Problem solving strategies:
- Look for a pattern
- Make an organized list
- Draw a table
- Guess and check (Trial and improvement)
- Work backwards
- Use logical reasoning
- Draw a diagram
- Solve a simpler problem
Now that we have had a look at the previous 7 problem solving strategies, it brings us to the last lesson. In this lesson we are going to have a look at solving a simpler problem.
Example:
There are 24 teams in a netball league. Each of these 24 teams, has to play each other twice during the season. How many matches will take place in a season?
Make the problem simpler by working with fewer teams first.
We can use 3 teams as a simpler problem:
Teams: A , B , C
We can also take these 3 teams so that each one plays against the other teams twice.
The matches will take place as follow: AB , AC, BC which is 3 matches.
We can see that each team only plays against another team 2 times.
If these matches had to be played twice, there will be 6 matches during the season.
Therefore: 3 teams x 2 matches = 6 matches
If there are 4 teams: A , B , C , D, the matches will take place as follow:AB , AC , AD , BC , BD , CD which is 6 matches.
If each match occurred twice, there will be 12 matches in total.
We can see that the teams plays against each other 3 times.
Therefore, 4 teams x 3 matches = 12 matches in total
If we had 5 teams, we can say that these teams will play 4 matches each.
Therefore, 5 teams x 4 matches = 20 matches in total.
Now that we have a calculation for a simpler sum, we can calculate the actual question.
24 teams, will play 23 matches. Therefore, 24 teams x 23 matches = 552 matches.
During the season, 552 netball matches will be played.
Activity:
Mr. Johnson wants to organize a knockout tournament for soccer. There are 14 teams in the tournament. How many matches will have to be played until the winner is found?
(NOTE: In a knockout tournament, the winners go to the next round, while the losers are knocked out of the tournament.)
Remember: There may be more than one way to solve a problem. The strategies discussed in this lesson as well as all the previous lessons are all just examples of how a problem can be solved.
Mathematics can be solved by using a lot of different strategies of problem solving or methods. That is what makes mathematics so much fun, there are always more than one way to calculate sums.