Applying the problem solving process

1. Applying the problem solving process

2. Essential Question: • How do I solve problems?

3. Review: What are the 4 steps of the Problem Solving Process?

4. Problem Solving Process • Understand the problem. • Make a plan to solve the problem. • In Computer science we call this plan an Algorithm • Carry out the plan. • Review and reflect on how the problem was solved.

5. What is an algorithm? Watch the video • https://www.youtube.com/watch?v=6hfOvs8pY1k

6. Algorithm: a set of instructions for completing a task • The word “algorithm” is derived from the name of Mohammed ibn Musa Al-Khowarizmi. He joined an academic center known as the House of Wisdom in Baghdad around 800 AD. His works transmitted the Hindu art of reckoning to the Arabs, and then to Europeand us.

7. Handshake Problem #1 • There are 20 people in a room, including you. You must shake hands with everyone else in the room. How many hands will you shake? If there are N (where N>0) people in the room, how many hands will you shake?

8. Understanding the problem • What data or information is known? • What is unknown? • What are the conditions?

9. Understanding the problem • What data or information is known? • There are 20 people

10. Understanding the problem • What is unknown? • How many hands I will shake.

11. Understanding the problem • What are the conditions? • Have to shake everybody’s hand once.

12. Plan the Solution • What is your plan to solve this problem? (How can you solve the problem?)

13. Plan the Solution • I am going to draw out the problem and count how many hands I will shake.

14. Carry out the plan • Using your plan, show your work and your solution. • How many hands will you shake?

15. Carry out the plan

16. Reflect and discuss your solution • How well did your plan work? Did you find the correct answer? What could you change about your plan?

17. Reflect and discuss your solution • My plan worked. I figured out how many hands I would shake. But it was a little tedious to draw out all the figures. Is there a pattern? • If there were only 10 people in the room, including me, then I would shake 9 hands. So the pattern seems to be 20-1=19, 10-1=9. • I could use a formula to make this easier. If there were N people in the room (as long as N>0) than the formula (Algorithm) is N-1

18. Try on your own: Handshake Problem #2 • There are 10 people in a room, including you. Each person in the room must shake hands one time, and only one time, with all the other people in the room. How many handshakes will occur? If there are 20 people in the room, how many handshakes will occur? If there are N (where N>0) people in the room, how many handshakes will occur?

19. Understanding the problem • What data or information is known? • What is unknown? • What are the conditions?

20. Understanding the problem • What data or information is known? • There are 10 people or N people in the room.

21. Understanding the problem • What is unknown? • Total number of handshakes.

22. Understanding the problem • What are the conditions? • Each person must shake hands only one time with all others in the room. • All of the handshakes must be added together.

23. Plan the Solution • What is your plan to solve this problem? (How can you solve the problem?)

24. Plan the Solution • Have the people line up in the room. The first person in the line walks down the line and shakes hands will all of the people in the line and then leaves the room. Count the number of handshakes and add to the total. • The next person in line walks down the line and shakes hands with all of the people left in the line and then leaves the room. Count the number of handshakes and add to the total. • This continues until there are only 2 people. They shake hands and leave together. Increase the total by one.

25. Carry out the plan • Using your plan, show your work and your solution. • How many handshakes will occur?

26. Carry out the plan • Now add up the # of handshakes: 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0 = 45 • For 10 people, the answer is the sum of the numbers from 1 to 9, which is 45. 9 is 10-1. • For 5 people, the answer is the sum of the numbers from 1-4, which is 10. 4 is 5-1. • For 2 people, the answer is the sum of the numbers from 1 to 1, which is 1. 1 is 2-1. • For N people, the answer is the sum of the numbers from 1 to (N-1).

27. Reflect and discuss your solution • How well did your plan work? Did you find the correct answer? What could you change about your plan?

28. Reflect and discuss your solution • Each person shakes hands with N-1 other person. The answer is not N(N-1), though, because each handshake counts as the one handshake for each person, but only one handshake for the total. The candy bar problem helped to start the plan for this problem, but I needed to adjust the plan to only allow one handshake between each pair in the room. • So the 10 people make 9 handshakes each, but each handshake happens between 2 people, and can only be counted once. I could “divide” the handshake and let each person count the handshake as a ½ handshake. So 10 people make 9 half-handshakes each = 45 handshakes. • N people make N-1 half-handshakes each = N(N-1)/2 • The sum of the numbers from 1 to N-1 = N(N-1)/2

29. Does the algorithm work? N(N-1)/2 10 (10-1)/2 = 10(9)/2 = 90/2 = 45 • Yes the algorithm works!

30. Try the algorithm N(N-1)/2 : 7 people? 7(7-1)/2 = 7(6)/2 = 42/2 = 21 handshakes total

31. Try the algorithm N(N-1)/2 : 50 people? 50(50-1)/2 = 50(49)/2 = 2450/2 = 1225 handshakes total

32. Summarize • How can you use the problem solving process in real life?