Fractions – A Simple Step Towards Understanding ‘The Bigger Picture’

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How to teach fractions to your kids while helping them understand the applied benefits of knowing the numerator, the denominator, and mapping the vinculum.

By Shomprakash Sinha Roy (For Pepper Content, Client: Cuemath)

Two out of three popular approaches in mathematical teaching for primary kids rely on the underlying assumptions that:

  1. Math can (and therefore should) be fun to learn.
  2. Mathematical clarity will help your kids in real-life scenarios.
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The trouble with introducing your kids to the idea of fractions is that it’s a reasonably complex subject to be brought forth ‘casually’ into a conversation, especially if you happen to be parenting a child who loves asking questions. Most importantly, we believe that it is crucial to let the ‘why’ of it sink in as deep as possible before attempting to tinker with the ‘what.’

Why Fractions

Just like geometry, trigonometry, the decimal system, and other basic pillars of mathematical understanding, the concept of fractions can sound alien and frightening to grasp for a young and impressionable mind. For a primary school-kid, it is understandably hard to wrap their head around words like “numerators,” “denominators,” and “vinculum.” At the same time, it is not prudent to place this fear under the category of xenophobia (because almost everything that kids have exposure towards in their growing years is inherently new – rather, new-er, compared to what they knew moments back). Every revelation, every snippet of wisdom or knowledge passed on to your kids has a special way of either capturing and ruling over their imagination or fading away into the murky waters of “topics to avoid or cringe at.”

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It is essential that you lay out the reasons for them to learn something new, purely from an existential perspective. This solidifies the emotional connection that your kids will have with that concept and will, in turn, boost the eagerness that they will proceed to use as learning fuel. For instance, when it comes to geometry, a good conversation starter is to start talking to your kids while they’re munching on a Pizza – to help them understand that two medium (9 inch) pizzas are smaller when put together, compared to one large (14 inch) crust. Kids are always fascinated with facts that seem to differ from their perceived reality. Over time, you can master the art of using these techniques to inspire the right amount and category of curiosity in your kids. This is one of the abilities that we take pride in – where we help your kids discover the many wonders of exploring numbers

The thing to remember is to always remain focused on the why and less on the what. Mathematics is fundamentally a great source of creative and analytical fuel for shaping up minds, and believe it or not; most kids are naturally inclined to dig deeper into their math skills and hone their understanding of numbers. It is just the added ‘blocks’ theed around ‘why vs. why-not’ that gives rise to their reluctance.

Keep finding ways to work around this challenge. Talk to your kids about real-life scenarios such as:

  • When you take your kids out shopping, explain how all the flashy discounts that scream “Up to 50% off!” are essentially helping you save a fraction of the amount of money you were going to spend.
  • When undertaking long journeys, if your kids have the habit of checking in with the “are we there yet?” adage, take the time to talk to them about having finished a quarter, three-quarters, or one-half of the journey, and wait for their questions to pour in.
  • Let them appreciate the ability to mentally ‘segment’ their school day. For instance, let them develop an understanding of what it means for ‘half of the day’ to be over, as opposed to a third of their day having gone past. 

These, and many other scenarios of real-world applicability, are what will make a real difference in urging your kids to explore fractions with an enhanced sense of appreciation.

Remembering Fractions (The Basics)

Four out of five good teachers are good learners themselves. When imparting impressionable information to your children, you must be very careful about the accuracy of what you pass on. If you need a reliable source of information or a repository of verified mathematical knowledge to bank on, we urge you to explore numbers with Cuemath before you start teaching your kids about fractions.

So, what is a fraction? Ideally, a fraction is anything that represents a smaller piece (or many smaller pieces) of the “whole.” Whenever we split anything up – be it pie, pizza, or the time on our hands, we use fractions. The sum of the parts is the original “whole” element that you decided to split.

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But the word “whole” has varying connotations, and just like different physical variables, the idea of the “whole” is also very much frame-dependent. If you’re in a supermarket, the “whole” could refer to either the entire store or to one packet of cereal – it totally depends on what you’ve chosen to split apart. You can think or talk about buying “half the store” or “half a kilo of rice” or “a third of all the items that constitute the masala aisle.”

But a foolproof and child-friendly way of introducing fractions (the simplest definition) is that a fraction is any part of a group, number, or whole.

Parts (Elements) Of A Fraction

What are the different components of a fraction? A fraction is always represented with three important parts, namely:

  1. The numerator (The number placed above the bar)
  2. The denominator (The number placed below the bar)
  3. The vinculum (The bar separating the numerator and the denominator)

Types Of Fractions – Unit Fractions And Non-Unit Fractions

Fractions, by and large, can be divided into two basic categories – unit fractions and non-unit fractions. A unit fraction is any representation that has one (1) as the numerator (the number on top) and a positive integer in the denominator (number at the bottom). A non-unit fraction, on the other hand, is any fraction with a numerator greater than one and a positive integer as the denominator.

Taking The Leap – From Objects To Numbers, And From Numbers To Fractions

It is important to remember that kids are always in “learning mode,” whether they are aware of it or not. In fact, science has shown that the effects of operant conditioning in a child’s formative years happen to most significantly impact their logical and analytical abilities in later life. And since fractions are an important gateway to the world of understanding probability, proportions, and pretty much all relative mathematical phenomena, you must exercise both patience and caution while helping your kids connect the dots between the real world and the world of numeric evaluation.

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Always be okay with taking it slow. Real-world objects, as mentioned above, are great tools to help your child break into numeric visualizations. But keeping in mind their ability to process large volumes of complex information in unexpected ways, always keep it simple. Start with objects that do not put too much pressure on their imagination – whole objects, like an entire candy bar, which can be split three ways between a mother, a child, and a father. Such exercises play a deeper role in cementing the idea of fractions as an ethical tool that your child will nurture and nourish for their entire life. It is this idea of “numbers being fair” that eventually makes numbers interesting. Use this to your advantage when teaching your kids about fractions.

Remember that as you go along, you kids always have a lot of information to process – so it is important to let their concepts evolve over time, instead of trying to overwhelm them with information all at once. Whenever you feel the frustration of explaining a new concept to a human being full of questions, pace, and pacify yourself with the knowledge that you’re doing the right thing already, it’s just how you do it that matters. If you’ve decided to teach your kids about fractions, you’re going to make life a lot easier for yourself later on when you start talking to them about advanced concepts such as decimals, percentages, and probability.

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Gamifying Fractions – Make Learning Fun

Always issue fun and engaging challenges to your kids after you realize that they’ve picked up on a key concept and picked it up well. For instance, if your kid develops a clear understanding regarding the difference between unit and non-unit fractions, try to gamify the experience of identifying these labels. If you’re on a drive with your kid sitting in the passenger seat, try to help them stay mindful about their mathematical intelligence by playing a “unit vs. non-unit” game. Ensure that there is a reward waiting for him or her at the end of the game. Every ten consecutive correct answers should earn them a treat – which could be additional playtime that day or an extra candy bar (go easy on the sugar, though). A much more rewarding incentive is usually for you to let them delve deeper into the subject you’re teaching. Make a wager that if they get five (or ten) consecutive answers right, then they will “earn” the right to know more about fractions. 

Remember that the learning process is always about having fun while discovering the laws that seem to govern the world around us. Help your child discover this, and you’ll get the job done in a fraction of the time.

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