Problem solving strategies
After completing the first 4 strategies, we can move on to strategy 5 and 6.
Work backwards and Use logical thinking.
- 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
5. Work backwards
A mathematical problem may have a series of steps where you have to find the initial (or first) value. To solve the problem, you can work backward, step-by-step until you get to the beginning.
Example:
Peter is running a 20km race, when he ran twice as far as his current distance, he will still have 4km to go. How far has he run?
NOTE: The race is 20 km long. If he still has 4 km to run, he already ran 16 km. But the 16 km is twice what Peter has already run. Thus, he has already run 8 km.
Activity:
Joe was walking from his home to the shop, to buy his mother a bread and a milk. The shop is 10 km from his home. After walking four times as far as he already has, he still has 2km to go. How many kilometers has he walked so far?
6. Use logical reasoning
To solve mathematical problems, we first have to decide how the facts relate to each other. We can then use logical reasoning step-by-step to find a reasonable solution.
Example:
Susan, José and Rose have a cat, a cockatoo and a dog, for pets but not necessarily in that specific order. Susan is allergic to feathers, the dog owner is Rose’s friend and Susan’s classmate. Match the owners with their pets.
- We can use the clues, one at a time.
- We can draw a table again to track our findings.
Susan is allergic to feathers, so she will not own a parrot.
The dog owner is Rose’s friend and Susan’s classmate, so neither of these owns a dog. Rose is also allergic to feathers, which we saw in the previous table.
Thus, this means that José must be the dog owner, Susan must be the cat owner and Rose is the cockatoo owner.
Activity:
Susan, José and Rose visited South-Africa, Namibia and Botswana. Susan has never been to Namibia. Rose works with the person who visited Botswana, but not the one who went to Namibia. Match the people with the places that they visited.