Using shortcuts in math calculations can be beneficial in various contexts. Many entrance exams in India have a large number of questions that need to be solved within a limited time frame. Employing shortcuts enables students to manage their time effectively and attempt a greater number of questions, potentially improving their overall score.
Another area where such shortcut calculations can come in handy is the Board exams. Students can solve problems more efficiently, leaving them with extra time to review their answers and minimize errors. In professions such as engineering, finance, and data analysis, individuals often need to perform calculations quickly and accurately. Knowing shortcuts can enhance productivity and efficiency in these fields.
Learning shortcuts often involves understanding the underlying principles and patterns in mathematical problems. This not only helps in quicker calculations but also enhances problem-solving skills and the ability to recognise patterns in different scenarios.
When individuals use shortcuts, they often bypass lengthy and error-prone steps. This can reduce the likelihood of making mistakes in calculations, particularly in situations where precision is crucial. Shortcuts are not limited to specific topics or types of problems. They can be applied across various mathematical concepts, making them versatile tools for solving a wide range of problems.
Knowing and applying shortcuts successfully can boost a student’s confidence in their mathematical abilities. This increased confidence can positively impact their overall approach to learning and problem-solving.
Let us take some examples that students can use
Are you looking for a shortcut to find out the cube roots of large numbers? Fret not there is a simple trick that can come in handy. For instance, you have to find out the cube root of 2744. Here is a simple trick Add all the numbers – 2+7+4+4= 17. Now subtract 3 from it= 14. This is your answer. Cross-check by multiplying 14 three times. Let’s take another example. Find out the cube root of 4096. Add these numbers – 4+0+9+6= 19. Subtract 3; the answer is 16. This is your answer.
Now, suppose you have to find the square root of the decimal number – 9.144576 and you are given four options:
1. 3.4
2. 3.0424
3. 3.04
4. 3.024
Look at the number of digits after the decimal; it is 6, half it. The answer is 3. Look for the option in the answer that has three numbers after the decimal. In this instance, it is No 4. That is your answer.
Take another example. Find the square root of 4.2025. Here are the options:
1. 2.5
2. 2.05
3. 2.005
4. 2.0005
How many digits are there after the decimal? It is 4; half it. The answer is 2. Your answer is No 2.
Let us take another example. Suppose you were asked to find the square root of 712336 and you are given 4 options.
1. 884
2. 874
3. 844
4. 804
Look at the last two digits; the number is 36. What is the square root of 36? It is 6. Now add 6 to 50= 56. Subtract 6 for 50= 44. Look for the answer that has 44 in the end. In this case, it is No 4. Your answer is 844.
However, Jyoti Khanna, PRT (Math), who teaches classes II to VI at Apeejay School, Model Town has a word of caution. “Shortcut methods can be very helpful in certain situations where speed is crucial, especially in exams like Olympiads. Students who are familiar with these tricks find it easier to crack exams, as pace plays a significant role. Additionally, shortcut methods prove useful in day-to-day life, such as determining divisibility rules in maps, and saving time and effort when dealing with larger numbers,” Khanna said.
She said that some schools prefer not to teach shortcut methods and stick to traditional, long methods. ”This choice is driven by the belief that students should first grasp the conceptual knowledge of a topic before learning tips and tricks. Schools fear that introducing shortcuts too early might lead students to prioritize quick solutions over understanding the underlying concepts. They worry that students might escape gaining in-depth knowledge and may struggle when faced with real-life problem-solving situations,” Khanna said and pointed out a major flaw in using shortcuts in calculations.
“One disadvantage of relying solely on shortcut methods is that students may lack a solid conceptual foundation. While they can solve problems quickly using tricks, they may struggle when confronted with unfamiliar scenarios that require a deeper understanding of the subject. The risk is that students may prioritise exam performance over genuine comprehension, leading to a potential gap in their conceptual knowledge,” Khanna said in conclusion.
