Creative problem solving or Non-Routine Mathematics involves finding solutions for unseen problems or situations that are different from structured Maths problems. There are no set formulae or strategies to solve them , and it takes creativity, flexibility and originality to do so. This can be done by creating our own ways to assess the problem at hand and reach a solution. We need to find our own solutions and sometimes derive our own formulae too.
A non-routine problem can have multiple solutions at times, the way each one of us has different approach and different solutions for our real-life problems.
Why non-routine Mathematics
- It’s an engaging and interesting way to introduce problem solving to kids and grown-ups.
- Its helps boost the brain power.
- It encourages us to think beyond obvious and analyse a situation with more clarity.
- Encourages us to be more flexible and creative in our approach and to think and analyse from an extremely basic level, rather than just learning Mathematical formulae and trying to fit them in all situations.
- Brings out originality, independent thought process and analytical skills as one must investigate a problem, reach a solution, and explain it too.
How to Analyse a Non-Routine Problem:
- Read the problem well and make note of the data given to you.
- Figure out clearly what is asked or what is expected from you.
- Take note of all the conditions and restrictions. This will help you get more clarity.
- Break up the problem into smaller parts , try to solve these smaller problems first.
- Make a note of data and properties or any similar situations ( faced earlier)
- Look for a pattern or think about a logical way of reaching a solution. Make a model or devise a strategy.
- Use this strategy and your knowledge to reach a solution.
Let’s try a few examples!
Example 1:
There are 50 chairs and stools altogether in a restaurant. Find the number of chairs and the number of stools, if each chair has 4 legs and each stool has 3 legs and there are 180 wooden legs in the restaurant?
Solution:
First thing that comes to our mind is that we have two algebraic equations here and solving simultaneous equations is the only way to get a solution.
Not really! A small child and a Non-Math student can solve it too.
Logic: Each piece of furniture has at least 3 legs (stools-3 legs, chairs -4 legs).
So, minimum number of legs (for 50 pcs of furniture) in the restaurant = 3 X 50 = 150 legs if there are only stools in the restaurant.
Chairs have 4 legs i.e., each extra leg belongs to a chair.
(we have already taken 3 legs of each chair and stool into account)
Number of extra wooden legs in the restaurant
= total number – minimum possible number of legs for 50 pcs of furniture
= 180 -150 = 30 legs
Each extra leg (4th leg) belongs to a chair.
Therefore, the number of chairs in the restaurant = 30
So, number of stools = 50-30=20
For more on this topic: Solving without Simultaneous Equations
Example 2:
A cube is painted from all sides. It is then cut into 27 equal small cubes. How many cubes
- Have 1 side painted?
- Have 3 sides painted?
Solution:
The cube is cut into 27 equal cubes of equal size that means it’s a 3x3x3 cube. Visualise the cube (have included 3x3x3 Rubix cube pic for reference)
a) Only the cubes at the centre of each face (that are located neither at corners nor along the edges) will have just one side painted.
In a 3 x 3 cube there is only one cube on each face which is located neither at corners nor along the edges.
There are 6 faces in any cube.
Therefore, 6 cubes have only one side painted.
b)The small cubes at the corners of the big cube have 3 sides painted.
There are 8 small corner cubes in the big cube.
Therefore, 8 cubes have 3 sides painted.