Kids are taught to identify patterns from a very young age. For example, activities like determining “what number comes next in the sequence 1, 3, 5,7”, helps kid notice the similarities and differences in identifying repeating patterns. The same approach can be applied by breaking down complex problems into patterns to eventually solve the larger problem. And, the best way to explain pattern recognition to young kids is by creating a visual representation. We used the same problem solving strategy to solve this critical thinking “Dividing Money in Bags ” math problem by identifying the pattern in the solution.
The “Dividing Money in Bags” Math Problem
A shopkeeper needs to divide 15 pennies into 4 bags. He has to divide the coins over the four bags, so that he can pay any sum of money from 1p to 15p without opening any bag. He can label each bag with the number of pennies inside it.
Can you find out how many pennies he needs to put in each bag?
How to solve it
Give this problem a try and leave your answer in the comments.
By visualizing the problem and documenting the solution, helped my kids quickly recognize the pattern and come up with the final solution.
Finally, can you work on your problem solving skills and find a pattern to solve the “Dividing money in bags” math problem ? How can the shopkeeper divide 7 pennies, 31 pennies, 63 pennies and more ? How many minimum number of bags he requires to make a combination of 7 pennies or 31 pennies and so on ?
We can try making combinations for 7 pennies and see the pattern. As a result, we can easily generalize it. So, for any number of ‘n’ bags, we can make 2^n – 1 combinations. For example, for 3 bags we can make 7 combinations, for 5 bags we can have 31 combinations and so on ).
Another way of looking at the solution is to express the numbers in binary format (i.e. base 2), where a 1 means include the bag with 2^n pennies, and 0 means don’t. For example,
The number 11 can be represented as 1011 ( base 2 ) in binary format.
1011 = 2^3 + 0^2 + 2^1 + 2^0 = 8 + 0 + 2 + 1
Therefore, it implies that we can get 11 pennies from Bag 4, 2 and 1.
Similarly, you can write all the numbers from 0 to 15 with 4 binary digits.
Moreover, if you are looking for ideas to teach your kids complex math concepts like Fibonacci, Symmetry and more in an easy and interesting way, then check some of them here.
- Fibonacci Series
- Symmetry – Fold and Hold Sequence
- Geometry – Sum of all angles of a Triangle
- Problem Solving – A Bag of Marbles
If you are looking for books on logical thinking and problem solving then these are some great picks.
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