14 Feb Solve Maths Problems Beyond The Use of Formulas
There is more than one way to solve mathematical problems and it isn’t always what you think it is. A lot of students think that without the formulas, there is no way to solve them.
While there is a certain level of truth to that thought, the fact is it is absolutely possible to get the answers without using formulas. Instead of relying solely on memorising the formulas and applying them to solve the math problems, it is more efficient to learn alternative ways.
Just wonder how capable it would be if you can get into maths solving equations without having to use any formula. Not relying on formulas also allow you to have a deeper understanding of the underlying principles in a problem,
Of course, there is also the added benefit of developing problem-solving skills when you learn more than one way to find answers to math problems. Let’s take a look at some alternative options other than formulas.
Logical Reasoning
It is the method that prioritises the reasoning behind each step taken into approaching a problem and finally coming to an answer. In this strategy, the problem itself is broken down into smaller steps. This is done by using deductive or inductive logic to come to an answer.
Here the focus is on clear understanding of the connections between elements of a problem, hence, requiring not using any formula. An example can be:
How to find the greatest common divisor (GCD) of two numbers — 48 and 18? Using the Euclidean algorithm instead of the GCD formula, you can find the answer. This involves —
- First dividing 48 by 18 that results in a remainder of 12
- Then diving 18 by the remainder obtained that is 12. This will result in 6 as a remainder.
- Now, finally dividing 12 by 6 to get the remainder as 0. The last remainder that gets you 0 is the GCD.
- Therefore, the GCD of 48 and 18 is 6.
The alternative strategy of logical reasoning is also a great support for developing systematic thinking.
Trial and Error
Solving a maths equation where the range of possibilities is limited can be difficult. The best way to take on such problems is with the trial and error method. While it is a time-consuming process, it also works the best dealing with such equations.
Let’s see how you can use this method.
➡️ Solve the equation x² – 5x + 6 = 0 by testing small integer values:
Test x = 2: 2² – 5(2) + 6 = 0. This works, so one root is x = 2.
Test x = 3: 3² – 5(3) + 6 = 0. This works, so the other root is x = 3.
Trial and error method directs students toward approaching mathematical problems with not just one but through exploring multiple approaches. Moreover, this strategy also teaches students the value of verification when it comes to math problems.
Pattern Recognition
Maths is a subject that involves patterns. If you pay close attention to it then you will be able to recognise them that will help you find the answer for the math problem.
The more you practice, the better you get at it that will eventually come handy in not relying on formulas. With observation of recurring relationships, students can gain the skill of predicting outcomes and intuitively solve problems.
Here’s an example: The sum of first n odd numbers. Using pattern recognition instead of a formula.
➡️ 1 = 1²
1 + 3 = 2²
1 + 3 + 5 = 3²
From this pattern, you can deduce that the sum of the first n odd numbers is always n².
Pattern recognition method is best in use for revealing inherent structure of numbers.
Conclusion
There are more ways for maths solving equations or solving any mathematical problem. Students must keep in mind that while using formulas is completely fine, their use must not overshadow the value of thoroughly understanding the principles and concepts.
If you are interested in learning mathematics in more alternative ways then consider joining our classes at Miracle Learning Centre