds seconds 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 minute 0.2 minutes 60 seconds seconds Cross multiply and divide to find the number of seconds: (0.2minutes)(60seconds)=(1 minute)(seconds) (0.2minutes)60seconds)=Seconds 1 minute Seconds=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.