In simple terms, a word problem usually represents a mathematical exercise where all the background information related to some challenge is presented in ordinary language. If you do not see mathematical notation and see text only, such kind of narration represents a Math word problem. They are also known as story problems where analysis, strategic thinking, and reverse engineering must be used. It is one of the reasons why university students should try their hand at solving different kinds of Math problems because it helps to understand mathematical problems in a deeper way while improving one’s basic cognitive functions.
The majority of word problems are usually examined on three analytical levels:
- Verbal formulation analysis.
- Evaluation of all underlying mathematical relations.
- Symbolic mathematic expressions.
It is one of the reasons why Data Science, Programming, Engineering, and Linguistic specialists are turning to metrics to identify the number of words as each sentence length is examined. The challenges like Algebra word problems must be approached by various schemes to analyze logico-mathematical patterns to see similar numbers (values), required quantities (things that you must identify), and auxiliary values (the intermediate peculiarities).
University students must use various modeling options by reading Math Word problems according to an outline. Likewise, if you create them yourself, think about asking questions.
Some basic examples would include:
Malcolm had $34.00, then spent $12.00. How much does he have now?
Engineerings in the province of Drenthe (Netherlands) use water pipes with a radius that equals 2 m. The water is rising at a specific rate of 4 cm/s. What is the rate that we have as the volume of water increases?
While the first Word Problem is easy to settle down as it uses the subtraction approach, our second example is dealing with what we are given and the identifier that must be identified (certain values).
How to Solve a Math Problem If You Are a University / College Student?
If you want to achieve success in Math problem solving, it is vital for every student to start with easy Math problems first and then proceed with approaching those that are more challenging. The most frequent issue among students is feeling confused when numbers are translated to a word problem that does not sound clear. When you do not choose relevant strategies, it is easy to get lost. Approaching one’s metacognitive skills, start with the basics and go backward just like reverse engineering.
Read The Question Again.
As a college student, you might know how difficult it is to read through your grading rubric. It works the same way here. Read it again and again until you truly understand it. If something does not make sense, read it aloud and ask someone else to help you. You can also highlight important pieces of information just like when dealing with equation solving.
Identify Valuable Data.
Sue is collecting helpful mobile apps for his autistic friend Liam’s birthday. She starts with $50 of her own, then her friend Mary gives her another $50. How much does Sue have now?
We gave this simplest primary school grade example to let you see that you must start with an addition. The trick is to find out what values we have got and what exactly we should identify. Regardless if you are a middle school student or a Good Will Hunting genius, it works the same way as one must have an outline where you must stay focused.
Think of an abstract problem and visualize it. You can draw a picture or make a graph because it helps you to think differently. You can also model it on the whiteboard by using organizers or color cards.
Challenging problem solving, many students often make educated guesses by adjusting an answer according to the original problem.
Research Similar Patterns.
Think about how to extract information and use all the relevant facts that can be compared for similarities (or differences). It will help to locate missing bits of data.
It is useful when you are dealing with complex Math problems. Look at the problem in a reverse way by asking a question and thinking about how a problem came to be.
Remember that speed is far not everything in Math because rushing to get an answer without proper analysis and checking is wrong! Think about taking one step at a time by making several checks before coming up with a final solution.
Extremely Hard Math Problems That No One Could Solve
If you have already gone through the basics and understand how to settle down linguistic mathematical problems, you might be asking yourself what is the hardest Math problem out there.
If you have heard about the famous Sum of Three Cubes problem that has been finally solved after 65 years, there are still some hard Math problems that are still unsolved.
- The Collatz Conjecture.
This one still remains unsolved, yet it has some updates like being all about function f(n), which takes even numbers and cuts them in half. The tricky part is that odd numbers get tripled and then added to number one. If you take any natural number, apply f, then do so again and again. You will eventually end up on one for every number that you have checked. Our Conjecture is that it remains so for all natural numbers (as long as they are positive from 1 through infinity.
- The Riemann Hypothesis.
Without a doubt, Riemann’s Hypothesis belongs to the most open problems in modern math. While it relates to several mathematical fields, it is also quite simple when one tries to explain it. It starts with a function that is also known as the Riemann Zeta Function.
For each s that we have, this function provides an infinite sum. It takes basic calculation to approach even the simplest values related to s.
For example, if our s value equals 2, then 𝜁(s) is the well-known series, It means 1 + 1/4 + 1/9 + 1/16 + and so on. The complex part that we have is that it adds up to exactly 𝜋²/6.
However, when s represents a complex number (like a + bi), using the imaginary number 𝑖—, finding out 𝜁(s) becomes complex. It is still unsolved and remains one of the ultimate math riddles!
It becomes that when 𝜁(s)=0, they have it summed up as “Every nontrivial zero of the Riemann zeta function has real part 1/2.“
Why Solving Math Problems Matters?
Think about starting with simple Math problems and then proceeding with the more complex ones. You do not have to show years of experience in subjects dealing with Math because it takes analysis and thinking differently. You should not ever set the limitations as you develop your brain. Think about possible solutions and do not forget to draw various problems. Starting with the text problems, visualization, and practical applicability, your brain will start with a mixture of calculation and evaluation. Taking a step-by-step approach, you will always explore things and keep your skills polished.