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Symmetry: A Powerful Problem solving Strategy

Dear Math enthusiasts, Some ideas get a WHOLE LOT more time in the maths classroom than others. These are the bigger , seemingly more important concepts Then there are the smaller ideas , which might take up a lesson, here or there - but nothing more. I want to share one example that, you will see, offers far more than we usually think. Nestled away, in a room labelled Geometry, symmetry is often ticked off and forgotten. Yet, viewed differently, it becomes a game-changing concept that can powerfully change the way students see maths, find meaning and solve problems. Symmetry: it's not just geometric That one moment forced me to check all of my prior assumptions - and opened up a completely new way of viewing symmetry's mathematical possibilities. What followed was this- If symmetry isn’t just geometric, where else can we see it? To answer this question, check out the following example (it's one we discussed earlier this week at our ...

Unforgettable development of Science

Technology and advancement have brought us so far that there were some jobs that are now obsolete or entirely changed. Following are some which are old forgotten jobs. Pre-radar Listener These were used to detect enemy aircraft. The pre-Radar listener is one of them. During war times these pre-radar listeners were used to detect the enemy approaches. They had built in a way that could capture sound from some good distances and were used for reporting and surveillance.

Tippe Top- What is Tippe Top and How does it works?

Playing with tops is probably one of the most loved game for kids all over the universe. One of the very popular top is Tippe Top. Spinning a Tippe top is fun and magical as well, initially it seems usual spinning top. But suddenly the magic happens. The top get reversed and start spinning all the way up side down. Is not this magical? See a small video below. This strange behavior of top is strange for even Nobel Laureate, Niels Bohr. ...

Unleashing the Power of Permutation and Combination: Exploring Possibilities

Binding Rope Around The Earth

Rope around The Earth: Wrap a thread tightly around the earth (along the equator). Now add an extra 2 meters of thread to this length and then wrap the new thread again around the earth in the same circular path (i.e. along the equator). (Image: Binding rope around the Earth) Now, how high do you think will the thread rise above from the ground ?(Or in other words, what will be the new radius corresponding to this new circumference?) Well, practically one might think that an addition of 2 meter won't make any difference since its too small compared to the size of the earth (which is ~6371000 meters in radius!). And even if it does, the difference will be so small (may be in millimeters or so) that it can easily be neglected? Well, le...

Geometrical Beauty of Circles

In our daily life, we come across many circular objects like coins, cakes, plates, wheels, wheelbarrows, brooches, bangles, flower beds, etc. So, the problem of finding perimeters and the area of plane circular figures have great practical importance. Review of Perimeter And Area of A Circle: Circle : A circle is a closed curve consisting of a set of all those points of the plane which are at a constant distance from a fixed point in the plane. Centre : The fixed point is called its centre. Radius : The constant distance is called its radius. It is the line segment joining any point on the boundary (circumference) to the centre. Circumference : The boundary (or perimeter) of a circle is called its circumference. The circumference of a circle bears a constant ratio with its diameter. this constant ratio is denoted by Pi ( p ), a Greek letter. In other words, ...

Why Math is So Hay Math Can Be So Challenging and How to Overcome

Mathematics, the subject that seems to strike fear into the hearts of many. If you're one of those who find themselves pondering, "Why is math so hard for me?" you're certainly not alone. In this article, we'll delve into the reasons people struggle with mathematics and explore why some individuals have an aversion to it. We'll also discuss why math can be so frustrating that it makes people cry, and most importantly, we'll provide you with tips on how to become a math wizard. So, let's embark on a journey to uncover the mysteries of math and learn how to conquer it with confidence Why Do People Struggle in Mathematics? 1. Complex Concepts: One reason many people find math challenging is the complexity of the concepts. From algebraic equations to calculus, math can seem like an insurmountable mountain of abstract ideas. Understanding these concepts can be a significant hurdle. 2. Lack of Foundation: Mathematics builds upon itself. If you missed crucial...

Golden Earring!

Here is an interesting math problem for you. Try it, and put your answer in a comment below. The Golden Earring Mystery I wish to cut a circle of radius r from a unit disk of gold, resulting in an earring whose center of mass is at the indicated point. What value of r will make my golden earring?

THE POWER OF VISUALIZATION

THE POWER OF VISUALIZATION from the Book: “ From Math Anxiety to Math Mastery in 6 Stages: Encoding Mathematical Symbolisms” A picture is worth a thousand words… and numbers, when we try to think mathematically. One has to use a lot of words and numbers to explain the difference between division as equal sharing and division as equal grouping . It is because mathematics engages both numerical and verbal reasoning. The two run alongside, entwine, criss-cross, meet or part ways. All these behaviors are deliberate and precise, and a slight change in accent can cause a change in meaning. When explaining the difference between “factors” and “factoring” a teacher has to consider the mathematical context which itself may require clarification. [ All that I have said so far can be demonstrated via one or two carefully crafted, evocative visuals. ] Mathematical concepts provoke visualization and a lot of them consist of dynamic imagery, of ideas caught in mo...

Representing Numbers by Area and Volumes of Objects

Representing Numbers by areas or volumes of objects can be a great way to visually connect various problems involving numbers. Sum of first n natural numbers is nothing but, the sum of n terms in arithmetic progression. In a general arithmetic progression with first term a and common difference d sum of n terms: S= n/2[ a + (a+( n-1)d)] This sum has a beautiful story of origin, Carl Friedrich Gauss. Story goes like this "In the 1780s a provincial German schoolmaster gave his class the tedious assignment of summing the first 100 integers. The teacher's aim was to keep the kids quiet for half an hour, but one young pupil almost immediately produced an answer: 1 + 2 + 3 + ... + 98 + 99 + 100 = 5,050. The smart aleck was Carl Friedrich Gauss, who would go on to join the short list of candidates for greatest mathematician ever. Gauss was not a calculating prodigy who added up all those numbers in his head. He had a deeper insight: If you "fold" the series of numbers in ...

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