Mathematics is a subject that often intimidates many, but it doesn’t have to be that way. With the right tricks and shortcuts, you can simplify complex calculations and make math more approachable and even enjoyable.

Contents

Squaring Numbers Trick 1: Squaring Numbers Ending in 5 Trick 2: Using the Difference of Squares Trick 3: Squaring a Three-digit Number Finding Square Roots Trick: Estimation and Refinement Spark Math Program: Elevating Mathematical Excellence Alignment with MOE and CCSS Comprehensive Skill Development Preparation for International Competitions

Squaring Numbers

Squaring a number means multiplying the number by itself. This can also be called ‘a number squared’. The symbol for squared is ².

While this might seem straightforward for smaller numbers, larger numbers can be more challenging. Here are some tricks to make squaring numbers easier:

Trick 1: Squaring Numbers Ending in 5

For any two-digit number ending in 5 (e.g., 15, 25, 35), you can quickly find its square using a simple trick:

Remove the 5 at the end.
Multiply the remaining digit(s) by itself plus one.
Append 25 to the result.

Example: Square of 25

Step 1: Remove the 5: We get 2.

Step 2: Multiply 2 by (2 + 1): 2×3=6.

Step 3: Append 25: The square of 25 is 625.

Trick 2: Using the Difference of Squares

The difference of squares formula states that (a + b)² = a² + b² + 2ab or (a – b)² = a² + b² – 2ab. The form where ‘b’ has a smaller value should be preferred. This can be useful for squaring numbers close to a base number.

Example: Square of 48

Step 1: Recognize that 48=50-2.

Step 2: Use the formula: (50−2)²=(50²+2²)−(2×50×2).

Step 3: Calculate:

50²=2500
4×50=−200
2²=4

Step 4: Add them up: 2500−200+4=2304.

So, 482=2304.

Trick 3: Squaring a Three-digit Number

Example: Square of 214

Step 1: Subtract the last digit from the number being squared.

214 – 4 = 210

Step 2: Add the last digit to the number being squared.

214 + 4 = 218

Step 3: Multiply the numbers from Step 1 and Step 2.

210 x 218 = 45,780

Step 4: Square the last digit of the number being squared and add it to the answer from Step 3.

Since 4² = 16, we add 45,780 + 16 = 45,969.

Finding Square Roots

Finding square roots can be challenging without a calculator, but some tricks can simplify the process. Here is a trick to find the square roots of a large number easily.

For example, let us find the square root of 4761.

Step 1: The unit digit in this number is 9, which can be a unit digit of its square root number such as 1 or 9. Because 1² is 1 and 9² is 81.
Step 2: Now let us consider the first two digits that is 47 which comes between the squares of 6 and 7 because 6² < 47< 7².
Step 3: We can assume that the tens digit of the square root of 4761 is the lowest among the two numbers i.e. 6 and we need to find the unit digit of the square root of the number 4761.
Step 4: Now, we need to find between 61 or 69 which is the square root of 4761.
Step 5: Since the tens digit is 6 and the next number is 7, we need to multiply both the numbers like 6 x 7 = 42 and since 42 is less than 47.
Step 6: Square root of 4489 will be the bigger number between 61 and 69 i.e. 69.

Therefore, √4761 = 69.

Spark Math Program: Elevating Mathematical Excellence

Mastering math shortcut tricks like squaring numbers, finding square roots, and calculating percentages not only simplifies complex calculations but also enhances overall mathematical proficiency. By practicing these techniques regularly, you’ll find yourself solving problems more efficiently whether in academic settings or real-life scenarios. So go ahead, give these tricks a try, and watch your math skills soar! The Spark Math program is a comprehensive and innovative educational initiative designed to enhance students’ mathematical skills and abilities, enabling them to excel in both academic settings and international math competitions.

Alignment with MOE and CCSS

Spark Math’s curriculum is carefully crafted to align with the MOE’s rigorous educational framework, ensuring that students receive a high-quality education consistent with national standards. This alignment guarantees that the program addresses essential mathematical concepts and skills required by the MOE, providing students with a solid foundation in mathematics. Additionally, Spark Math adheres to the CCSS, which emphasizes critical thinking, problem-solving, and analytical skills. By integrating these standards, Spark Math ensures that students are not only proficient in mathematical computations but also adept at applying their knowledge to real-world situations.

Comprehensive Skill Development

The Spark Math program employs a multifaceted approach to skill development, incorporating various teaching methodologies and resources. Interactive lessons, engaging activities, and practical exercises are designed to stimulate students’ interest in mathematics while reinforcing their understanding of key concepts. The program covers a wide range of topics, from basic arithmetic to advanced algebra and geometry, ensuring a thorough grasp of fundamental principles. Regular assessments and feedback mechanisms help track students’ progress, identify areas for improvement, and provide targeted support where needed.

Preparation for International Competitions

One of the standout features of Spark Math is its focus on preparing students for international math competitions. The program includes specialized training modules aimed at honing problem-solving skills and fostering a competitive spirit. Students are exposed to challenging problems that require creative thinking and advanced reasoning, mirroring the types of questions encountered in prestigious competitions such as the International Mathematical Olympiad (IMO), Math Kangaroo, AMC and other global contests. By participating in these rigorous preparatory sessions, students gain confidence and competence, positioning them as strong contenders on the international stage. Click here to book a free trial class!